TCS conducts written test and three rounds of interview to select
freshers as assistant system engineer in their organisation. In the
first round they conduct one and half hour written test, followed by
three interview rounds namely Technical round, Managerial round, and HR
round. The written test has email writing component.
Test pattern:
Duration for test: 10 min + 80 min = 90 min.
You have to write an email using the given clues in around 70 words. You have to type the email in the space given. The most important thing is you have to use all the phrases given without missing even single one.
After the email writing, you have to take an aptitude test of 30 questions in 80 minutes.
Syllabus for written test:
According to the model questions given in the TCS recruitment portal https://nextstep.tcs.com we can assume the following chapters are very important. There is no verbal part in TCS aptitude test except for email writing. 1/3rd negative marking will be there.
Important topics: Number system, Equations, Ratio and Proportion, Percentages, Profit and Loss, Time and Work, Time speed Distance, Areas and Mensuration, Averages, Permutations and Combinations, Probability, Plane geometry, Seating Arrangements, Sets, Progressions.
Interview process:
There is no hard and fast rule that you may be asked only Technical questions in technical interview. or HR questions in HR interview. You have to prepare well before for all the types of interviews.
For technical interview, you have to focus on C, DBMS and JAVA. It is important you have to be through with at least a couple of your core subjects.
For HR interview you have to study all the questions given in www.campusgate.co.in along with their suggested answers
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QUESTIONS
1. The rupee/coin changing machine at a bank has a flaw. It gives 10 ten rupee notes if you put a 100 rupee note and 10 one rupee coins if you insert a 10 rupee note but gives 10 hundred rupee notes when you put a one rupee coin!
Sivaji, after being ruined by his rivals in business is left with a one rupee coin and discovers the flaw in the machine by accident. By using the machine repeatedly, which of the following amounts is a valid amount that Sivaji can have when he gets tired and stops at some stage (assume that the machine has an infinite supply of notes and coins):
Answer: B
Explanation:
The process works like this:
Rs.1 Coin ⇒ 10 × 100 = Rs.1000
Rs.100 ⇒ 10 × 10
Rs.10 ⇒ 1 × 10
Sivaji gets more money when he inserts a rupee coin only. For each rupee coin he gets his money increased by 1000 times. Suppose he inserted 1 rupee coin and got 1000 rupees and again converted this into coins. So he ends up with 1000 coins. Now of this, he inserts one coin, he gets 1000. So he has 1999 with him. Now if he inserts another coin, he has 1998 + 1000 = 2998.
2. Seven movie addicts- Guna, Isha, Leela,
Madhu, Rinku, Viji and Yamini attend a film festival. Three films are
shown, one directed by Rajkumar Hirani ,one by S.Shankar,and one by Mani
Ratnam. Each of the film buffs sees only one of the three films. The
films are shown only once, one film at a time. The following
restrictions must apply :
- Exactly twice as many of the film buffs sees the S.shankar film as see the Rajkumar Hirani film.
- Guna and Rinku do not see the same film as each other.
- Isha and Madhu do not see same film as each other.
- Viji and Yamini see the same film as each other.
- Leela sees the S.Shankar film.
- Guna sees either the Rajkumar Hirani film or the Mani Ratnam film.
Which one of the following could be an accurate matching of the film buffs to films ?
(A) Guna: the S.Shankar film; Isha: the Mani Ratnam film; Madhu: the S.Shankar film
(B) Guna: the Mani Ratnam film; Isha: the Rajkumar Hirani film; Viji: the Rajkumar Hirani film
(C) Isha : the S.Shankar film; Rinku: the Mani Ratnam film; Viji: the Rajkumar Hirani film
(D) Madhu: the Mani Ratnam film; Rinku: the Mani Ratnam film; Viji: the Mani Ratnam film
Answer: Option C
Explanation:
Guna × Rinku
Isha × Madhu
(Viji + Yamini)
Leela - Film: Shankar
Guna = RKH/Mani Ratnam
The following options are possible:
We will take options and check them.
Option A: Guna should not watch Shankar's Film. So ruled out
Option B:
Now Yamini also watch RKH. Which is not possible.
Option C:
As Guna should not be watching Shankar's movie she should watch Mani ratnam's which is not possible.
Option D:
3. Which of the following numbers must be added to 5678 to give a remainder of 35 when divided by 460?
Answer: C
Explanation:
5678 - 35 + (one of the answer option) should be divisible by 460. Only option C satisfies.
4. Find the probability that a leap year chosen at random will have 53 Sundays.
Answer: B
Explanation:
A leap year has 366 day which is 52 full weeks + 2 odd days. Now these two odd days may be (sun + mon), (mon + tue), .... (Sat + sun). Now there are total 7 ways. Of which Sunday appeared two times. So answer 2/7
5. An ant starts moving on the mesh shown below along the wires towards a food particle.If the ant is at the bottom-left corner of cell A and the food is at the top-right corner of cell F, then find the number of optimal routes for the ant.
Answer: B
Explanation:
(Please read "Counting" to understand this question: Click here )
Total ways to move from A to the junction: There are 13 upward ways, 3 right side ways this Ant can move. Now these 16 ways may be in any order. So number of ways of arrangements =16!13!×3! = 560
Similarly, from the junction to F, Total 12 upward ways and 5 right-side ways. These 17 ways can be in any order. So Total ways =17!12!×5! = 6188
Total ways to move from A to F = 560 × 6188 = 3465280
6. You have been given a physical balance and 7 weights of 52, 50, 48, 44, 45, 46 and 78 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 183 kgs.
Answer: A
Explanation:
52+50+78 = 180
7. Two consecutive numbers are removed from the progression 1, 2, 3, ...n. The arithmetic mean of the remaining numbers is 26 1/4. The value of n is
Answer: C
Explanation:
As the final average is 105/4, initial number of pages should be 2 more than a four multiple. So in the given options, we will check option C.
Total =n(n+1)2=50×512=1275
Final total =48×1054=1260
So sum of the pages = 15. The page numbers are 7, 8
8. You need a 18% acid solution for a certain test, but your supplier only ships a 13% solution and a 43% solution. You need 120 lts of the 18% acid solution. the 13% solution costs Rs 82 per ltr for the first 67 ltrs, and Rs 66 per ltr for any amount in access of 67 ltrs. What is the cost of the 13% solution you should buy?
Answer: C
Explanation:
Let us assume we need "a" liters of 13% acid solution and "b" liters of 43% acid solution. Now
⇒18=a×13+b×43a+b
⇒ab=51
So we need 100 liters of 13% acid solution, and 20 liters of 18% acid solution.
Final cost = 82 × 67 + 66 × 33 = 7672
9. A spherical solid ball of radius 58 mm is to be divided into eight equal parts by cutting it four times longitudinally along the same axis.Find the surface area of each of the final pieces thus obtained( in mm^2) ? (where pi= 22/7)
Answer: B
Explanation:
If a sphere is cut into 8 parts longitudinally, It something looks like below
18(4×π×582)+π×582
= 5046pi
10. There is a lot of speculation that the economy of a country depends on how fast people spend their money in addition to how much they save. Auggie was very curious to test this theory.
Auggie spent all of his money in 5 stores. In each store, he spent Rs.4 more than one-half of what he had when he went in. How many rupees did Auggie have when he entered the first store?
Answer:
Explanation:
As he has spent all his money, He must spend Rs.8 in the final store.
a simple equation works like this. Amount left =12x−4
For fifth store this is zero. So x = 8. That means he entered fifth store with 8.
Now for fourth store, amount left = 8 so12x−4=8⇒ x = 24
For third store, amount left = 24 so12x−4=24⇒ x = 56
For Second store, amount left = 56 so12x−4=56⇒ x = 120
For first store, amount left = 120 so12x−4=120⇒ x = 248
So he entered first store with 248.
11. A sudoku grid contains digits in such a manner that every row, every column, and every 3x3 box accommodates the digits 1 to 9, without repetition. In the following Sudoku grid, find the values at the cells denoted by x and y and determine the value of 6x + 15y.
Answer: B
Explanation:
So x = 5, y = 3.
6x + 15y = 75
12. In how many ways can the letters of the english alphabet be arranged so that there are seven letter between the letters A and B, and no letter is repeated
Answer: B. Option A also correct.
Explanation:
We can fix A and B in two ways with 7 letters in between them. Now 7 letters can be selected and arranged in between A and B in24P7 ways. Now Consider these 9 letters as a string. So now we have 26 - 9 + 1 = 18 letters
These 18 letters are arranged in 18! ways. So Answer is 2 x24P7 x 18!
Infact, 2 x24P7 x 18! = 36 x 24!. So go for Option B as it was given as OA.
13. A certain function f satisfies the equation f(x)+2*f(6-x)=x for all real numbers x. The value of f(1) is
Answer: C
Explanation:
Put x =1 ⇒ f(1)+2*f(6-1) = 1 ⇒ f(1) + 2*f(5) = 1
Put x = 5 ⇒ f(5)+2*f(6-5) = 5 ⇒ f(5) + 2*f(1) = 5
Put f(5) = 5 - 2*f(1) in the first equation
⇒ f(1) + 2*(5 - 2*f(1)) = 1
⇒ f(1) + 10 - 4f(1) = 1
⇒ f(1) = 3
14. Professor absentminded has a very peculiar problem, in that he cannot remember numbers larger than 15. However, he tells his wife, I can remember any number up to 100 by remembering the three numbers obtained as remainders when the number is divided by 3, 5 and 7 respectively. For example (2,2,3) is 17. Professor remembers that he had (1,1,6) rupees in the purse, and he paid (2,0,6) rupees to the servant. How much money is left in the purse?
option
A. 59
B. 61
C. 49
D. 56
Answer: D
Explanation:
Let the money with the professor = N
Then N = 3a +1 = 5b + 1 = 7c + 6.
Solving the above we get N = 181
(Explanation: See LCM formula 1 and 2: Click here)
When a number is divided by several numbers and we got same remainder in each case, then the general format of the number is LCM (divisors).x + remainder.
In this case 3, 5 are divisors. So N = 15x + 1. Now we will find the number which satisfies 15x + 1 and 7c + 6.
⇒ 15x + 1 = 7c + 6 ⇒ c =15x−57 ⇒ c = 2x+x−57
Here x = 5 satisfies. So least number satisfies the condition is 5(15)+1 = 76.
(x = 12 also satisfies condition. So substituting in 15x + 1 we get, 181 which satisfies all the three equations but this is greater than 100)
Similarly Money given to servant = M = 3x + 2 = 5y = 7z + 6
Solving we get M = 25.
(125 also satisfies but this is next number)
Now N - M = 56
15. The sum of three from the four numbers A, B, C, D are 4024, 4087, 4524 and 4573. What is the largest of the numbers A, B, C, D?
a. 1712
b. 1650
c. 1164
d. 1211
Answer: a
Explanation:
a+b+c=4024
b+c+d= 4087
a+c+d=4524
a+b+d=4573
Combining all we get 3(a+b+c+d) = 17208
⇒ a + b + c +d = 3736
Now we find individual values. a = 1649, b = 1212, c = 1163, d = 1712. So maximum value is 1712.
16. Anand packs 304 marbles into packets of 9 or 11 so that no marble is left. Anand wants to maximize the number of bags with 9 marbles. How many bags does he need if there should be atleast one bag with 11 marbles
a. 33
b. 32
c. 31
d. 30
Answer: B
Explanation:
Given 9x + 11y = 304.
x =304−11y9 = 33+7−2y9+y
So y = - 1 satisfies. Now x = 35,
Now other solutions of this equation will be like this. Increase or decrease x by 11, decrease or increase y by 9. So we have to maximise x. next solution is x = 24 and y = 8. So bags required are 32.
17. When Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha?
a. 37
b. 44
c. 45
d. 40
Answer: D
Explanation:
Let the age of Usha is 3x then Nisha is x and Asha is 25
Also Usha 34, Nisha y, and Asha 2y.
We know that 3x - 34 = x - 2y = 25 - 2y
Solving above three equations we get x = 9, y = 16
Their ages are 34, 16, 32. whose sum = 82. So after 18 years their ages will be equal to 100. So Usha age is 34 + 6 = 40
18. Find the number of zeroes in the expression 15*32*25*22*40*75*98*112*125
a. 12
b. 9
c. 14
d. 7
Answer: B
Explanation:
Maximum power of 5 in the above expression can be calculated like this. Count all the powers of 5 in the above expression. So number of zeroes are 9. (Read this chapter)
19. Two vehicles A and B leaves from city Y to X. A overtakes B at 10:30 am and reaches city X at 12:00 pm. It waits for 2 hrs and return to city Y. On its way it meets B at 3:00 pm and reaches city Y at 5:00 pm. B reaches city X, waits for 1hr and returns to city Y. Afer how many hours will B reach city Y from the time A overtook him fro the first time?
a. 50 hrs
b. 49.5 hrs
c. 41.5 hrs
d. 37.5 hrs
Answer: C
Explanation:
Let us understand the diagram. Vehicle A overtaken B at 10.30 am and reached X at 12 pm. It started at 2 pm and met B at 3 pm at Q. It means, Vehicle A took one hour to cover distance 'n', So it should be at Q at 11 pm. It is clear that Vehicle A takes 0.5 hour to cover distance 'm'. Now vehicle B travelled from 10.30 am to 3 pm to meet A. So it took 4.5 hours to cover m. So Speeds ratio = 4.5 : 0.5 = 9 : 1.
Now Vehicle A took a total of 1.5 + 3 = 4.5 hours to travel fro P to Y. So It must take 4.5 × 9 + 1 = 41.5 hours
20. Two identical circles intersect so that their centres, and the points at which they intersect,
form a square of side 1 cm. The area in sq. cm of the portion that is common to the two
circles is:
a. (π/2) – 1
b. 4
c. √2 – 1
d. √5
Answer:
Explanation:
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1) The water from one outlet, flowing at a constant rate, can fill the swimming pool in 9 hours. The water from second outlet, flowing at a constant rate can fill up the same pool in approximately in 5 hours. If both the outlets are used at the same time, approximately what is the number of hours required to fill the pool?
Ans: Assume tank capacity is 45 Liters. Given that the first pipe fills the tank in 9 hours. So its capacity is 45 / 9 = 5 Liters/ Hour. Second pipe fills the tank in 5 hours. So its capacity is 45 / 5 = 9 Liters/Hour. If both pipes are opened together, then combined capacity is 14 liters/hour. To fill a tank of capacity 45 liters, Both pipes takes 45 / 14 = 3.21 Hours.
2) If 75 % of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percentage answered both correctly?
It is a problem belongs to sets. We use the following formula n(A∪ B) = n(A) + n(B) - n(A∩ B)
Here n(A∪ B) is the people who answered atleast one of the questions.
It was given that 20% answered neither question then the students who answered atleast one question is 100% - 20% = 80%
Now substituting in the formula we get 80% = 75% + 55% - n(A∩ B)
⇒ n(A∩ B) = 50%
3) A student's average ( arithmetic mean) test score on 4 tests is 78. What must be the students score on a 5th test for the students average score on the 5th test to be 80?
Ans: We know that Average=Sum of the observations No of observations
So Sum of 4 test scores = 78× 4=312
Sum of 5 tests scores = 80× 5=400
⇒ 5th test score=400-312=88
Alternative method: If the student scores 78 in the fifth test also, what could be his average? No change. Is it not?
But to bring the average to 80, he must have scored enough marks extra so that each of the five subject scores increase upto 80. i.e., he should have scored 2 x 5 = 10 runs extra in the fifth subject. So 5th subject score is 78 + 10 = 88
4) Rural households have more purchasing power than do urban households at the same income level, since some of the income urban and suburban households use for food and shelter can be used by the rural households for other needs. Which of the following inferences is best supported by the statement made above?
(A) The average rural household includes more people than does the average urban or suburban household.
(B) Rural households have lower food and housing costs than do either urban or suburban households.
(C) Suburban households generally have more purchasing power than do either rural or urban households.
(D) The median income of urban and suburban households is generally higher than that of rural households.
(E) All three types of households spend more of their income on housing than on all other purchases combined.
Ans: If average rural household includes more people, then how come they have more purchasing power? Infact, they have less purchasing power as they have to feed more people. Option A ruled out.
Option C does not explain why rural households have more purchasing power than urban. Ruled out.
If median income of urban and suburban households is generally higher than rural households they are likely to have more purchasing power, assuming other parameters constant. But this does not explain why rural households have more purchasing power. Options D ruled out.
Option E does not provide any explanation why rural households have more purchasing power. Ruled out.
Option B is correct as, If rural households spend less income on food and shelter due to less prices they definitely have more disposable income to spend.
5) Jose is a student of horticulture in the University of Hose. In a horticultural experiment in his final year, 200 seeds were planted in plot I and 300 were planted in plot II. If 57% of the seeds in plot I germinated and 42% of the seeds in plot II germinated, what percent of the total number of planted seeds germinated?
Ans: Total seeds germinated in Plot I = 57% of 200 = 114
Total seeds germinated in Plot II = 42% of 300 = 126
Total germinated seeds = 114 + 126 = 240
The percentage of germinated seeds of the total seeds =240500×100 = 48%
6) A closed cylindrical tank contains 36π
cubic feet of water and its filled to half its capacity. When the tank
is placed upright on its circular base on level ground, the height of
water in the tank is 4 feet. When the tank is placed on its side on
level ground, what is the height, in feet, of the surface of the water
above the ground?
Ans: We know that the volume of cylinder =πr2h
Given tank hight = 4ft.⇒ πr24 = 36π
⇒ r = 3
So the radius is 3 which means the diameter is 6.
As the cylinder is filled to initially exactly half of the capacity, When this cylinder is placed on its side, Water comes upto the height of the radius.
So water comes upto 3 ft.
7) The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of the teachers would then be 25 to 1 What is the present number of teachers?
Assume the present students and teachers are 30K, K
After new recruitments of students and teachers the strength becomes 30K + 50, K + 5 respectively. But given that this ratio = 25 : 1
⇒30K+50K+5=251
Solving we get K = 15
So present teachers are 15.
8) College T has 1000 students. Of the 200 students majoring in one or more of the sciences,130 are majoring in Chemistry and 150 are majoring in Biology. If at least 30 of the students are not majoring in either Chemistry or Biology, then the number of students majoring in both Chemistry and Biology could be any number from
If we assume exactly 30 students are not majoring in any subject then the students who take atleast one subject = 200 - 30 = 170
We know that n(A∪ B) = n(A) + n(B) - n(A∩ B)
⇒ 170 = 130 + 150 - n(A∩ B)
Solving we get n(A∩ B) = 110.
i.e., Students who can take both subjects are 110
But If more than 30 students are not taking any subject, what can be the maximum number of students who can take both the subjects?
As there are 130 students are majoring in chemistry, assume these students are taking biology also. So maximum students who can take both the subjects is 130
So the number of students who can take both subjects can be any number from 110 to 130.
9) Kelly and Chris are moving into a new city. Both of them love books and thus packed several boxes with books. If Chris packed 60% of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number of boxes Chris packed?
Simple questions. If chris packs 60% of the boxes, kelly packs remaining 40%
So Kelly : Chris = 40% : 60% = 2 : 3
10) Among a group of 2500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from 2500 people, what is the probability that the person selected will be one who invests in municipal bonds but not in oil stocks?
Ans: Here 2500 is redundant
From the diagram we know that only ones who invested in municipal bonds are 28%, the probability is 28 / 100 = 7/25
11) Machine A produces bolts at a uniform rate of 120 every 40 second, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?
Ans: Machine A produces 120/40 = 3 bolts in 1 second and machine B produces 100/20 = 5 bolts in one second.
Hence, both of them will produce 8 bolts per second.
Hence, they wil take 200/8 = 25 seconds to produce 200 bolts.
12) How many prime numbers between 1 and 100 are factors of 7150?
Ans: 7, 150 =2×52×11×13
So there are 4 distinct prime numbers that are below 100
13) Analysing the good returns that Halocircle Insurance Pvt Ltd was giving, Ratika bought a 1-year, Rs 10,000 certificate of deposit that paid interest at an annual rate of 8% compounded semi-annually.What was the total amount of interest paid on this certificate at maturity?
This is a question on compound interest to be calculated semi annually.
In the case of semi annual compounding, Interest rate becomes half and Number of periods becomes 2 per year.
So A = P(1+R100)n
⇒A=10,000(1+4100)2=10,000×2625
= 10,816
Interest = A - P = 10, 816 - 10,000 = 816
14) Juan is a gold medalist in athletics. In the month of May, if Juan takes 11 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
Ans: If juan takes 11 seconds to run Y yards, for 1 yard he will take 11 / y seconds. To run x yards his time will be 11 / y× x = 11x/ y
15) A certain company retirement plan has a rule of 70 provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1986 on her 32nd birthday first be eligible to retire under this provision?
Assume it has taken x years to the female employee to reach the rule of 70.
So her age should be 32 + x. Also she gains x years of experience.
⇒ (32 + x) + x = 70
⇒ x = 19.
Her age at the time of retirement = 1986 + 19 = 2005
16) Of the following, which is the closest approximation of (50.2*0.49)/199.8 ?
ans: For approximation (50.2× 0.49)/199.8 can be taken as
50× 0.5/200 = 25/200 = 1/8 = 0.125
17) Andalusia has been promoting the importance of health maintenance. From January 1,1991 to January 1,1993, the number of people enrolled in health maintenance organizations increased by 15 percent. The enrollment on January 1,1993 was 45 million. How many million people(to the nearest million) was enrolled in health maintenance organizations on January 1,1991?
Ans: If a number K is to be increased by x % it should be multiplied by(100+x)100
So When the enrollment in January 1, 1991 is multiplied by(100+x)100 we got 45 million.
K×(100+15)100=45
K =45×100115 = 39.13
18) What is the lowest possible integer that is divisible by each of the integers 1 through 7, inclusive?
Ans: If a number has to be divisible by each number from 1 to 7, that number should be L.C.M of(1,2,3,4,5,6,7) = 420
19) If the area of a square region having sides of length 6 cms is equal to the area of a rectangular region having width 2.5 cms, then the length of the rectangle, in cms, is
Ans: Given Area of the square = Area of rectangle
⇒a2=l.b
Substituting the above values in the formula
⇒62=l.2.5
⇒ l = 14.4 cm
20) A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 2500 gallons of water evaporate from the tank, the remaining solution will be approximately what percentage of sodium chloride?
Ans: Sodium chloride in the original solution = 5% of 10,000 = 500
Water in the original solution = 10,000 - 500 = 9,500
If 2,500 Liters of the water is evaporated then the remaining water = 9,500 - 2,500 = 7,000
Sodium chloride concentration =500500+7000×100 = 6.67 %
(concentration should be calculated always on the total volume)
21) After loading a dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day of the crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by two crews did the day crew load?
Assume the number of boxes loaded in dayshift is equal to 4, then the number of boxed loaded in night shift = 3
Assume the worked on dayshift = 5, then workers on night shift = 4
So boxes loaded in day shift = 4 x 5 = 20, and boxes loaded in night shift = 3 x 4 = 12
so fraction of boxes loaded in day shift =2020+12=58
22) A bakery opened yesterday with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon and 80 % of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday?
Ans: If half of the rolls were sold by noon, the remaining are 50 % (40) = 20.
Given 80% of the remaining were sold after the noon to closing time⇒ 80% (20) = 16
Unsold = 20 - 16 = 4
23) If N=4P, where P is a prime number greater than 2, how many different positive even divisors does n have including n?
Ans: N =22×P1
We know that total factors of a number which is in the format ofaP×bQ×cR... = (P + 1). (Q + 1). (R + 1) .... = (2 + 1).(1 + 1) = 6
Also odd factors of any number can be calculated easily by not taking 2 and its powers.
So odd factors of22×P1 = the factors of P1 = (1 + 1) = 2
Even factors of the number = 6 - 2 = 4
24) A dealer originally bought 100 identical batteries at a total cost of q rupees. If each battery was sold at 50 percent above the original cost per battery, then, in terms of q, for how many rupees was each battery sold?
Ans: Per battery cost = q / 100
If each battery is sold for 50% gain, then selling price =CostPrice×(100+Gain100)
⇒ q100×(100+50100)=3q200
25) The price of lunch for 15 people was 207 pounds, including a 15 percent gratuity of service. What was the average price per person, EXCLUDING the gratuity?
Ans: Let the net price excluding the gratuity of service = x pounds
Then, total price including 15% gratuity of service =x×(100+15100) = 1.15 x pounds
So, 1.15 x = 207 pounds
⇒ x = 207 / 1.15 = 180 pounds
Net price of lunch for each person = 180 / 15 = 12 pounds
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Directions:
Test pattern:
Duration for test: 10 min + 80 min = 90 min.
You have to write an email using the given clues in around 70 words. You have to type the email in the space given. The most important thing is you have to use all the phrases given without missing even single one.
After the email writing, you have to take an aptitude test of 30 questions in 80 minutes.
Syllabus for written test:
According to the model questions given in the TCS recruitment portal https://nextstep.tcs.com we can assume the following chapters are very important. There is no verbal part in TCS aptitude test except for email writing. 1/3rd negative marking will be there.
Important topics: Number system, Equations, Ratio and Proportion, Percentages, Profit and Loss, Time and Work, Time speed Distance, Areas and Mensuration, Averages, Permutations and Combinations, Probability, Plane geometry, Seating Arrangements, Sets, Progressions.
Interview process:
There is no hard and fast rule that you may be asked only Technical questions in technical interview. or HR questions in HR interview. You have to prepare well before for all the types of interviews.
For technical interview, you have to focus on C, DBMS and JAVA. It is important you have to be through with at least a couple of your core subjects.
For HR interview you have to study all the questions given in www.campusgate.co.in along with their suggested answers
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QUESTIONS
1. The rupee/coin changing machine at a bank has a flaw. It gives 10 ten rupee notes if you put a 100 rupee note and 10 one rupee coins if you insert a 10 rupee note but gives 10 hundred rupee notes when you put a one rupee coin!
Sivaji, after being ruined by his rivals in business is left with a one rupee coin and discovers the flaw in the machine by accident. By using the machine repeatedly, which of the following amounts is a valid amount that Sivaji can have when he gets tired and stops at some stage (assume that the machine has an infinite supply of notes and coins):
| a. 26975 | b. 53947 |
| c. 18980 | d. 33966 |
Explanation:
The process works like this:
Rs.1 Coin ⇒ 10 × 100 = Rs.1000
Rs.100 ⇒ 10 × 10
Rs.10 ⇒ 1 × 10
Sivaji gets more money when he inserts a rupee coin only. For each rupee coin he gets his money increased by 1000 times. Suppose he inserted 1 rupee coin and got 1000 rupees and again converted this into coins. So he ends up with 1000 coins. Now of this, he inserts one coin, he gets 1000. So he has 1999 with him. Now if he inserts another coin, he has 1998 + 1000 = 2998.
Now each of these numbers are in the form of 999n + 1. So option B can be written as 54 × 999 + 1.
- Exactly twice as many of the film buffs sees the S.shankar film as see the Rajkumar Hirani film.
- Guna and Rinku do not see the same film as each other.
- Isha and Madhu do not see same film as each other.
- Viji and Yamini see the same film as each other.
- Leela sees the S.Shankar film.
- Guna sees either the Rajkumar Hirani film or the Mani Ratnam film.
Which one of the following could be an accurate matching of the film buffs to films ?
(A) Guna: the S.Shankar film; Isha: the Mani Ratnam film; Madhu: the S.Shankar film
(B) Guna: the Mani Ratnam film; Isha: the Rajkumar Hirani film; Viji: the Rajkumar Hirani film
(C) Isha : the S.Shankar film; Rinku: the Mani Ratnam film; Viji: the Rajkumar Hirani film
(D) Madhu: the Mani Ratnam film; Rinku: the Mani Ratnam film; Viji: the Mani Ratnam film
| a. A | b. C |
| c. D | d. B |
Explanation:
Guna × Rinku
Isha × Madhu
(Viji + Yamini)
Leela - Film: Shankar
Guna = RKH/Mani Ratnam
The following options are possible:
| RKH | Shankar | Mani Ratnam |
| 1 | 2 | 4 |
| 2 | 4 | 1 |
Option A: Guna should not watch Shankar's Film. So ruled out
Option B:
| RKH | Shankar | Mani Ratnam |
| Isha | _ | Guna |
| Viji | _ | _ |
Option C:
| RKH | Shankar | Mani Ratnam |
| Viji | Isha | Rinku |
| Yamini | Leela | _ |
Option D:
| RKH | Shankar | Mani Ratnam |
| Guna | Leela | Madhu |
| _ | Isha | Rinku |
| _ | _ | Viji and Yamini |
3. Which of the following numbers must be added to 5678 to give a remainder of 35 when divided by 460?
| a. 955 | b. 980 |
| c. 797 | d. 618 |
Explanation:
5678 - 35 + (one of the answer option) should be divisible by 460. Only option C satisfies.
4. Find the probability that a leap year chosen at random will have 53 Sundays.
| a. 1/7 | b. 2/7 |
| c. 1/49 | d. 3/7 |
Explanation:
A leap year has 366 day which is 52 full weeks + 2 odd days. Now these two odd days may be (sun + mon), (mon + tue), .... (Sat + sun). Now there are total 7 ways. Of which Sunday appeared two times. So answer 2/7
5. An ant starts moving on the mesh shown below along the wires towards a food particle.If the ant is at the bottom-left corner of cell A and the food is at the top-right corner of cell F, then find the number of optimal routes for the ant.
| a. 13884156 | b. 3465280 |
| c. 4368 | d. 6748 |
Explanation:
(Please read "Counting" to understand this question: Click here )
Total ways to move from A to the junction: There are 13 upward ways, 3 right side ways this Ant can move. Now these 16 ways may be in any order. So number of ways of arrangements =
Similarly, from the junction to F, Total 12 upward ways and 5 right-side ways. These 17 ways can be in any order. So Total ways =
Total ways to move from A to F = 560 × 6188 = 3465280
6. You have been given a physical balance and 7 weights of 52, 50, 48, 44, 45, 46 and 78 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 183 kgs.
| a. 180 | b. 181 |
| c. 182 | d. 178 |
Explanation:
52+50+78 = 180
7. Two consecutive numbers are removed from the progression 1, 2, 3, ...n. The arithmetic mean of the remaining numbers is 26 1/4. The value of n is
| a. 60 | b. 81 |
| c. 50 | d. Cannot be determined |
Explanation:
As the final average is 105/4, initial number of pages should be 2 more than a four multiple. So in the given options, we will check option C.
Total =
Final total =
So sum of the pages = 15. The page numbers are 7, 8
8. You need a 18% acid solution for a certain test, but your supplier only ships a 13% solution and a 43% solution. You need 120 lts of the 18% acid solution. the 13% solution costs Rs 82 per ltr for the first 67 ltrs, and Rs 66 per ltr for any amount in access of 67 ltrs. What is the cost of the 13% solution you should buy?
| a. 8002 | b. 7012 |
| c. 7672 | d. 7342 |
Explanation:
Let us assume we need "a" liters of 13% acid solution and "b" liters of 43% acid solution. Now
So we need 100 liters of 13% acid solution, and 20 liters of 18% acid solution.
Final cost = 82 × 67 + 66 × 33 = 7672
9. A spherical solid ball of radius 58 mm is to be divided into eight equal parts by cutting it four times longitudinally along the same axis.Find the surface area of each of the final pieces thus obtained( in mm^2) ? (where pi= 22/7)
| a. 3365pi | b. 5046pi |
| c. 1682pi | d. 3346pi |
Explanation:
If a sphere is cut into 8 parts longitudinally, It something looks like below
Now We have to find the surface area of one piece. This is 18th of the initial sphere + 2 × area of the half circle
= 18(4πr2)+π×r2
= = 5046pi
10. There is a lot of speculation that the economy of a country depends on how fast people spend their money in addition to how much they save. Auggie was very curious to test this theory.
Auggie spent all of his money in 5 stores. In each store, he spent Rs.4 more than one-half of what he had when he went in. How many rupees did Auggie have when he entered the first store?
| a. 248 | b. 120 |
| c. 252 | d. 250 |
Explanation:
As he has spent all his money, He must spend Rs.8 in the final store.
a simple equation works like this. Amount left =
For fifth store this is zero. So x = 8. That means he entered fifth store with 8.
Now for fourth store, amount left = 8 so
For third store, amount left = 24 so
For Second store, amount left = 56 so
For first store, amount left = 120 so
So he entered first store with 248.
11. A sudoku grid contains digits in such a manner that every row, every column, and every 3x3 box accommodates the digits 1 to 9, without repetition. In the following Sudoku grid, find the values at the cells denoted by x and y and determine the value of 6x + 15y.
| a. 87 | b. 75 |
| c. 66 | d. 99 |
Explanation:
6x + 15y = 75
12. In how many ways can the letters of the english alphabet be arranged so that there are seven letter between the letters A and B, and no letter is repeated
| a. 24P7 * 2 * 18! | b. 36 * 24! |
| c. 24P7 * 2 * 20! | d. 18 * 24! |
Explanation:
We can fix A and B in two ways with 7 letters in between them. Now 7 letters can be selected and arranged in between A and B in
These 18 letters are arranged in 18! ways. So Answer is 2 x
Infact, 2 x
13. A certain function f satisfies the equation f(x)+2*f(6-x)=x for all real numbers x. The value of f(1) is
| a. 1 | b. 2 |
| c. 3 | d. Cannot be determined |
Explanation:
Put x =1 ⇒ f(1)+2*f(6-1) = 1 ⇒ f(1) + 2*f(5) = 1
Put x = 5 ⇒ f(5)+2*f(6-5) = 5 ⇒ f(5) + 2*f(1) = 5
Put f(5) = 5 - 2*f(1) in the first equation
⇒ f(1) + 2*(5 - 2*f(1)) = 1
⇒ f(1) + 10 - 4f(1) = 1
⇒ f(1) = 3
14. Professor absentminded has a very peculiar problem, in that he cannot remember numbers larger than 15. However, he tells his wife, I can remember any number up to 100 by remembering the three numbers obtained as remainders when the number is divided by 3, 5 and 7 respectively. For example (2,2,3) is 17. Professor remembers that he had (1,1,6) rupees in the purse, and he paid (2,0,6) rupees to the servant. How much money is left in the purse?
option
A. 59
B. 61
C. 49
D. 56
Answer: D
Explanation:
Let the money with the professor = N
Then N = 3a +1 = 5b + 1 = 7c + 6.
Solving the above we get N = 181
(Explanation: See LCM formula 1 and 2: Click here)
When a number is divided by several numbers and we got same remainder in each case, then the general format of the number is LCM (divisors).x + remainder.
In this case 3, 5 are divisors. So N = 15x + 1. Now we will find the number which satisfies 15x + 1 and 7c + 6.
⇒ 15x + 1 = 7c + 6 ⇒ c =
Here x = 5 satisfies. So least number satisfies the condition is 5(15)+1 = 76.
(x = 12 also satisfies condition. So substituting in 15x + 1 we get, 181 which satisfies all the three equations but this is greater than 100)
Similarly Money given to servant = M = 3x + 2 = 5y = 7z + 6
Solving we get M = 25.
(125 also satisfies but this is next number)
Now N - M = 56
15. The sum of three from the four numbers A, B, C, D are 4024, 4087, 4524 and 4573. What is the largest of the numbers A, B, C, D?
a. 1712
b. 1650
c. 1164
d. 1211
Answer: a
Explanation:
a+b+c=4024
b+c+d= 4087
a+c+d=4524
a+b+d=4573
Combining all we get 3(a+b+c+d) = 17208
⇒ a + b + c +d = 3736
Now we find individual values. a = 1649, b = 1212, c = 1163, d = 1712. So maximum value is 1712.
16. Anand packs 304 marbles into packets of 9 or 11 so that no marble is left. Anand wants to maximize the number of bags with 9 marbles. How many bags does he need if there should be atleast one bag with 11 marbles
a. 33
b. 32
c. 31
d. 30
Answer: B
Explanation:
Given 9x + 11y = 304.
x =
So y = - 1 satisfies. Now x = 35,
Now other solutions of this equation will be like this. Increase or decrease x by 11, decrease or increase y by 9. So we have to maximise x. next solution is x = 24 and y = 8. So bags required are 32.
17. When Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha?
a. 37
b. 44
c. 45
d. 40
Answer: D
Explanation:
Let the age of Usha is 3x then Nisha is x and Asha is 25
Also Usha 34, Nisha y, and Asha 2y.
We know that 3x - 34 = x - 2y = 25 - 2y
Solving above three equations we get x = 9, y = 16
Their ages are 34, 16, 32. whose sum = 82. So after 18 years their ages will be equal to 100. So Usha age is 34 + 6 = 40
18. Find the number of zeroes in the expression 15*32*25*22*40*75*98*112*125
a. 12
b. 9
c. 14
d. 7
Answer: B
Explanation:
Maximum power of 5 in the above expression can be calculated like this. Count all the powers of 5 in the above expression. So number of zeroes are 9. (Read this chapter)
19. Two vehicles A and B leaves from city Y to X. A overtakes B at 10:30 am and reaches city X at 12:00 pm. It waits for 2 hrs and return to city Y. On its way it meets B at 3:00 pm and reaches city Y at 5:00 pm. B reaches city X, waits for 1hr and returns to city Y. Afer how many hours will B reach city Y from the time A overtook him fro the first time?
a. 50 hrs
b. 49.5 hrs
c. 41.5 hrs
d. 37.5 hrs
Answer: C
Explanation:
Let us understand the diagram. Vehicle A overtaken B at 10.30 am and reached X at 12 pm. It started at 2 pm and met B at 3 pm at Q. It means, Vehicle A took one hour to cover distance 'n', So it should be at Q at 11 pm. It is clear that Vehicle A takes 0.5 hour to cover distance 'm'. Now vehicle B travelled from 10.30 am to 3 pm to meet A. So it took 4.5 hours to cover m. So Speeds ratio = 4.5 : 0.5 = 9 : 1.
Now Vehicle A took a total of 1.5 + 3 = 4.5 hours to travel fro P to Y. So It must take 4.5 × 9 + 1 = 41.5 hours
20. Two identical circles intersect so that their centres, and the points at which they intersect,
form a square of side 1 cm. The area in sq. cm of the portion that is common to the two
circles is:
a. (π/2) – 1
b. 4
c. √2 – 1
d. √5
Answer:
Explanation:
We have to find the area of the blue shaded one and double it to get the
area common to the both. Now this can be calculated as Area of the
sector OAB - Area of the Triangle OAB.
As OA and OB are perpendicular, area of the sector OAB = 90360π(1)2 = π4
Area of the triangle OAB = 12×1×1 = 12
Area common to both = ___________________________________________________________________
1) The water from one outlet, flowing at a constant rate, can fill the swimming pool in 9 hours. The water from second outlet, flowing at a constant rate can fill up the same pool in approximately in 5 hours. If both the outlets are used at the same time, approximately what is the number of hours required to fill the pool?
Ans: Assume tank capacity is 45 Liters. Given that the first pipe fills the tank in 9 hours. So its capacity is 45 / 9 = 5 Liters/ Hour. Second pipe fills the tank in 5 hours. So its capacity is 45 / 5 = 9 Liters/Hour. If both pipes are opened together, then combined capacity is 14 liters/hour. To fill a tank of capacity 45 liters, Both pipes takes 45 / 14 = 3.21 Hours.
2) If 75 % of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percentage answered both correctly?
It is a problem belongs to sets. We use the following formula n(A
Here n(A
It was given that 20% answered neither question then the students who answered atleast one question is 100% - 20% = 80%
Now substituting in the formula we get 80% = 75% + 55% - n(A
3) A student's average ( arithmetic mean) test score on 4 tests is 78. What must be the students score on a 5th test for the students average score on the 5th test to be 80?
Ans: We know that Average
So Sum of 4 test scores = 78
Sum of 5 tests scores = 80
Alternative method: If the student scores 78 in the fifth test also, what could be his average? No change. Is it not?
But to bring the average to 80, he must have scored enough marks extra so that each of the five subject scores increase upto 80. i.e., he should have scored 2 x 5 = 10 runs extra in the fifth subject. So 5th subject score is 78 + 10 = 88
4) Rural households have more purchasing power than do urban households at the same income level, since some of the income urban and suburban households use for food and shelter can be used by the rural households for other needs. Which of the following inferences is best supported by the statement made above?
(A) The average rural household includes more people than does the average urban or suburban household.
(B) Rural households have lower food and housing costs than do either urban or suburban households.
(C) Suburban households generally have more purchasing power than do either rural or urban households.
(D) The median income of urban and suburban households is generally higher than that of rural households.
(E) All three types of households spend more of their income on housing than on all other purchases combined.
Ans: If average rural household includes more people, then how come they have more purchasing power? Infact, they have less purchasing power as they have to feed more people. Option A ruled out.
Option C does not explain why rural households have more purchasing power than urban. Ruled out.
If median income of urban and suburban households is generally higher than rural households they are likely to have more purchasing power, assuming other parameters constant. But this does not explain why rural households have more purchasing power. Options D ruled out.
Option E does not provide any explanation why rural households have more purchasing power. Ruled out.
Option B is correct as, If rural households spend less income on food and shelter due to less prices they definitely have more disposable income to spend.
5) Jose is a student of horticulture in the University of Hose. In a horticultural experiment in his final year, 200 seeds were planted in plot I and 300 were planted in plot II. If 57% of the seeds in plot I germinated and 42% of the seeds in plot II germinated, what percent of the total number of planted seeds germinated?
Ans: Total seeds germinated in Plot I = 57% of 200 = 114
Total seeds germinated in Plot II = 42% of 300 = 126
Total germinated seeds = 114 + 126 = 240
The percentage of germinated seeds of the total seeds =
6) A closed cylindrical tank contains 36
Ans: We know that the volume of cylinder =
Given tank hight = 4ft.
So the radius is 3 which means the diameter is 6.
As the cylinder is filled to initially exactly half of the capacity, When this cylinder is placed on its side, Water comes upto the height of the radius.
So water comes upto 3 ft.
7) The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of the teachers would then be 25 to 1 What is the present number of teachers?
Assume the present students and teachers are 30K, K
After new recruitments of students and teachers the strength becomes 30K + 50, K + 5 respectively. But given that this ratio = 25 : 1
Solving we get K = 15
So present teachers are 15.
8) College T has 1000 students. Of the 200 students majoring in one or more of the sciences,130 are majoring in Chemistry and 150 are majoring in Biology. If at least 30 of the students are not majoring in either Chemistry or Biology, then the number of students majoring in both Chemistry and Biology could be any number from
If we assume exactly 30 students are not majoring in any subject then the students who take atleast one subject = 200 - 30 = 170
We know that n(A
Solving we get n(A
i.e., Students who can take both subjects are 110
But If more than 30 students are not taking any subject, what can be the maximum number of students who can take both the subjects?
As there are 130 students are majoring in chemistry, assume these students are taking biology also. So maximum students who can take both the subjects is 130
9) Kelly and Chris are moving into a new city. Both of them love books and thus packed several boxes with books. If Chris packed 60% of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number of boxes Chris packed?
Simple questions. If chris packs 60% of the boxes, kelly packs remaining 40%
So Kelly : Chris = 40% : 60% = 2 : 3
10) Among a group of 2500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from 2500 people, what is the probability that the person selected will be one who invests in municipal bonds but not in oil stocks?
Ans: Here 2500 is redundant
From the diagram we know that only ones who invested in municipal bonds are 28%, the probability is 28 / 100 = 7/25
11) Machine A produces bolts at a uniform rate of 120 every 40 second, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?
Ans: Machine A produces 120/40 = 3 bolts in 1 second and machine B produces 100/20 = 5 bolts in one second.
Hence, both of them will produce 8 bolts per second.
Hence, they wil take 200/8 = 25 seconds to produce 200 bolts.
12) How many prime numbers between 1 and 100 are factors of 7150?
Ans: 7, 150 =
So there are 4 distinct prime numbers that are below 100
13) Analysing the good returns that Halocircle Insurance Pvt Ltd was giving, Ratika bought a 1-year, Rs 10,000 certificate of deposit that paid interest at an annual rate of 8% compounded semi-annually.What was the total amount of interest paid on this certificate at maturity?
This is a question on compound interest to be calculated semi annually.
In the case of semi annual compounding, Interest rate becomes half and Number of periods becomes 2 per year.
So A = P
= 10,816
Interest = A - P = 10, 816 - 10,000 = 816
14) Juan is a gold medalist in athletics. In the month of May, if Juan takes 11 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
Ans: If juan takes 11 seconds to run Y yards, for 1 yard he will take 11 / y seconds. To run x yards his time will be 11 / y
15) A certain company retirement plan has a rule of 70 provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1986 on her 32nd birthday first be eligible to retire under this provision?
Assume it has taken x years to the female employee to reach the rule of 70.
So her age should be 32 + x. Also she gains x years of experience.
Her age at the time of retirement = 1986 + 19 = 2005
16) Of the following, which is the closest approximation of (50.2*0.49)/199.8 ?
ans: For approximation (50.2
50
17) Andalusia has been promoting the importance of health maintenance. From January 1,1991 to January 1,1993, the number of people enrolled in health maintenance organizations increased by 15 percent. The enrollment on January 1,1993 was 45 million. How many million people(to the nearest million) was enrolled in health maintenance organizations on January 1,1991?
Ans: If a number K is to be increased by x % it should be multiplied by
So When the enrollment in January 1, 1991 is multiplied by
K =
18) What is the lowest possible integer that is divisible by each of the integers 1 through 7, inclusive?
Ans: If a number has to be divisible by each number from 1 to 7, that number should be L.C.M of(1,2,3,4,5,6,7) = 420
19) If the area of a square region having sides of length 6 cms is equal to the area of a rectangular region having width 2.5 cms, then the length of the rectangle, in cms, is
Ans: Given Area of the square = Area of rectangle
Substituting the above values in the formula
20) A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 2500 gallons of water evaporate from the tank, the remaining solution will be approximately what percentage of sodium chloride?
Ans: Sodium chloride in the original solution = 5% of 10,000 = 500
Water in the original solution = 10,000 - 500 = 9,500
If 2,500 Liters of the water is evaporated then the remaining water = 9,500 - 2,500 = 7,000
Sodium chloride concentration =
(concentration should be calculated always on the total volume)
21) After loading a dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day of the crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by two crews did the day crew load?
Assume the number of boxes loaded in dayshift is equal to 4, then the number of boxed loaded in night shift = 3
Assume the worked on dayshift = 5, then workers on night shift = 4
So boxes loaded in day shift = 4 x 5 = 20, and boxes loaded in night shift = 3 x 4 = 12
so fraction of boxes loaded in day shift =
22) A bakery opened yesterday with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon and 80 % of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday?
Ans: If half of the rolls were sold by noon, the remaining are 50 % (40) = 20.
Given 80% of the remaining were sold after the noon to closing time
Unsold = 20 - 16 = 4
23) If N=4P, where P is a prime number greater than 2, how many different positive even divisors does n have including n?
Ans: N =
We know that total factors of a number which is in the format of
Also odd factors of any number can be calculated easily by not taking 2 and its powers.
So odd factors of
Even factors of the number = 6 - 2 = 4
24) A dealer originally bought 100 identical batteries at a total cost of q rupees. If each battery was sold at 50 percent above the original cost per battery, then, in terms of q, for how many rupees was each battery sold?
Ans: Per battery cost = q / 100
If each battery is sold for 50% gain, then selling price =
25) The price of lunch for 15 people was 207 pounds, including a 15 percent gratuity of service. What was the average price per person, EXCLUDING the gratuity?
Ans: Let the net price excluding the gratuity of service = x pounds
Then, total price including 15% gratuity of service =
So, 1.15 x = 207 pounds
Net price of lunch for each person = 180 / 15 = 12 pounds
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