# TCS Aptitude-reasoning placement papers

TCS Aptitude-reasoning placement papers

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: (1/A) + (1/B) = 1/T
So when you solved, and got 14/45, that was equal to 1/T. To find T, you need to take the reciprocal; T = 45/14,
(3.21)
u
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?

ans: n(a ^ b) =n(a)+n(b)-n(a v b)
= 0.75+0.55-0.8
= 0.5
(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: 4 tests sum=78*4=312
5 tests sum=80*5=400
then 5th test score=400-312=88
(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: B

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: 200 * 57 % = 114 and 300* 42% = 126.
Total = 240 out of 500.
(48%).

6) A closed cylindrical tank contains 36 pie 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: What given Volume = 36
Height = 4ft
Volume = Pi* r2 * h
36 = Pi*r2 * 4
r2 =9
r = 3
So the radius is 3 which means the diameter is 6.

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?

ans: 30/1 = s/t Current student to teacher ratio
s+50/t+5 = 25/1 Future student to teacher ratio
solving the first equation first equation for s gives s = 30t.
Substitute this value of s into the second equation, and solve for t.
s+50/t+5 = 25/1
30t + 50 = 25t + 125 multiply both sides by t+5
5t = 75 simplify by subtraction
t = 15
(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

ans: total=200
neither>=30
chemistry=130
bio=130
maximum common=minimum of the two=130
if neither=30
then common=150+130+30-200=110
range is 110-130

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?

ans: 100-60=40
40:60=2:3

10) A drug that is highly effective in treating many types of infection can, at present, be obtained only from the bark of the ibora, a tree that is quite rare in the wild. It takes the bark of 5,000 trees to make one kilogram of the drug. It follows, therefore, that continued production of the drug must inevitably lead to the ibora’s extinction. Which of the following, if true, most seriously weakens the argument above?

ans: The ibora can be propagated from cuttings and grown under cultivation.

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 seconds 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.
(25)

12) Wood smoke contains dangerous toxins that cause changes in human cells. Because wood smoke presents such a high health risk, legislation is needed to regulate the use of open-air fires and wood burning stoves

ans: In valleys where wood is used as the primary heating fuel, the concentration of smoke results in poor air quality.

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?

ans: @8%, for half year you get 400/- 10000x 8/100×1/2=400
for the next year there will be interest on your investment of 10000 and also on your accrue interest of Rs.400/-
that means another 400/+ interest on 400/- @8% for half year.=400+ (400×8/100×1/2)
400+400+16=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: 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?

ans: The female employee must gain at least 70 points.
Now she has 32 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2 * (number of years) = 70
(Number of years) = 19
So, 1986 + 19 = 2005

16) Homeowners aged 40 to 50 are more likely to purchase ice cream and are more likely to purchase it in larger amounts than are members of any other demographic group. The popular belief that teenagers eat more ice-cream than adults must, therefore, be false. The argument is flawed because the author _____

ans: fails to distinguish between purchasing and consuming

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: let there are ‘x’ population at jan1,1991
15% of x = 15/100*(x)
(x)+[15/100*(x)]=45 /* as there is 15% increase from 1991 to 1993*/
x=39.13

18) What is the lowest possible integer that is divisible by each of the integers 1 through 7, inclusive?

ans: L.C.M of(1,2,3,4,5,6,7)=2*2*3*5*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: Area of a Square
s x s
6 x 6 = 36
Area of a Rectangle
lw
?(2.5)
=36 as it is equal to the area of a square
36/2.5 = 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: Original =10,000 —-> sodium chloride = 5% ie 500
New = 10,000-2,500 = 7500.
New % = (500/7500) * 100
= 6.67%

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?

ans: Number of workers
Day shift: 5 workers (this is an easy number to find 4/5 of)
Night shift: 4 workers (4/5 of 5 = 4)
Day shift: 4 boxes per worker
Night shift: 3 boxes per worker (3/4 of 4 = 3)
Day shift: 5 workers times 4 boxes per worker = 20 boxes
Night shift: 4 workers times 3 boxes per worker = 12 boxes
Combined total boxes for both shifts = 20 + 12 = 32
Of the 32 boxes, the day shift loaded 20 of them.
20/32 = 5/8

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: 4 rolls were not sold………….half of them were sold by noon…….so 20 rolls remain….and then 20% were not sold,, so 20% of the 20 rolls is 4 then it is the answer

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: 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: bought for q/100 dollars per battery
each battery sold with profit 50% is
q/100 + q/100*50/100
=q/100+q/200
=3q/200

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 + 0.15 x = 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

26) 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

27) How many prime numbers between 1 and 100 are factors of 7150?

ans: 7,150 = 2 * 5 * 5 * 11 * 13
so there are 4 distinct prime numbers that are below 100

28) Guitar Strings often go dead – become less responsive and bright in tone – after a few weeks of intense use. A researcher whose son is a classical guitarist hypothesized that dirt and oil, rather than changes in the material properties of the string, were responsible. Which of the following investigations is most likely to yield significant information that would help evaluate the researcher’s hypothesis?

ans: Determining whether smearing various substances on new guitar strings causes them to go dead

29) Red blood cells in which the malarial-fever parasite resides are eliminated from a person’s body after 120 days. Because the parasite cannot travel to a new generation of red blood cells, any fever that develops in a person more than 120 days after that person has moved to a malaria free region is not due to malarial parasite. Which of the following, if true, most seriously weakens the conclusion above?

ans: In some cases, the parasite that causes malarial fever travels to cells of the spleen, which are less frequently eliminated from a person’s body than are red blood cells.

30) 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: 7/25

31) When a polygraph test is judged inconclusive, this is no reflection on the examinee. Rather, such a judgment means that the test has failed to show whether the examinee was truthful or untruthful. Nevertheless, employers will sometime refuse to hire a job applicant because of an inconclusive polygraph test result. Which of the following conclusions can most properly be drawn from the information above?

ans: An inconclusive polygraph test result is sometimes unfairly held against the examinee

32) Country Club has an indoor swimming club. Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?

ans: Suppose there are x members, non pass members arre 7x/10 which are equal to 12 + 30 = 42
7x/10 = 42
x = 60
There are 60 members in that club

ans: R G W B Y is the bead pattern and it repeats.
Bead want to end with White.
So, the 3rd, 8th, 13th, 18th… beads will be W.
this can be expressed as 5n+3,where n is an integer.(counting no of white bead)
Test each of the answer choices to determine which is multiple of 5 plus a value of 3.Of the options ,only 68=5(13)+3 can be written in the form 5n+3.
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33 A dog taken four leaps for every five leaps of hare but three leaps of the dog is equal to four leaps of the hare. Compare speed?
Let the distance covered by dog in 1 leap is x and hare covered 1 leap is y.
then, 3x = 4y
=> x =(4/3) y
=> 4x =(16/3) y

Then, The ratio of speeds of dog and hare = Ratio of distances covered by them in the same time
= 4x : 5y
= (16/3)y : 5y
=(16/3) : 5
= 16:15 Ans…=16:15

34 There are two boxes,one containing 39 red balls & the other containing 26 green balls.you are allowed to move the balls b/w the boxes so that when you choose a box random & a ball at random from the chosen box,the probability of getting a red ball is maximized.this maximum probability is
a)60 b)50 c)80 d)30

the probability of getting a red ball should be maximized so we will keep 1 red ball in the first box and transfer remaining 38 red balls to other box which has green. The reason for doing this only this combination will make the probability of getting red ball is maximum (i.e) 1.
In the question its mentioned that first we have to choose a box at random.
So 2 boxes are there, probability of selecting a bag is 1/2
Probability of getting red ball from first box is 1
Probability of getting green ball from second box is 38/64
So (1/2)*1 for first box and (1/2)*(38/64) for box 2
answer is (1/2)*1 + ((1/2)*(38/64) which is approximately 0.8
Next number in the given series 1, 7, 8, 49, 50, 56, 57, 343
344 because
1*7=7
7+1-8
7*7=49
49+1=50
8*7=56
56+1=57
49*7=343
343+1=344
ans= 344
q.1 in how many ways can 3 postcards can be posted in 5 postboxes?
q.2.in how many ways can 5 postboxes hold 3 post cards?
q.1 in how many ways can 3 postcards can be posted in 5 postboxes?

first post card can be posted in any of the 5 post boxes =5c1 ways
second post card can be posted in any of the 5 post boxes =5c1 ways
third post card can be posted in any of the 5 post boxes =5c1 ways

number of ways=5c1*5c1*5c1=125=5^3

q.2.in how many ways can 5 postboxes hold 3 post cards?
first post box can hold 3 post cards in 3c1 ways
second post box can hold 3 post cards in 3c1 ways
third post box can hold 3 post cards in 3c1 ways
fourth post box can hold 3 post cards in 3c1 ways
fifth post box can hold 3 post cards in 3c1 ways
so number of ways =3c1*3c1*3c1*3c1*3c1=3^5

35 A number has exactly 3 prime factors, 125 factors of this number are perfect squares and 27 factors of this number are perfect cubes. overall how many factors does the number have???
Answer for this question is 729
The explanation goes like this
Let a,b,c be three prime no.
since the no. of perfect square as a factor is 125
which can only be if every prime no. has power in the multiple of 2 including zeros(bcoz any no. to the power of zero is a perfect square)
so power must be 0,2,4,6,8
thereby 5*5*5=125
Since no. of cube as a factor is 27
therefore power in the prime no. will be in the multiple of 3
so power are 0,3,6
hence the no. N=a^8*b^8*c^8
hence total no. of factor is (8+1)(8+1)(8+1)=729
there r three buckets..of 8,5 n 3 litres…out of which only 8 ltr bucket is fully filled…u hv to fill exact 4-4 ltr liquid in 8 and 5 litre bucket by using only these buckets in minimm num of steps……
8ltr 5ltr 3ltr
initially 8 0 0
step1 3 5 0
step2 3 2 3
step3 6 2 0
step4 6 0 2
step5 1 5 2
step 6 1 4 3
step 7 4 4 0
total 7 steps

36 The climb from foot to top of a hill 800 meters, Jack can climb at 16 meters per minute and rests for two minutes or 20meters per 2 minutes and rest for one minute. Paul can climb at 10 meters per one minute and rest for one minute or16 meters per minute and rest for 2 minutes. If take has to reach the top in exactly two hours. What is the maximum number of rests that he can take?
a) 41 b) 42 c) 40 d) 43
total=800m
16m per min means for 1m=800/16 =50min to climb
10m per min means for 1m=800/10=80min to climb for paul …..the total time is 2hours==120min….so,time taken for rest by paul is 120-80=40min
length of minute hand is 5.4 cm, area covered by this in 10 min is ?

a)50.97 b)57.23 c)55.45 d)59.14
t will be (3.14*5.4*5.4)*10/60 = 15.26 cm2.

37 Raj tossed 3 dices and there results are noted down then what is the probability that raj gets 10?
a) 1/72 b) 1/9 c) 25/216 d)1/8
ossible event…….(1,3,6)(1,4,5)(1,5,4)(1,6,3)(2,2,6)(2,3,5)(2,4,4)(2,5,3)(2,6,2)(3,1,6)(3,2,5)(3,3,4)(3,4,3)(3,5,2)(3,6,1)(4,1,5)(4,2,4)(4,3,3)(4,4,2)(4,5,1)(5,1,4)(5,2,3)(5,3,2)(5,4,1)(6,1,3)(6,2,2)(6,3,1)
total 27 possible event
so probability = 27/216 i.e 1/8

Probability of a sum of 3: 1/216 = 0.5%
Probability of a sum of 4: 3/216 = 1.4%
Probability of a sum of 5: 6/216 = 2.8%
Probability of a sum of 6: 10/216 = 4.6%
Probability of a sum of 7: 15/216 = 7.0%
Probability of a sum of 8: 21/216 = 9.7%
Probability of a sum of 9: 25/216 = 11.6%
Probability of a sum of 10: 27/216 = 12.5%
Probability of a sum of 11: 27/216 = 12.5%
Probability of a sum of 12: 25/216 = 11.6%
Probability of a sum of 13: 21/216 = 9.7%
Probability of a sum of 14: 15/216 = 7.0%
Probability of a sum of 15: 10/216 = 4.6%
Probability of a sum of 16: 6/216 = 2.8%
Probability of a sum of 17: 3/216 = 1.4%
Probability of a sum of 18: 1/216 = 0.5%

38 Apple costs L rupees per kilogram for first 30kgs and Q rupees per kilogram for each additional kilogram. If the price of 33 kilograms is 11.67and for 36kgs of Apples is 12.48 then the cost of first 10 kegs of Apples is
a) 3.50 b) 10.53 c) 1.17 d)2.8
30L+3Q=11.67
30L+6Q=12.48
————
3Q=.81 Q= .27
from that L=0.362 cost of 10 kg apple is 10*.362=3.6
The letters in the word ABUSER are permuted in all possible ways and arranged in alphabetical order then find the word at position 49 in the permuted alphabetical order?
a) ARBSEU
b) ARBESU
c) ARBSUE
d) ARBEUS
AB**** =4!= 24 ways
AE****=4!=24 ways next word is 49th so
AR**** in alphabetical order **** will be BESU
ans is B

39 A is twice efficient than B. A and B can both work together to complete a work in 7 days. Then find in how many days A alone can complete the work?
ans is 10.5
gn:
A+B=(1/7)
A=2B
=>B=1/21
A=2/21
=>A take (21/2)=10.5 days to complete the work.
In 8*8 chess board what is the total number of squares.
1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2=204….
formula=1^2+2^2+3^2+….+n^2

40 X,Y,W,Z ARE INTEGER THE EXPRESSION X-Y-Z IS EVEN&Y-W-Z ODD IF X IS EVEN THEN WHICH OF FOLLOWING IS TRUE(a)Y MUST BE ODD(b)Y-Z MUST BE ODD(c)W MUST BE ODD(d)Z MUST BE ODD
Ans.(c)W must be ODD
X-Y-Z=even and X even no.
hence (y-z) must be even because (even -even = even)
and y-w-z=y-z-w=odd and (y-z) is even so W must be odd because (even – odd=odd)
hence option (c) is correct

41 Two cyclist begin training on oval racecourse at same timethe professional cyclist complete each lap in 4 sec noves take 6 mintue how many mintue after start will both cyclist pass at exactly same spot where they begin to cycle(a)10(b)8(C)14(D)12
ans is d.
simply LCM of 4 and 6.
which of following true:A occur only B or C occur B occur D&E occurf occur if Cnot occur g occur if A and F occur option A occur whenever F occur2)F never occur3) G not occur if D not occur4)none of these
3) g nt occure i d not occure
a=>b or c
b=>d & e
f=>c not
g =>a & f
1) a occure whenevr f :- depen on c where as ‘a’ can occure if ‘c’ not ..so this is not true
2) f nevr occure => depnd on c only n c is indipendent …if c not occure f will occure ….so this is also not true
3) g not occure if d not:-g depnd on a & f …if d not ocuure b will not occure (as b=>d&e) a will occure if c occure…if c occure f will not occure …hence g will not occure…this is true
House1 is older than H2, H3 is taller than H4,H4 is older than H1…(i)H1 is older than H3 (ii)H2 is taller than H4 (a)only 1 (b)both (c)neither (d)only2

42 In how many ways can 20 identical pencils be distributed among three girls so that each gets at least 1 pencil? now A’+B’+C”=17,
number of non negative integers of A’,B’,C’ are (17+3-1)C(3-1)
so total Combinations are 19c2=19*9 = 171,
simple formula for this kind of problems is
(n-1)c(r-1)
so 19c2= 171
if p(x)=ax^4+bx^3+cx^2+dx+e has roots at x=1,2,3,4 & p(0)=48.what is p(5)
if 1 is a root then x-1 is a factor of p(x)
similarly x-2 is a factor,x-3 ,x-4 are factors
but p(x) is 4th degree polynomial therefore it can be in the form
p(x) = Q(x-1)(x-2)(x-3)(x-4) , where Q is a constant
but given p(0) =48
therefore 24 Q =48
Q=2
p(x) =2(x-1)(x-2)(x-3)(x-4)
p(5)= 2*4*3*2*1 = 48
1!+2!+3!…+50! divided by 5!
remainder will be ?
1!+2!+3!…+50! divided by 5!
remainder will be whatever is obtained by dividing 1!+2!+3!+4! with 5!.
so remainder is obtained by dividing (1+2+6+24)= 33 with 5! ( 120).
so remainder is 33.

43 If there are Six periods in each working day of a school, In how many ways can one arrange 5 subjects such that each subject is allowed at least one period?
we have 5 sub and 6 periods so their arrangement is 6P5 and now we have 1 period which we can fill with any of the 5 subjects so 5C1
6P5*5C1=3600

44 An article manufactured by a company consists of two parts X and Y. In the process of manufacturing of part X, 9 out 100 parts many be defective. Similarly , 5 out of 100 are likely to be defective in the manufacturer of Y. Calculate the probability that the assembled product will not be defective?
a)0.6485
b)0.6565
c)0.8645
d)none of these
ans=c (0.8645)
probablity of nondefective of x= 91/100=.91
probablity of non defective of y= 95/100=.95
so, probablity of nondefective product=.91*.95=0.8645

45 There are six multiple choice questions in the examination. How many sequences of anwers are possible, if the first two question have 3 choices each, the next two have 4 choice each and last two have 5 choices each?
3c1*3c1*4c1*4c1*5c1*5c1=3600
for any one of first three option of Q.1 we have three options in Q.2 4 option in Q.3…..this goes on…
ind the area (in square units) of the triangle formed by 2x+3y=5, y=x and X-Axis.
the points of intersection for lines:
2x+3y=5 and x=y => 5x=5 => x=1 and y=1 =>(1,1)
x=y and y=0(x-axis) => x=0 and y=0 =>(0,0)
2x+3y=5 and y=0(x-axis) => 2x=5 => x=5/2 and y=0 =>(5/2,0)

area of triangle with vertices (x1,y1),(x2,y2),(x3,y3) is
|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|/2
=|1(0-0)+0(0-1)+5/2(1-0)|/2
=|1+5/2|/2
=7/4 sq units…

46 Arun was all bent on building a new house. He carefully got the blue print of his house designed buy his friend Ashwin, a civil engineer. He wanted to build a room of dimension 27 by 48 ft and lay tiles in this room. Each tile was of dimension 2 by 3 ft. How many tiles should Arun buy?
27*48/2*3=216

47 Roy is now 4 year older than Erik and half of that amount than Lewis.If in two years Roy will be twice as old as Erick,then in two year what would be Roy age multiplied by Lewis age??
ans is 48 firstly two equation from 1st sentence ..
suppose roy=x, erik=y, lewis=z
so x=y+4….(1)
2nd is x=z+2…(2) (Roy is now 4 year older than Erik and half of that amount than Lewis so 4/2=2)
also after 2 years erik and roy relation wil b
x+2=2(y+2).. (3)
so put this into 1st equ. u will get y=2..
and then x=6,z=4(by substituting other)
nw asking multiplication after two years of roy n lewis is (6+2)*(4+2)=48..
if there are maximum acute angles then how many convex hectagons are there there can be max 3 acute angles in a convex polygon which is a triangle.

48 The number of bacteria was growing in a city exponentially.at 4 pm yesterday , the number of bacteria was 400 and at 6 pm yesterday it was 3600.How many bacteria were there at 7pm yesterday?
The number of bacteria was growing in a city exponentially.at 4 pm yesterday , the number of bacteria was 400 and at 6 pm yesterday it was 3600.How many bacteria were there at 7pm yesterday?

.49 There are 12 children in a family .the youngest 1 is a boy.then find the probabality of finding boy in the family.
a)4096
b)2048
c)2
d)2!
Probability cannot be more than 1..it ranges from 0 to 1..
there can be two options..either a boy/girl in a family
asked is to find a boy=1/2
given 12 children but it is already mentioned that the youngest is a boy so no need to count that..
hence,1/2*1/2*1/2……(11 times)=1/2048 option b..but the option is wrong..it should be 1/2048

50 A volume of 10936 l is in a conatiner of sphere . how many semispheres of volume 4 l each will be required to transfer all the water into small semispheres?
v10936/4=2734…..is the ans
a volume of A are having in a container of sphere. how many semi hemispheres of B volume each will be required to transfer all the A in to semi hemispheres?
ans is A/B.

51 My name is PREET.But my son accidentally types the by interchanging a pair of letters in my name.What is the probability that despite this interchange, the name remains unchanged? a.5% b.20% c.25% d.12.5%
10%
Selecting any two – 5C2 = 10[ treating E AND E as distinct)
Selecting EE = 1
1/10 * 100 = 10%

TCS 2013 placement new pattern questions 02

1 Four friends namely Rahul, Ravi, Rajesh and Rohan contested for a dairy milk chocolate. To decide which friend will get the chocolate they decided to throw two dice. Every friend was asked to choose a number and if the sum of the numbers on two dice equals that number, the concerned person will get the chocolate. Rahul’s choice was7, Ravi’s choice was 9, Rajesh’s choice was 10 and Rohan’s choice was 11. Who has the maximum probability of winning the amount.

a) Rahul b) Ravi c) Rajesh d) Rohan
Rahul has chosen 7, similarly Ravi-9,Rajesh-10,Rohan-11
(1,1)(1,2)(1,3)(1,4)(1,5)(1,6) Sum of the digits are= 2,3,4,5,6,7
(2,1)(2,2)(2,3)(2,4)(2,5)(2,6) Sum of the digits are= 3,4,5,6,7,8
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)Sum of the digits are= 4,5,6,7,8,9
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)Sum of the digits are= 5,6,7,8,9,10
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)Sum of the digits are= 6,7,8,9,10,11
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)Sum of the digits are= 7,8,9,10,11,12

Among these 7 comes 6 times, 9 comes 4times, 10 comes 3times,11 comes only 2 times.
So the maximum probability goes to Rahul

2 Messrs. Siva Constructions, leading agents in Chennai prepared models of their lands in the shape of a rectangle and triangle. They made models having same area. The length and width of rectangle model are 24 inches and 8 inches respectively. The base of the triangle model is 16 inches. What is the altitude of triangle model from the base to the top?

a) 24 inches b) 8 inches c) 20 inches d) 32 inches
Area of a rectangle= Area of the Triangle
So, l*b=1/2(b*h)
24*8=1/2(16*8)
therefore 24inches will be the answer

3 There is a 12*6 grid..grid contains 1*1 squares..what is d total number of squares..(consider 1*1,2*2,3*3,4*4,5*5,6*6 size squares as well).Lady has 25 blues, 7 red,9 yellow gloves and hats.how many gloves of same colour.
(max + min + 2) = 25 + 9 +2=36
1!+2!+…..=50!=?
3.10350532 Ã— 10^64
Anita make cube with dimension 5*5*5 using 1*1*1 cubes.find no. Of cubes to make it hollow of same shape.
To make the 5*5*5 hollow, the inner cubic part must be removed. This would constitute one cube each from front,back,top,bottom,left and right ! Since the 5*5*5 is made up of 1*1*1 cubes, 3*3*3 cubes (i.e. 5-2*5-2*5-2) would have to be removed to make it hollow with the shape retained. 27 cubes would be removed, remaining 125-27=98.
1) if 3y + x > 2 and x + 2y
let 3y+x=2
y+2y+x=2
2y+x=2-y(ans)
3y > 2 -x
2y > 4/3 – 2x/3
x+2y > 4/3 + x/3
x + 2y > 1/3(4 + x)

4 Tim and Elan are 90 km from each other, they start to move each other simultaneously, Tim at speed 10 and Elan 5kmph, if every hour they double their speed what is the distance that Tim will pass until he meet Elan?
Tim and Elan will cover the distance in ratio of 2: 1 in same time.
so out of 90 kms, Tim will travel 60 kms and Elan will travel 30 mtrs.
he length and breadth of a field is 300x400ft,if there are 3 ants on average per square inch of field,find the approximate number of ants in field
as 300 ft=3600 inch and 400 ft=4800 inch.then area in sqr inch=17280000
1 sqr inch need 3 ant hence 17280000 sqr inch need 3*17280000 ants.
.diagonal of a square is double the side of an equilateral triangle find the ratio of area of triangle to area of square
let sides of equilateral triangle be ‘a’, therefore area= √3/4 * a^2

now, diagonal of square is 2a therefore sides of square will be √2*a
and area of square = 2 a^2

hence, ratio = (√3/4* a^2)/(2* a^2)

5 Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, .i.e the point lies on one side of the line while the others lie on the other side.
The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position(.i.e no three points in P lie on a line) is
a)3 b)5 c) 2 d)1

The meaning of this question is little complicated. In easy language the question should be:

6 There are some points in the plane. We have to make a separation between these points by forming a line in such a way that one point could be separate from the others. No 3 points are in a line. Maximum no of methods for plotting the line and minimum no of methods for plotting the line will be (arrangement of points is your choice)

For Maximize: The number of methods, Points should be drawn in the circumference of the CIRCLE So answer would be the number of total point in the plane.

For minimize: The number of methods we should draw 3 points in a TRIANGLE and all other point inside this triangle in such a way that no 3 points could be in a line.

If it will be allowed to draw the points in a line then minimum possibilities will be 2 only, because if we take all points in a line then you can separate only the corner points from the others.

For example
If we have 10 points then maximum possibilities = 10
and minimum = 3

similarly for 5 points
Max = 5, Min = 3

for 19
max= 19 Min = 3
f(x)=f(f(x))=f(x^2)….how many such functions with degree >2 exist
does not exist….
In a sequence of integers, A(n)=A(n-1)-A(n-2),where A(n) is the nth term in the sequence, n is an integer and n>=3, A(1)=1,A(2)=1. Calculate S(1000), where S(1000) is the sum of first 1000 terms.
check it now
A(1)=1,A(2)=1.
A(3)=A(2)-A(1) acc to the given formula A(n)=A(n-1)-A(n-2)
A(3)=1-1=0.
similarliy,A(4)=A(3)-A(2)=0-1=-1.
A(5)=A(4)-A(3)=-1-0=-1.
A(6)=A(5)-A(4)=-1-(-1)=0.
after 6th term seq is repeating like…1,1,0,-1,-1,0…after every 6 terms
so the sum of these 6 terms are 1+1+0+(-1)+(-1)+0=0.
now we have to find sum of 1000 terms…
sum of first 600 terms is 0…(as consider 1,1,0,-1,-1,0 as one sequence,now consider 166 seq i.e 166*6=996 terms)
so the sum of first 996 terms is 0…after that 4 terms come i.e 1,1,0,-1
so the sum of last 4 terms = 1+1+0+(-1)=1.

7 planet four firesides in 4-dimensional space and thus the currency used by it’s residentds are 3-dimensional objects. the rupee notes are cubical in shape while their conis are spherical. however the coni minting machinery lays out some stipulations on the size of the coins. the diameter of the conins should be at least 64 mm and not exceed 512 mm. given a conin the diameter of the next larger coin is at least 50% greater . the diameter of the coin must allways be an integer you are asked to disign a set of coins of different diameters with these requirements and your goal is to desing as many coins as possible. how many coins can you desing
1st coin=64cm
2nd “=64+32(50% of 64)=96cm
similarly 3rd=96+48=144
4th=144+72=216
5th=216+108=324
6th=324+112=436
7th not possible
ans is 6

8 There are 3 boys A, B, C and 2 Girls D, E. E always sit right to A. Girls never sit in extreme positions and in the middle position. C always sits in the extreme positions. Who is sitting immediate right to E?
ns is either B or C
POSSIBLE WAYS TO SIT
1) B/C D A E C/B
2) A E B D C

9 What is reminder when 6^17+17^6 is devided by 7?
(7-1)^17 + (7*2+3)^6
binomial theorem
-1+3^6=728
728%7=0
(40*40* 40-31*31*31)/(40*40+40*31+31*31)=?a simle calcutation
(a^3-b^3)/(a^2+ab+b^2)
a-b
40-31=9

10 In base 7,a number is written only using the digits 0,1,….6.the number 135 in base 7 is 1×7^2+3×7+5=75 in base 10.what is the sum of the same of the base 7 numbers 1234 and 6543 in base 7?
11110
1234
6543
——-
11110 which is 7^4+7^3+7^2+7= 2401+343 +49+7= 2800

11 There are 20 balls which are red,blue or green,If 7 balls are green and the sum of red balls and green balls is less than 13,atmost how many red balls are there
5, atmost there can be 5 red balls so that sum of green and red can be less than 13 (7+5=12)
3y+x>2 and x+2y-1
y
the ans is y>1.
explanation:
x+2y-1=0
so x+2y=1
now 3y+x>2 given
we can write in this way x+2y+y>2
then putting x+2y=1 we get 1+y>2 =>y>2-1=>y>1

12 Find the no of zeros in the product of 1^1*2^2*3^3*…..*49^49??
total zeros at the end of product 5^5 x 10^10 x 15^15 x 20^20 x 25^25 x 30^30 x 35^35 x 40^40 x 45^45 will be 5+10+15+20+50+30+35+40+45 = 250 zeros

13 n! has 13 zeros than wat is the higest and lowest value of n??
Here we have to consider only the 5,10,15,20…. these terms..
so form (5,10,15,20,30,35,40,45,55 ) we got 1 no of zero from each.
Now from 25(5*5) and 50(5*5*2) we got 2 no of zeroes form each.
so upto 55 factorial we get (9+4)= 13 zeroes.
so 55! is the smallest value and 59! is the largest value.

The sequence {A(n)} is defined by A(1)=2 and A(n+1)=A(n)+2n. What is the value of A(100).
The sequence {A(n)} is defined by A(1)=2 and A(n+1)=A(n)+2n.
The value of A(100)=A(99+1)=A(99)+2*99
=A(98)+2*98+2*99
=A(97)+2*97+2*98+2*99

A(100)=A(1)+2*1+2*2+2*3+……+2*98+2*99
= 2+(2*1+2*2+2*3+……+2*98+2*99)
= 2+2(1+2+3+…..+98+99)
= 2+2(sum of the first 99 natural numbers)
= 2+2(99*100/2) [sum of the first n natural numbers={n*(n+1)/2}]
= 2+9900
= 9902
14 A,B COMMON TO ALL THREE. THEN ATLEAST 1 ELEMNT COMMON TO 2 IE X1,X2,X2,X3,X3,X1. FINDMINIMUM ELEMENTS IN EACH GROUP. ANSWER IS 4.

15 Directions for Q. 1 to Q. 5: Refer the data:
J, K, L, M and N collected stamps. They collected a total of 100 stamps. None of them collected less than 10.
No two among them collected the same number.
(i) 3 collected the same number as K and M together.
(ii) L collected 3 more than the cube of an integer
(iii) The no. collected by J was the square of an integer.
(iv) Total no. collected by K was either the square or cube of an integer.

1. The no. collected by J was:
(1) 27 (2) 49 (3) 36 (4) 64

2. The no. collected by K was:
(1) 16 (2) 27 (3) 25 (4) 36

3. The difference of numbers collected by L & M was:
(1) 3 (2) 2 (3) 5 (4) 9

in the question the number collected by J should be cube of the integer and l should collect 3 more than square of integer.
J+L+N=K+M
so the sum of J+L+N=K+M=50
l=3^2+3=12
so J=3^3=27
n=50-27-12=11
now k is either square or cube so possibilty are 36 or 16.and m=14 or 34
so j=27
now value for k can come after solving question 3
m-l=14-12=2 or 34-12=22
so there is 2 in option so value of m is 14 and k=36.

16 Bhanu spends 30% of his income on petrol on scooter. ? of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol then what is the expenditure on house rent?

let the income x,so in petrol he spends 3x/10 rs,remaining x-3x/10=7x/10 on house rent and balance on.now 3x/10=300,so x=1000,on house rent he spends rs 700-balane..
Let exp(m,n) = m to the power n. If exp(10, m) = n exp(2, 2) where to and n are integers then n = exp(m,n) = m to the power n= m^n

exp(10, m) = n exp(2, 2) = n*2^2 = 4*n
10^m =4*n
when m=2,
n=25
so min integer values of m and n are 2 and 25 respectively.
A Grocer bought 24 kg coffee beans at price X per kg. After a while one third of stock got spoiled so he sold the rest for \$200 per kg and made a total profit of twice the cost. What must be the price of X?
A. \$33 1/3 B. 66 2/3 C.44 4/9 D.50 1/3
ns: C. 44 4/9

cost price= 24*X \$,
spoiled= 24*1/3=8 kg, now total amount= (24-8)=16 kg
selling price= 16*200\$ =3200\$
profit= (3200-24*X)
profit=2* cost , (3200-24*X)= 2*24*X, x=44 4/9

17 The age of two people is in the ratio 6:8. the sum of their ages is 77. after 2 years the ratio of their ages becomes 5:7. wat is their present age?
The ratio of two people be 6x and 8x
sum of their ages is 6x+8y=77
after 2 yrs,ratio is 5:7,so,
(6x+2)/(8x+2)=5/7
on cross multiplying this,
x=2
hence age of a person 6(2)=12

hence another person ages is 8(2)=16

MOTHER +DAUGHTER+INFANT AGE IS 74. MOTHER AGE IS 46 MORE THEN DAUGHTER AND INFANT.
AND INFANT AGE IS 0.4 OF DAUGHTER. FIND DAUGHTERS AGE.
M+D+I = 74 ..,.,.Equ..1

I=0.4D
M=D+0.4D+46

M=1.4D+46
put in equ 1
1.4D+46+D+0.4D=74 as I=0.4D
2.8D=74-46
D=28/2.8
D=10.,.,.
,
16 Mr and mrs smith had invited 9 of their friend and their spouses for party at wiki beachresort.the stand for group photograph if mr smith never stand next to mrs smith then how many way group arrange in row(A)20!(B)19!+18!(C)18*19!(D)2*19!
simplest… ans is 18*19!
method ..: mr and mrs smith never b together so out of 20(with both them) 19 can b any place so total = 19!
also 1 of them can stand with other so 18 places /..
so total is 18*19!..
19!*18bcoz along with mr and mrs smith can be arranged in 19!*2 (2 bcoz of mr and mrs smith arrangement) all together can be arranged in 20! ways so no mr and mrs smith can be arranged in 20!-19!*2 =19!*18
Is this solution Helpfull? Yes (8) | No (2) viresh (4 Day ago)
20!-(19!*2)
total possibility minus they will be together
A father purchases dress for his three daughter. The dresses are of same color but of different size .the dress is kept in dark room .What is the probability that all the three will not choose their own dress…
a dosesnot choose his dress 2/3
b dosesnot choose his dress 1/2
c dosesnot choose his dress 1 total 1/3

17 Leena cuts small cubes of 3 cubic cm each.She joined it to make a cuboid of length 10 cm,width 3cm, and depth 3 cm.How many more cubes does she need to make a perfect cube?
a)910 b)250 c)750 d)650
ns is a)910. To make cube we need 10*10*10=1000. now we have only 10*3*3=90.so the more cube we need are 1000-90=910.

18 Q:- A boy wants to make cuboids of dimension 5m,6m & 7m from small cubes of .03m^3.Later he realized that he can make some cuboids by making it hollow.Then it takes some cubes less.What is the number of cubes to be removed
a)2000 b)5000 c)3000 d)7000
Volume of the cuboid= 5*6*7
No of cubes needed = (5*6*7)/0.03 = 7000
Volume of hollow cube= (5-2)(6-2)(7-2)
No of cubes needed = (5-2)(6-2)(7-2)/0.03 = (3*4*5)/0.03= 2000
So, number of cubes to be removed = 7000 – 2000 = 5000

19 An empty tankbe filled with aninlet pipe ‘A’ in 42 minutes. after 12 minutes an outlet pipe ‘B’ is opened which can empty the tank in 30 minutes. After 6 minutes another inlet pipe ‘C’ opened into the same tank, which can fill the tank in 35 minutes and the tank is filled find the time taken to fill the tank?
he milk and water in two vessels A and B are in the ratio 4 : 3 and 2: 3 respectively. In what ratio, the liquids in both the vessels be mixed to obtain a new mixture in vessel C containing half milk and half water?
let c.p. of 1liter milk is 1RS.
now milk in 1st mixer is 4/7 and in 2nd mixure is 2/5.
milk in finle mixer is 1/2
now from mixure formula..
4/7 2/5
1/2
1/10 1/14
so ratio is 14/10 =7/5
20 How many kgs. of wheat costing Rs. 8 per kg must be mixed with 86 kg of rice costing Rs. 6.40 per kg so that 20% gain may be obtained by Belling the mixture at Rs. 7.20 per kg ?
Ex. 4. .How many kgs. of wheat costing Rs. 8 per kg must be mixed with 86 kg of rice costing Rs. 6.40 per kg so that 20% gain may be obtained by Belling the mixture at Rs. 7.20 per kg ?

Sol. S.P. of 1 kg mixture = Rs. 7.20,Gain = 20%.
? C.P. of 1 kg mixture = Rs.[(100/120)*7.20]=Rs. 6.
By the rule of alligation, we have:
C_P. of 1 kg wheat of 1st kind C.P. of 1 kg wheat of 2nd kind
(800p) . (540 p)
Mean price
( 600 p)
60 200
Wheat of 1st kind: Wheat of 2nd kind = 60 : 200 = 3 : 10.
Let x kg of wheat of 1st kind be mixed with 36 kg of wheat of 2nd kind.
Then, 3 : 10 = x : 36 or lOx = 3 * 36 or x = 10.8 kg.

21 In what ratio must water be mixed with milk to gain 20 % by selling the mixture at cost price?
let the sp op 1 l mix is =re 1
cp =(100/120)*1=5/6
cp of one let. water =0
so ratio=1-(5/6)/(5/6)-0=1/5
so required ratio =1:5

How much water must be added to 60 litres of milk at 1 Â½ litres for Rs. 2
So as to have a mixture worth Rs.10 2/3 a litre ?
x=(sin nx/n)=?
x=(sin nx/n)
so,
nx=sin nx

sin is one to one function and there is only one case for φ=0 where sinφ=φ
so nx=0
so x=0 (n!=0)
ans will be 0