Aptitude Test 7

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Instruction:

Total number of questions : 20.

Time alloted : 30 minutes.

Each question carry 1 mark, no negative marks.

The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:

1677

1683

2523

3363

Answer: Option B

Explanation:

L.C.M. of 5, 6, 7, 8 = 840.

Required number is of the form 840k + 3

Least value of k for which (840k + 3) is divisible by 9 is k = 2.

Required number = (840 x 2 + 3) = 1683.

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If 144 = 14.4 , then the value of x is:

0.144 x

0.0144

1.44

14.4

144

Answer: Option A

Explanation:

144 = 14.4

0.144 x

144 x 1000 = 14.4

144 x

x = 14.4 = 0.0144

1000

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617 + 6.017 + 0.617 + 6.0017 = ?

6.2963

62.965

629.6357

None of these

Answer: Option C

Explanation:

  617.00
    6.017
    0.617
 +  6.0017
  --------
  629.6357
  ---------

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3 - 1 2 simplifies to:

3

None of these

Answer: Option C

Explanation:

3 - 1 2 = (3)² + 1 2 - 2 x 3 x 1

3 3 3

= 3 + 1 - 2

3

= 1 + 1

3

= 4

3

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The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

23 years

24 years

25 years

None of these

Answer: Option A

Explanation:

Let the average age of the whole team by x years.

11x - (26 + 29) = 9(x -1)

11x - 9x = 46

2x = 46

x = 23.

So, average age of the team is 23 years.

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The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

8, 20, 28

16, 28, 36

20, 35, 45

None of these

Answer: Option B

Explanation:

Let their present ages be 4x, 7x and 9x years respectively.

Then, (4x - 8) + (7x - 8) + (9x - 8) = 56

20x = 80

x = 4.

Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.

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Direction (for Q.No. 7):

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and

Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
Give answer(E) if the data in both Statements I and II together are necessary to answer the question.

Divya is twice as old as Shruti. What is the difference in their ages?
I.
Five years hence, the ratio of their ages would be 9 : 5.
II.
Ten years back, the ratio of their ages was 3 : 1.

I alone sufficient while II alone not sufficient to answer

II alone sufficient while I alone not sufficient to answer

Either I or II alone sufficient to answer

Both I and II are not sufficient to answer

Both I and II are necessary to answer

Answer: Option C

Explanation:

Let Divya's present age be D years and Shruti's present age b S years

Then, D = 2 x S D - 2S = 0 ....(i)

I. D + 5 = 9 ....(ii)

S + 5 5

II. D - 10 = 3 ....(iii)

S - 10 1

From (ii), we get : 5D + 25 = 9S + 45 5D - 9S = 20 ....(iv)

From (iii), we get : D - 10 = 3S - 30 D - 3S = -20 ....(v)

Thus, from (i) and (ii), we get the answer.

Also, from (i) and (iii), we get the answer.

I alone as well as II alone give the answer. Hence, the correct answer is (C).

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(256)^0.16 x (256)^0.09 = ?

256.25

Answer: Option A

Explanation:

(256)^0.16 x (256)^0.09 = (256)^{(0.16 + 0.09)}

= (256)^0.25

= (256)^(25/100)

= (256)^(1/4)

= (4⁴)^(1/4)

= 4^4(1/4)

= 4¹

= 4

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Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?

5 : 7 : 8

20 : 49 : 64

38 : 28 : 21

None of these

Answer: Option B

Explanation:

Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.

Then, 14x : 8y : 7z = 5 : 7 : 8.

Now, 14x = 5 98x = 40y y = 49 x

8y 7 20

And, 14x = 5 112x = 35z z = 112 x = 16 x.

7z 8 35 5

x : y : z = x : 49 x : 16 x = 20 : 49 : 64.

20 5

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10.

A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?

Rs. 7500

Rs. 8000

Rs. 8500

Rs. 9000

Answer: Option D

Explanation:

Let B's capital be Rs. x.

Then, 3500 x 12 = 2

7x 3

14x = 126000

x = 9000.

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Direction (for Q.No. 11):

Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
Give answer(E) if the data in both Statements I and II together are necessary to answer the question.

11.

Ravi, Gagan and Nitin are running a business firm in partnership. What is Gagan's share in the profit earned by them?
I.
Ravi, Gagan and Nitin invested the amounts in the ratio of 2 : 4 : 7.
II.
Nitin's share in the profit is Rs. 8750.

I alone sufficient while II alone not sufficient to answer

II alone sufficient while I alone not sufficient to answer

Either I or II alone sufficient to answer

Both I and II are not sufficient to answer

Both I and II are necessary to answer

Answer: Option E

Explanation:

Let us name Ravi, Gagan and Nitin by R, G and N respectively.

I. R : G : N = 2 : 4 : 7.

II. N = 8750..

From I and II, we get:

When N = 7, then G = 4.

When N = 8750, then G = 4 x 8750 = 5000.

7

Thus, both I and II are needed to get the answer.

Correct answer is (E).

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12.

A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:

Answer: Option B

Explanation:

Let the required number of revolutions made by larger wheel be x.

Then, More cogs, Less revolutions (Indirect Proportion)

14 : 6 :: 21 : x 14 x x = 6 x 21

x = 6 x 21

14

x = 9.

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13.

10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

Cannot be determined

None of these

Answer: Option C

Explanation:

1 woman's 1 day's work = 1

70

1 child's 1 day's work = 1

140

(5 women + 10 children)'s day's work = 5 + 10 = 1 + 1 = 1

70 140 14 14 7

5 women and 10 children will complete the work in 7 days.

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14.

Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:

60 gallons

100 gallons

120 gallons

180 gallons

Answer: Option C

Explanation:

Work done by the waste pipe in 1 minute = 1 - 1 + 1

15 20 24

= 1 - 11

15 120

= - 1 . [-ve sign means emptying]

40

Volume of 1 part = 3 gallons.

40

Volume of whole = (3 x 40) gallons = 120 gallons.

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15.

A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?

65 sec

89 sec

100 sec

150 sec

Answer: Option B

Explanation:

Speed = 240 m/sec = 10 m/sec.

24

Required time = 240 + 650 sec = 89 sec.

10

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16.

A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?

3.6 sec

18 sec

36 sec

72 sec

Answer: Option C

Explanation:

Speed of train relative to jogger = (45 - 9) km/hr = 36 km/hr.

= 36 x 5 m/sec

18

= 10 m/sec.

Distance to be covered = (240 + 120) m = 360 m.

Time taken =		360	sec	= 36 sec.
		10

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17.

Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

12 sec

24 sec

48 sec

60 sec

Answer: Option B

Explanation:

Relative speed = = (45 + 30) km/hr

= 75 x 5 m/sec

18

= 125 m/sec.

6

We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.

So, distance covered = Length of the slower train.

Therefore, Distance covered = 500 m.

Therefore Required time = 500 x 6 = 24 sec.

125

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18.

A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?

40 minutes

1 hour

1 hr 15 min

1 hr 30 min

Answer: Option C

Explanation:

Rate downstream = 1 x 60 km/hr = 6 km/hr.

10

Rate upstream = 2 km/hr.

Speed in still water = 1 (6 + 2) km/hr = 4 km/hr.

2

Required time = 5 hrs = 1 1 hrs = 1 hr 15 min.

4 4

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19.

8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 81. How much wine did the cask hold originally?

18 litres

24 litres

32 litres

42 litres

Answer: Option B

Explanation:

Let the quantity of the wine in the cask originally be x litres.

Then, quantity of wine left in cask after 4 operations = x 1 - 8 4 litres.

x

x(1 - (8/x))⁴ = 16

x 81

1 - 8 4 = 2 4

x 3

x - 8 = 2

x 3

3x - 24 = 2x

x = 24.

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20.

A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

Answer: Option A

Explanation:

Total number of balls = (2 + 3 + 2) = 7.

Let S be the sample space.

Then, n(S) = Number of ways of drawing 2 balls out of 7

= ⁷C₂ `

= (7 x 6)

(2 x 1)

= 21.

Let E = Event of drawing 2 balls, none of which is blue.

n(E) = Number of ways of drawing 2 balls out of (2 + 3) balls.

= ⁵C₂

= (5 x 4)

(2 x 1)

= 10.

P(E) = n(E) = 10 .

n(S) 21

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