Aptitude Test 8

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Instruction:

Total number of questions : 20.

Time alloted : 30 minutes.

Each question carry 1 mark, no negative marks.

One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?

Rs. 30,000

Rs. 50,000

Rs. 60,000

Rs. 90,000

Answer: Option C

Explanation:

Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 - x) respectively. Then,

1 x = 1 (150000 - x)

3 2

x + x = 75000

3 2

5x = 75000

6

x = 75000 x 6 = 90000

5

Savings in Public Provident Fund = Rs. (150000 - 90000) = Rs. 60000

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1.5625 = ?

1.05

1.25

1.45

1.55

Answer: Option B

Explanation:

   1|1.5625( 1.25
    |1
    |-------
  22| 56
    | 44
    |-------
 245| 1225
    | 1225
    |-------
    |    X
    |-------

1.5625 = 1.25.

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The square root of 64009 is:

253

347

363

803

Answer: Option A

Explanation:

   2|64009( 253
    |4
    |----------
  45|240
    |225
    |----------
 503|  1509
    |  1509
    |----------
    |     X
    |----------

64009 = 253.

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Direction (for Q.No. 4):

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.

What is the average age of children in the class?
I.	The age of the teacher is as many years as the number of children.
II.	Average age is increased by 1 year if the teacher's age is also included.

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 D

Explanation:

Let there be x children.

I gives, age of teacher = x years.

II gives, average age of (x + 1) persons = (x + 1) years.

Teacher's age = (x + 1) (x + 1) - x² = (x² + 1 + 2x) - x² = (1 + 2x)

Thus, teacher's age cannot be obtained.

Correct answer is (D)

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The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?

Cannot be determined

None of these

Answer: Option D

Explanation:

Let the ten's digit be x and unit's digit be y.

Then, x + y = 15 and x - y = 3 or y - x = 3.

Solving x + y = 15 and x - y = 3, we get: x = 9, y = 6.

Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9.

So, the number is either 96 or 69.

Hence, the number cannot be determined.

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Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.

Answer: Option A

Explanation:

Let the number be x.

Then, x + 17 = 60

x

x² + 17x - 60 = 0

(x + 20)(x - 3) = 0

x = 3.

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Direction (for Q.No. 7):

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.

What is the two-digit number whose first digit is a and the second digit is b?. The number is greater than 9.
I.	The number is multiple of 51.
II.	The sum of the digits a and b is 6.

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 A

Explanation:

From statement I:

A two digit number, greater than 9 and multiple of 51 should be 51 itself.

Because, 2 x 51 = 102 (3 digit number). Therefore, I alone sufficient to answer.

From statement II:

A two digit number, greater than 9 and sum of the digit is 6.

It can be 15, 24, 33, 42, 51. So we cannot determine the required answer from the statement II alone.

Thus, I alone give the answer while II alone not sufficient to answer.

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Direction (for Q.No. 8):

Each of these questions is followed by three statements. You have to study the question and all the three statements given to decide whether any information provided in the statement(s) is redundant and can be dispensed with while answering the given question.

What will be the ratio between ages of Sam and Albert after 5 years?
I.	Sam's present age is more than Albert's present age by 4 years.
II.	Albert's present age is 20 years.
III.	The ratio of Albert's present age to Sam's present age is 5 : 6.

Any two of I, II and III

II only

III only

I or III only

II or III only

Answer: Option A

Explanation:

Clearly, any two of the given statements will give the answer and in each case, the third is redundant.

Correct answer is (A).

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In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is of the number of students of 8 years age which is 48. What is the total number of students in the school?

120

150

100

Answer: Option E

Explanation:

Let the number of students be x. Then,

Number of students above 8 years of age = (100 - 20)% of x = 80% of x.

80% of x = 48 + 2 of 48

3

80 x = 80

100

x = 100.

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10.

When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?

Rs. 21,000

Rs. 22,500

Rs. 25,300

Rs. 25,800

Answer: Option C

Explanation:

85 : 18700 = 115 : x

x = 18700 x 115 = 25300.

85

Hence, S.P. = Rs. 25,300.

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11.

A man completes

of a job in 10 days. At this rate, how many more days will it takes him to finish the job?

7	1
	2

Answer: Option B

Explanation:

Work done = 5

8

Balance work = 1 - 5 = 3

8 8

Let the required number of days be x.

Then, 5 : 3 = :: 10 : x 5 x x = 3 x 10

8 8 8 8

x = 3 x 10 x 8

8 5

x = 6.

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12.

A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:

20 days

22	1	days
	2

25 days

30 days

Answer: Option B

Explanation:

Ratio of times taken by A and B = 1 : 3.

The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.

If difference of time is 2 days, B takes 3 days.

If difference of time is 60 days, B takes 3 x 60 = 90 days.

2

So, A takes 30 days to do the work.

A's 1 day's work = 1

30

B's 1 day's work = 1

90

(A + B)'s 1 day's work = 1 + 1 = 4 = 2

30 90 90 45

A and B together can do the work in 45 = 22 1 days.

2 2

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13.

One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:

81 min.

108 min.

144 min.

192 min.

Answer: Option C

Explanation:

Let the slower pipe alone fill the tank in x minutes.

Then, faster pipe will fill it in x minutes.

3

1 + 3 = 1

x x 36

4 = 1

x 36

x = 144 min.

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14.

Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

Answer: Option B

Explanation:

Due to stoppages, it covers 9 km less.

Time taken to cover 9 km 9 x 60 min = 10 min.

54

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15.

The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is:

70 km/hr

75 km/hr

84 km/hr

87.5 km/hr

Answer: Option D

Explanation:

Let the speed of two trains be 7x and 8x km/hr.

Then, 8x = 400 = 100

4

x = 100 = 12.5

8

Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.

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Direction (for Q.No. 16):

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.

16.

A boat takes a total time of three hours to travel downstream from P and Q and upstream back from Q to P. What is the speed of the boat in still water?
I.	The speed of the river current is 1 km per hour.
II.	The distance between P and Q is 4 km.

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:

I. Speed of the current = 1 km/hr.

II. PQ = 4 km.

Let the speed of the boat in still water be x km/hr. Then,

4 + 4 = 3. This gives x.

(x + 1) (x - 1)

Correct answer is (E).

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17.

What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 p.c.p.a.?

Rs. 9000.30

Rs. 9720

Rs. 10123.20

Rs. 10483.20

None of these

Answer: Option C

Explanation:

Amount

= Rs. 25000 x 1 + 12 3

100

= Rs. 25000 x 28 x 28 x 28

25 25 25

= Rs. 35123.20

C.I. = Rs. (35123.20 - 25000) = Rs. 10123.20

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18.

The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?

Cannot be determined

None of these

Answer: Option A

Explanation:

15000 x 1 + R 2 - 15000 - 15000 x R x 2 = 96

100 100

15000 1 + R 2 - 1 - 2R = 96

100 100

15000 (100 + R)² - 10000 - (200 x R) = 96

10000

R² = 96 x 2 = 64

3

R = 8.

Rate = 8%.

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19.

At what time between 7 and 9 o'clock will the hands of a clock be in the same straight line but, not together?

5 min. past 7

5	2	min. past 7
	11

5	3	min. past 7
	11

5	5	min. past 7
	11

Answer: Option D

Explanation:

When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.

At 7 o'clock, they are 25 min. spaces apart.

Minute hand will have to gain only 5 min. spaces.

55 min. spaces are gained in 60 min.

5 min. spaces are gained in 60 x 5 min = 5 5 min.

55 11

Required time = 5 5 min. past 7.

11

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20.

Three unbiased coins are tossed. What is the probability of getting at most two heads?

Answer: Option D

Explanation:

Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}

Let E = event of getting at most two heads.

Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.

P(E) = n(E) = 7 .

n(S) 8

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