TATCS5 Detailed Solutions

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01 Ans:[a]

Let the C.P of the 1st

car be x and 2nd

be y.

x + y = 150,000

1.2 x = 0.8 y, or y = 1.5x. Substituting,

2.5x = 150,000, or x = 60,000

02 Ans:[a]

Number 7 occurs more often (1, 6), (2, 5), (3, 4), (4, 2) (5, 2), (6, 1)6 times. Whereas number 9 occurs

4 times (3, 6) (4, 5) (5, 4), (6, 3), number 10 occurs 3 times (4, 6), (5, 5), (6, 4) and number 11 occurs 2

times (5, 6), (6, 5). So the most probable friend to win the chocolate is Rahul

03 Ans:[c]

J+L+N=K+M

L can take only one value which is 11 (2^3+3) (30 is not possible because only there is only 20 for the

remaining two and one of them will have less than 10 and that is not possible)

J also can take only one value which is 27.

J + L + N = 50.

Therefore, N = 50 L J = 50 11 27 = 12.
04 Ans:[c]

n(a b) =n(a)+n(b)-n(a b)

= 0.75+0.55-0.8

= 0.5 = 50%

Alternatively, this problem can be solved using the Venn diagram method.

05 Ans:[c]

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

06 Ans:[c]

When the tank is placed on its side, it would still be half filled and the height of the water would equal

half the diameter, which is radius.

* r2 * 4 = 36 , therefore r = 3.

07 Ans:[b]

30/1 = s/t

s+50/t+5 = 25/1

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

5t = 75, t = 15

TATCS5 Detailed Solutions

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08 Ans:[c]

Applying Fermats little theorem,

617

/7

/7 * rem of 66

/7 * rem of 62

/7 * rem of 62

/7 * rem of 6/7

= 1 * 1 * 1 * 1 * 6 = remainder is 6.

1176

/7

Adding both remainders and dividing by 7, leads to a remainder of zero.

09 Ans:[b]

Tims speed is always going to be twice that of Elan. So the distances traveled will be ratio 2:1.
Therefore,
distance covered by Tim is 60 km.

10 Ans:[b]

v = 2 m/min

Initially, x = v * t

When the speed increases by 1 km/hr,

x = (2+1) * (t 2/3)

The information in both statements together is sufficient to find the total distance passed by turtle.

11 Ans:[b]

If P(0) is 48, then P(5) too has to be 48, as x has roots at 1, 2, 3 and 4.

12 Ans:[c]

If the increase is 10% and the decrease is 10%, then the final price will go down by 1%. One can apply
the

formula for successive increase/decrease here.

13 Ans:[a]

The first thing is x is a negative number. And to satisfy the condition x

< 1/100, x should lie in the range

1/10 < x < 0.

14 Ans:[b]

At least one of them to choose correct dresses: A B C, A C B, C B A, B A C

For none of them to choose correct dresses: B C A, C A B

Probability is 2/6 = 1/3

15 Ans:[a]

If h is the height of triangle model, then 24*8 = 16*h/2 h= 24 inches

16 Ans:[c]

13C1*2C1*2C1/52C3 = 0.00235

17

Ans:[b]

Let the speed of the motorboat in still water be v, then

Solving for v, we get v = 22 km/h.

TATCS5 Detailed Solutions

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18 Ans:[b]

Problems like this can be solved using the allegation method,

 4/7 2/5

1/2

1/10 1/14

14 : 10

7 : 5

19

Ans:[c]

20 Ans:[d]

Out of 4 boxes 2 can be picked in

C2 ways, i.e, 6 ways. Out of these 6 ways, only one will have yellow-
blue combination. All other remaining combinations will have green or red or both. The answer is 5.

21 Ans:[c]

There are 20 people in total and they can be arranged in 20! Ways. Now we have to subtract out the

number of ways where Mr and Mrs Smith are together.

They can arrange themselves together in 19 places (1,2) (2,3) (3,4).(19,20). Since the husband and wife

can interchange their places, there are 38 different ways they can be together.

In these 38 different ways, the remaining 18 people can arrange in 18! Ways. So there are 38(18!) ways

the Mr and Mrs Smith can be together. We need to subtract out this from 20!

20! 38(18!) = 20! 2(19!) = 18*19! ways.

22 Ans:[c]

You can have registration plates of 5,4,3,2 or 1 digits

So, it's 5*4*3*2*1 + 5*4*3*2 + 5*4*3 +5*4 + 5

=120 + 120 + 60 + 20 +5

=> 325

23 Ans:[a]

Total CP = 20 * 30 + 40*25= 1600

SP = 125/100 * 1600= 2000

SP for 20 kg mix = 26*20 =520

Rem SP = 2000-520 = 1480

The SP for 40 kg = 1480/40 = Rs37

 TATCS5 Detailed Solutions

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24 Ans:[a]

Assume C takes 20 Days. Now B takes 4/5 (20) = 16 days. A takes 3/4(16) = 12

Now their efficiencies ratio = 1/20 : 1/16 : 1/12 = 12 : 15 : 20

B's share in the profit of Rs.40000 = 15/47 (40000) = Rs.12765

25 Ans:[a]

Ratio = sqrt3*a^2/8a^2....i.e., 3/8.

26 Ans:[a]

Using 5 letters one can form 10 combinations and the only way that the name remains unchanged is

when both Es are getting interchanged. That is one of 10, which is 10%.

27 Ans:[d]

If Thursdays and Sundays occur 4 times, then the days between them Friday and Saturday also will

occur 4 times. The remaining days Mon, Tue and Wed will occur 5 times. Hence the month starts on

Monday.

28 Ans:[c]

1 ft = 12 inch. Therefore, the dimensions are 3600 * 4800 = 17280000 sq. inches.
3 ants per inch means, 17280000*3 = 51840000.

Alternative way: Since we multiply by 3, 51840000 is the only option divisible by 3.

29 Ans:[d]

5! is 120 and all numbers from 5! to 50! are divisible by 5!. We have to check for the first 4 numbers i.e,

from 1! to 4!. The addition is 1+2+6+24 = 33. Therefore, the remainder is 33.

30 Ans:[d]

The five subjects can be done in 5! ways. The remaining 1 period can be any of the 5 subjects and it can

come in at any of the 6 different periods. So 5 * 6 = 30 ways.

The total ways is 5! * 30 = 3600 ways.