1000+ Free Aptitude Test Questions and Answers Pdf - 1

Question: 1

The sum of two numbers is 15 and the sum of their squares is 113. Find the numbers.

(A) 5, 6

(B) 6, 7

(D) 8, 9

View Answer

Ans: C

Let the numbers be x and (15 - x).

Then, x² + (15 – x)² = 113 ⇒ x² + 225 + x² - 30x = 113

⇒ 2x² - 30x + 112 = 0 ⇒ x² - 15x + 56 = 0 ⇒ (x - 7) (x - 8) = 0

⇒ x = 7 or x = 8.

So, the numbers are 7 and 8.

Question: 2

The difference between integers is 5. Their product is 500. Find the numbers.

(A) 15, 20

(B) 18, 20

(D) 30, 25

View Answer

Ans: C

Let the integers be x and (x+5). Then,

x (x + 5) = 500

⇔ x² + 5x - 500 = 0

⇔ (x + 25) (x - 20) = 0

⇔ x = 20.

So, the numbers are 20 and 25.

Question: 3

The difference between two numbers is 1365. When the larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number is

(A) 240

(B) 260

(D) 280

View Answer

Ans: C

Let the number be x and (x + 1365)

Then, x + 1365 = 6x + 15

⇔ 5x = 1350

⇔ x = 270.

Question: 4

The difference between two numbers is 3 and the difference between their squares is 63. Which is the larger number?

(A) 9

(B) 10

(D) 16

View Answer

Ans: C

Let the numbers be x and y.

Then, x² - y² = 63 and x - y = 3.

On dividing, we get : x + y = 21.

Solving x + y = 21 and x – y = 3.

We get : x = 12 and y = 9.

∴ Larger number = 12.

Question: 5

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?

(A) 69

(B) 78

(D) cannot be determined

View Answer

Ans: D

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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