** Company: ** TCS

Aptitude Test-1

1A work has to be completed by 12 persons in 15 days. If three persons are absent from first day itself, then by what percentage should the remaining people increase their rate of working in order to complete the work in time?

a. 33 1/3 %

b. b. 33%

c. c. 30%

d. d. None of these

Using variation concept, we have

M1D1R1=M2D2R2

W1 W2

12*15*R1=9*15*R2

R2= 4R1/3

Percentage increase in rate (R1/3)*100= 33 1/3 %

R1

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2. There is one wooden cylinder of height 7cm and radius 3cm. Find the volume of the biggest possible combination of a solid hemisphere and a solid cone which can be made from it?

a. 12cm3

b. 18cm3

c. 30 cm3

d. 21 cm3

The common radius of the biggest combination of cone and hemisphere= 3cm

The height of the cone=Height of the cylinder-Radius of the hemisphere= 7-3=4cm

Volume of the combination= Volume of the cone+Volume of the hemisphere

Volume of the cone= 1/3r2h= 1/3*3*3*4=12cm3

Volume of the hemisphere= 2/3r3= 2/3*3*3*3= 18cm3

Volume of the combination= 12+18= 30 cm3

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3. Consider the statement and decide which of the given assumptions is implicit

Statement: “You must learn to refer to dictionary if you want to become a good writer”-A advises B

Assumptions: I. Only writers refer to the dictionary

II. All writers good or bad refer to the dictionary

a. Assumption I is implicit

b. Assumption II is implicit

c. Either assumptions I or II is implicit

d. Neither assumptions I nor II is implicit

It does not follow from the statement that only writers and nobody else refers to the dictionary.

Also, nothing is mentioned about bad writers. So, both the assumptions I and II are not implicit.

Hence, the answer is (d)

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4. If N chocolates are divided among 6 boys, each gets an equal number of chocolates. Find N, if it is a perfect cube and is divisible by the first three perfect squares?

a. 216

b. b. 36

c. c. 64

d. d. None of these

N is a multiple of 6 and divisible by the first three perfect squares, ie. 1,4 and 9.

Least possible number must be a multiple of 36 and a perfect cube.

So 36*6= (6)3 is the answer.

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5. There are 56 rooms in the ground floor of a 12 storied building. The number of rooms in each floor is 2 more than the floor just below. How many rooms are there in the building?

a. 800

b. b. 804

c. c. 672

d. d. None of these

56,58,60…

These are in AP. First term, a= 56

Common difference, d= 2

Number of terms, n= 12

Total rooms= n/2 [2a+(n-1)d]= 12/2[2*56+(12-1)2]=804

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6. There are some monkeys on two trees T1 and T2. If two monkeys jump from T1 to T2 the number of monkeys on each tree will be equal. If two monkeys jump from T2 to T1, number of monkeys on T1 would be double the number of monkeys on T2. Find the initial number of monkeys on T1 and T2 respectively.

a. 10 and 13

b. 14 and 10

c. 10 on both

d. None of these

Let the initial number of monkeys on T1 be x and the number of monkeys on T2 be y.

x-2=y+2

x-y=4……….(1)

Further x+2=2(y-2)

x=2y-6………(2)

By solving (1) and (2) we get

x=14 and y=10.

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7. A sheet of paper has statements numbered from 1 to 40. For all values of n from 1 to 40, statement n says: ‘Exactly n of the statements on this sheet are false.’ Which statements are true and which are false?

a. All the statements are false

b. The 39th statement is true and the rest are false

c. The odd numbered statements are true and the even numbered statements are false

d. The even numbered statements are true and the odd numbered statements are false

Explanation: 3rd and 4th option does not satisfy the given condition and all the

statement cannot be false. So, option The 39th statement is true and the rest are false is answer

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8. A man standing at a point A can take one step to the right with a probability of 1/3 and one step to the left with a probability of 2/3. The process continues in the same manner after each step. What is the probability that he is at point A after 23 steps?

a. 1/323

b. 1/311.1/212

c. 23C11 (1/323)

d. None of these

Answer: Choice (4). He can never be at the starting point after an odd number of steps.

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9. On planet Zoisa, where d represents the diameter in mm and t the number of years since the solar blast. The blast occurred 24 years back. Narayan recorded the radius of some Jinosha at a particular spot. What would be the radius of Jinosha, after Narayan’s recording?

a. 8

b. 16

c. 12

d. 24

Explanation: d = 4 * sqrt(t-8)

t=24

thus d = 4 * sqrt(24-8)

d = 4*sqrt (16)

d=4*4= 16

Therefore, radius= 16/2=8mm

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10) Amit throws a biased coin on which the head appears in 65% of the situations. In a game involving this coin, if Amit is paid Rs.15 per head and he has to pay Rs.20 for a tail, then in the long run, per game Amit makes an average.

a) profit of Rs.2.25

b) loss of Rs.2.25

c) profit of Rs.2.75

d) loss of Rs.2.75

Explanation: Probability of getting a head is 0.65 and tail is 0.35 i.e. P(H) = 0.65, P(T) = 0.35

Expected value = 0.65 x 15 – 0.35 x 20 = 2.75

Hence Amit gains Rs.2.75 per game on an average.

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11) Twelve men can complete 24 units of work in some days. If the volume of work is 100% more and the number of men is 33(1/3)% less, eight more days are required to complete the work. In how many days can fifty percent of the original number of men complete the original work?

a) 8

b) 4

c) 12

d)6

Explanation: Let the number of days that the group of 12 men take to do the work of 24 units be x.

m1d1/w1 = m2d2/w2

12x/24 = 2/3[12(x + 8)] ÷ 48

x = 4 days.

50% of the original number of men will take 8 days to complete the work.

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12) A sheet of paper has statements numbered from 1 to 40. For each value of n from 1 to 40, statement n says “At least n of the statements on this sheet are true.” Which statements are true and which are false?

a)The odd numbered statements are true and the even numbered are false

b)The even numbered statements are true and the odd numbered are false.

c)The first 13 statements are true and the rest are false.

d)The first 26 statements are false and the rest are true.

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13) Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 3 and 5?

a) 1/2

b) 2/5

c) 8/15

d) 9/20

Explanation: Here, S = { 1, 2, 3, 4, ….., 19, 20}.

Let E = event of getting a multiple of 3 = {3, 6, 9, 12, 15, 18, 5, 10, 20}

=P(E) = n(E)/n(S) = 9/20.

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14) In a triangle, the sum of the lengths of two sides is √3 times the length of the third side. Which of the following is a possible combination of the angles of the triangle?

a) 900, 450, 450

b) 900, 600, 300

c) 600, 600, 600

d) None of these

Explanation: The sines of the angles of a triangle are in the same ratio as the ratio of corresponding sides.

=sinA : sinB : sinC = a : b : c

sin900 : sin600: sin300 = 1 : (√3/2) : (1/2)

= 2 : √3 : 1 = a : b : c and (a + c) = √3(b), the required condition is satisfied. Other options can be verified as false using a similar approach.

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15) Which of the following can be a product of two 3-digit numbers **3 and **8?

a) 1010024

b) 991014

c) 9124

d) None

Explanation: When two 3-digit numbers are multiplied, the product must consist of 5 or 6 digits only.

Product cannot contain 4 or 7 digits.

So, the required number can be 991014.

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16) On the planet Lunar eclipse, there are 8 days in a week- Sunday to Saturday and another day called Lunar day. There are 36 hours in a day and each hour has 90 min while each minute has 60 sec. As on earth, the hour hand covers the dial twice every day. Find the approximate angle between the hands of a clock on Lunar eclipse when the time is 12:40 am.

a)111

b)89

c)251

d)71

Explanation: Angle traced by hour hand in 12.40 hrs = (360/18) * ( 112/9) = 2240/9.

Angle traced by minute hand in 40 min = (360/90) * 40 = 160.

Angle between hour hand and minute hand = (2240/9) – 160 = 88.88.

Approximately 89 degrees.

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17) The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the forerunners in the technology front, Tirnop continues to lead the way in products and services in India. At Tirnop, all programmers are equal in every respect. They receive identical salaries ans also write code at the same rate.Suppose 12 such programmers take 12 minutes to write 12 lines of code in total. How many lines of code can be written by 72 programmers in 72 minutes?

a) 12

b) 72

c) 432

d) 6

Explanation:

No of people time work

12 12 12

72 72 x

Work = No of people * time

(12 * 12) /12 = ( 72 * 72 ) / x

i.e. ( P1 * T1 ) / W1 = ( P2 * T2 ) / W2

X = 72 * 72 / 12 = 432.

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18) Vivek managed to draw 7 circles of equal radii with their centres on the diagonal of a square such that the two extreme circles touch two sides of the square and each middle circle touches two circles on either side. Find the ratio of the radius of the circles to the side of the square.

a)1:(2+ 6√2)

b)1:(4+ 7√3)

c)(2+ 7√2):1

d)1:(2+ 7√2)

Explanation: The extreme circles will have radius perpendicular to sides of square so the part of diagonal till the centre of circle will be √(2) * r and remaining portion is r , 5 more circles will contribute 10r and last circle will contribute r + √(2) * r .

Length of diagonal = 12r + 2√(2) r = √(2) * s where s -> side of square.

So, ratio of r:s = 1/( 2 + 6 * √(2)) = 1: [ 2+ 6 √(2)]

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19 A man riding a cycle at 12km/hr can reach a town in 4 hours 30 min. If he is delayed by 1 hour 30min.at the start, then in order to reach his destination in time, he should ride with a speed of:

a)15km/hr

b)16km/hr

c)18km/hr

d)20km/hr

Distance=(speed*Time)=(12*9/2)km=54km

Time left now=3 hours

New speed=(54/3)km/hr=18km/hr

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20 In a triangle ABC, D,E and F, which are the midpoints of the sides AB,BC and CA respectively, are joined. Again, in the DEF,G,H and I,which are the midpoints of the sides DE,EF and FD respectively,are joined. What is the area of GHI if the area of ABC is 192 sq.units (in sq.units)?

a)6

b)48

c)12

d)36

Area of DEF =4*Area of HIG

Area of ABC =4*Area of DEF

192=4* Area of DEF; Area of DEF =192/4=48

Area of DEF =4*Area of HIG; Area of HIG= 48/4=12

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21In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there ?

a)159

b)194

c)205

d)209

We may have (1boy and 3 girls)or(2boys and 2 girls)or(3 boys and 1 girl)or (4 boys)

Required no of ways =(6C1*4C3)+(6c2*4C2)+(6C3*4C1)+(6C4)

=(6C1*4C1)+(6C2*4C2)+(6C3*4C1)+(6C2)

=(6*4)+(6*5/2*1 * 4*3/2*1)+(6*5*4/3*2*1 * 4)+(6*5/2*1)

=(24+90+80+15)=209

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22 Re-arrange and categorize the word IARLGOTLA

a)Mobile Phone

b)animal

c) Vehicle

d)Furniture

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23Two vessels A and B contain milk and water mixed in the ratio 4:3 and 2:3. In what ratio must these mixtures be mixed to form a new mixture containing half milk and half water:

a)7:5

b)1:2

c)2:1

d)6:5

Milk in 1 litre of A=4/7litre, Milk in 1 litre of B=2/5 litre

Milk in ! litre of final mix=1/2litre Let cost of 1 litre of milk be Re1.

C.P of 1 litre of A=Re 4/7 C.P of 1 litre of B =Re 2/5

Mean price=Re1/2

By the rule of allegation

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24There are 12 pipes that are connected to a tank. Some of them are fill pipes and the others are drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipes can drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, an empty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes?

a) 6

b) 8

c) 7

d) 5

Let there be ‘n’ fill pipes attached to the tank.

Therefore, there will be 12 – n drain pipes attached to the tank

Each fill pipe fills the tank in 8 hours. Therefore, each of the fill pipes will fill 1/8 th of the tank in an hour.Hence, n fill pipes will fill n* 1/8 =n/8 of the tank in an hour.Each drain pipe will drain the tank in 6 hours. Therefore, each of the drain pipes will drain 1/6 th of the tank in an hour.

Hence, (12 – n) drain pipes will drain (12-n)*1/6 th of the tank in an hour.When all these 12 pipes are kept open, it takes 24 hours for an empty tank to overflow. Therefore, in an hour 1/24 th of the tank gets filled.Hence, n/8 – 12-n/6=1/24

i.e.3n-4(12-n)/24=1/24 or 7n – 48 = 1 => 7n = 49 or n = 7.

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25 If west is called as North-East,North-East as East, East is called as South-West,South-West is called as North, North is called as North-west,North-West as South and Soouth is called as South-East, then pole star in which direction?

a)North-East

b)North-West

c)North

d)South-West

Ans b)

Since Pole Star is always in North, and in code North is said North-West, Hence Pole Star will be in North_West

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26 A car left Canterbury at 7.12 am and arrived in Birmingham, 180 miles distant at 10.57 am. What was its average speed in miles per hour?

a)42

b)44

c)46

d)48

Time taken = 3 hours 45m = 3.75 hours (15/4 hours if you prefer fractions).

Speed = distance / time taken = 180 / 3.75 = 48 mph

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27 In the following experiment specify appropriate sample space

A person is nothing down the number of accidents along a busy highway during a year

a)S={0,1,2,3….}

b)S={0}

c)S={1,2,3..}

d)None of these

The number of accidents along a busy highway during the year of observation can be either 0(for no accident) or 1 or 2,or some other positive integer. Thus,a sample space associated with this experiment is S= S={0,1,2,3….}

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28 Sharma and his wife appear in an interview for two vacancies in the same post. The probability of Sharma’s selection is (1/7) and the probability of his wife’s selection is (1/5). What is the probability that only one of them is selected ?

a) 4/5

b) 2/7

c) 8/15

d) 4/7

Explanation

Let A = Event that Sharma is selected

Let B = Event that his wife is selected

Then P(A) = 1/7 and P(B) = 1/5

:. P( ‘A’) = (1-1/7) = 6/7 and P (B’) ( 1- 1/5) = 4/5.

Required probability = P [(A and not B) or (B and not A)

= P [(A and B’) or (B and A’)]

= P (A and ‘B’) + P( B and A’)

= P(A).P(B’) + P(B).P(A’ ) = (1/7 *4/5 ) + (1/5 * 6/7) = 10/35

= 2/7

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29. A speaks truth in 75% cases and B in 80% of the class. In what percentage of cases are they likely to contradict each other, narrating the same incident ?

a) 5%

b) 15%

c) 35%

d) 45%

Let A = Event that A speaks the truth

And B = Event that B speaks the truth.

Then, P(A) = 75/100 = ¾, P(B) = 80/100 = 4/5.

P (A’) = (1-3/4) = ¼ and P(B’) = (1-4/5) = 1/5

P( A and B contradict each other)

= P [(A speaks the truth and B tells a lie) or (A tells a lie and B speaks the truth)]

= P [A and B’) or (A’ and B)

= P (A and B’) + P(A’ and B)

= P(A).P(B’) + P(A’).P(B )

= (3 /4 x 1/5 ) +(1/4 x 4/5) = (3/20 + 1/5) = 7/20 = ((7/20) x 100)% = 35%

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30.On an empty tank, an inlet pipe ‘A’ is opened which can fill the tank 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. What is the total time taken to fill the tank ?

a) 66 minutes

b) 60minutes

c)48 minutes

d) none of these

Ans : Option A

Explanation :-

Suppose tank capacity = L.C.M. = 210 ltrs

:. Water flow of A = 210/42= 5ltrs/min.

Water flow of B = 210/30= 7ltrs/min.

Water flow of C = 210/35= 6ltrs/min.

Let X be the time all three are opened together

Hence 12*5 (A alone) + 6*(5-7) (A & B together) + X*(5-7+6)

(all opened together) = 210

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31. Aiswarya and Anaswara started traveling from the point ‘P’ at 8 a.m. in opposite directions at the speed of 3m/s and 4m/s respectively. On the way Anaswara met Albin who was traveling in the opposite direction at the speed of 8m/sec, at 8.15 a.m.. What will be the Angle between minute hand and hour hand when Albin meet Aiswarya.

a)1980

b)2400

c)420

d)240

Answer :- Option C

Explanation :-

After 15 minutes i.e. 8.15 a.m.

Aiswarya traveled = (15*60) *3 =2700m

Anaswara traveled = (15*60) *4 =3600m

Time taken by Albin to meet Aiswarya = d1+d2/[speed of Albin – speed of Aiswarya]

T = 2700 + 3600 /8-3

= 6300/5 = 1260 sec.

= 1260/60 = 21 min.

Meeting time b/w Aiswarya & Albin = 8.15 + 21 = 8.36 a.m.

The angle b/w minute and hour hand = (11/2)m – 30h

= /(11/2)36 – 30*8)/ = /198-240/ = 42 The Angle is 420

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32.From a pack of 52 cards , two cards are drawn together at random. What is the probability of both the cards being Queen.

a) 1/15

b) 25/57

c) 35/256

d) 1/221

Let S be the sample space. Then,

n(S) 52C2 =(52 x 51)/ (2 x 1) = 1326

Let E = event of getting t queens out of 4.

:. n(E) =4C2 = (4 x 3)/ (2 x 1) = 6

:. P(E) = n(E)/ n(S) = 6/1326 = 1/221

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33.In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize ?

a) 1/13

b) 2/5

c) 2/7

d) 5/7

P (getting a prize) = 10/(10 +25) = 10/35 = 2/7

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34. Tom lies on Mondays, Tuesdays and Wednesdays, and tells the truth on the other days of the week. Jerry, on the other hand, lies on Thursdays, Fridays and Saturdays, but tells the truth on the other days of the week. Now they make the following statements to Mikie – Tom: Yesterday was one of those days when I lie. Jerry: Yesterday was one of those days when I lie too. What day is it?

a)Thursday

b)Tuesday

c)Sunday

d)Monday

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35. On a Christmas winter, a hunter leaves his cabin early in the morning and walks one mile due North. Here he sees an owl and starts chasing it for one mile due west before he is able to shoot the owl. After shooting the owl, he picks it one mile due south back to his cabin where he started that morning. What color is the owl?

a)Brown

b)Black

c)Grey

d)White

Explanation: Only white owls lives in poles during winter

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36The average speed of a bus without stoppages is 40 kmph and with stoppages is 26 kmph. How many minutes per hour does the bus stop ?

a) 21minutes

b) 34 minutes

c) 17 minutes

d) 24 minutes

Expla : 40 km can be covered in 60 minutes without stoppages and 26 km can be covered in 60 minutes with stoppages.i.e. difference 14 km can’t be covered due to stoppages.

:. 40 km takes 60 minutes implies

14 km takes (14/40) x 60 = 21 minutes

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