Aptitude Test 3

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Instruction:

Total number of questions : 20.

Time alloted : 30 minutes.

Each question carry 1 mark, no negative marks.

Find the lowest common multiple of 24, 36 and 40.

120

240

360

480

Answer: Option C

Explanation:

 2 | 24  -  36  - 40
 --------------------
 2 | 12  -  18  - 20
 --------------------
 2 |  6  -   9  - 10
 -------------------
 3 |  3  -   9  -  5
 -------------------
   |  1  -   3  -  5
   
L.C.M.  = 2 x 2 x 2 x 3 x 3 x 5 = 360.

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Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?

16 years

18 years

28 years

24.5 years

None of these

Answer: Option D

Explanation:

Let Rahul's age be x years.

Then, Sachin's age = (x - 7) years.

x - 7 = 7

x 9

9x - 63 = 7x

2x = 63

x = 31.5

Hence, Sachin's age =(x - 7) = 24.5 years.

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The value of [(10)¹⁵⁰ � (10)¹⁴⁶]

1000

10000

100000

10⁶

Answer: Option B

Explanation:

(10)¹⁵⁰ � (10)¹⁴⁶ = 10¹⁵⁰

10¹⁴⁶

= 10^{150 - 146}

= 10⁴

= 10000.

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1	+	1	= ?
1 + a^{(n - m)}		1 + a^{(m - n)}

a^{m + n}

Answer: Option C

Explanation:

1 + 1 =

1 + 1

1 + aⁿ

a^m

1 + a^m

aⁿ

1 + a^{(n - m)} 1 + a^{(m - n)}

= a^m + aⁿ

(a^m + aⁿ) (a^m + aⁿ)

= (a^m + aⁿ)

(a^m + aⁿ)

= 1.

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A student multiplied a number by	3	instead of	5	.
	5		3

What is the percentage error in the calculation?

34%

44%

54%

64%

Answer: Option D

Explanation:

Let the number be x.

Then, error = 5 x - 3 x = 16 x.

3 5 15

Error% = 16x x 3 x 100 % = 64%.

15 5x

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A shopkeeper sells some articles at the profit of 25% on the original price. What is the exact amount of profit? To find the answer, which of the following information given in Statements I and II is/are necessary?
I.	Sale price of the article
II.	Number of articles sold

Only I is necessary

Only II is necessary

Either I or II is necessary

Both I and II are necessary

None of these

Answer: Option D

Explanation:

Gain = 25% of C.P.

In order to find gain, we must know the sale price of each article and the number of articles sold.

Correct answer is (D).

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The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

8 : 9

17 : 18

21 : 22

Cannot be determined

Answer: Option C

Explanation:

Originally, let the number of boys and girls in the college be 7x and 8x respectively.

Their increased number is (120% of 7x) and (110% of 8x).

120 x 7x and 110 x 8x

100 100

42x and 44x

5 5

The required ratio = 42x : 44x = 21 : 22.

5 5

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If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?

2 : 5

3 : 7

5 : 3

7 : 3

Answer: Option C

Explanation:

Let 40% of A = 2 B

3

Then, 40A = 2B

100 3

2A = 2B

5 3

A = 2 x 5 = 5

B 3 2 3

A : B = 5 : 3.

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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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Direction (for Q.No. 10):

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

10.

How much did Rohit get as profit at the year-end in the business done by Nitin, Rohit and Kunal?
I.	Kunal invested Rs. 8000 for nine months, his profit was times that of Rohit's and his investment was four times that of Nitin.
II.	Nitin and Rohit invested for one year in the proportion 1 : 2 respectively.
III.	The three together got Rs. 1000 as profit at the year end.

Only I and II

Only I and III

Question cannot be answered even with the information in all the three statements.

All I, II and III

None of these

Answer: Option D

Explanation:

I and II give:

K = Rs. (8000 x 9) for 1 month = Rs. 72000 for 1 month.

N = Rs. 1 x 8000 x 12 for 1 month = Rs. 24000 for 1 month.

4

R = Rs. 48000 for 1 month.

K : N : R = 72000 : 24000 : 48000 = 3 : 1 : 2.

III gives, total profit = Rs. 1000.

Rohit's share = Rs. 1000 x 2 = Rs. 333 1

6 3

Correct answer is (D).

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11.

It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:

2 : 3

3 : 2

3 : 4

4 : 3

Answer: Option C

Explanation:

Let the speed of the train be x km/hr and that of the car be y km/hr.

Then, 120 + 480 = 8 1 + 4 = 1 ....(i)

x y x y 15

And, 200 + 400 = 25 1 + 2 = 1 ....(ii)

x y 3 x y 24

Solving (i) and (ii), we get: x = 60 and y = 80.

Ratio of speeds = 60 : 80 = 3 : 4.

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Direction (for Q.No. 12):

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.

12.

The towns A, B and C are on a straight line. Town C is between A and B. The distance from A to B is 100 km. How far is A from C?
I.	The distance from A to B is 25% more than the distance from C to B.
II.	The distance from A to C is of the distance C to B.

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:

.__________.______________________________________.
A     x    C            (100 - x)                 B

Let AC = x km. Then, CB = (100 -x) km.

I. AB = 125% of CB

100 = 125 x (100 - x)

100

100 - x = 100 x 100 = 80

125

x = 20 km.

AC = 20 km.

Thus, I alone gives the answer.

II. AC = 1 CB

4

x = 1 (100 - x)

4

x = 100

x = 20.

AC = 20 km.

Thus, II alone gives the answer.

Correct answer is (C).

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13.

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

1 : 3

3 : 2

3 : 4

None of these

Answer: Option B

Explanation:

Let the speeds of the two trains be x m/sec and y m/sec respectively.

Then, length of the first train = 27x metres,

and length of the second train = 17y metres.

27x + 17y = 23

x+ y

27x + 17y = 23x + 23y

4x = 6y

x = 3 .

y 2

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14.

The diagonal of a rectangle is 41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:

9 cm

18 cm

20 cm

41 cm

Answer: Option B

Explanation:

l² + b² = 41.

Also, lb = 20.

(l + b)² = (l² + b²) + 2lb = 41 + 40 = 81

(l + b) = 9.

Perimeter = 2(l + b) = 18 cm.

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Direction (for Q.No. 15):

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.

15.

Is a given rectangular block, a cube?
I.	At least 2 faces of the rectangular block are squares.
II.	The volume of the block is 64.

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:

I gives, any two of l, b, h are equal.

II gives, lbh = 64.

From I and II, the values of l, b, h may be (1 ,1 , 64), (2 ,2 ,16), (4, 4, 4).

Thus, the block may be a cube or cuboid.

Correct answer is (D).

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16.

How many times in a day, are the hands of a clock in straight line but opposite in direction?

Answer: Option B

Explanation:

The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).

So, in a day, the hands point in the opposite directions 22 times.

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17.

In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:

117

Answer: Option A

Explanation:

Let S be the sample space and E be the event of selecting 1 girl and 2 boys.

Then, n(S) = Number ways of selecting 3 students out of 25

= ²⁵C₃ `

= (25 x 24 x 23)

(3 x 2 x 1)

= 2300.

n(E) = (¹⁰C₁ x ¹⁵C₂)

= 10 x (15 x 14)

(2 x 1)

= 1050.

P(E) = n(E) = 1050 = 21 .

n(S) 2300 46

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18.

One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card?

Answer: Option B

Explanation:

Clearly, there are 52 cards, out of which there are 12 face cards.

P (getting a face card) = 12 = 3 .

52 13

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Direction (for Q.No. 19):

Insert the missing number.

19.

11, 13, 17, 19, 23, 29, 31, 37, 41, (....)

Answer: Option A

Explanation:

Numbers are all primes. The next prime is 43.

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Direction (for Q.No. 20):

Find out the wrong number in the series.

20.

15, 16, 34, 105, 424, 2124, 12576

105

424

2124

Answer: Option E

Explanation:

2^nd term = (1^st term) x 1 + 1 = 15 x 1 + 1 = 16.

3^rd term = (2^nd term) x 2 + 2 = 16 x 2 + 2 = 34.

4^th term = (3^th term) x 3 + 3 = 34 x 3 + 3 = 105.

5^th term = (4^th term) x 4 + 4 = 105 x 4 + 4 = 424

6^th term = (5^th term) x 5 + 5 = 424 x 5 + 5 = 2125

6^th term should 2125 instead of 2124.

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