Aptitude

Question: The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
[A].

3

[B].

4

[C].

9

[D].

Cannot be determined

Answer: Option B

Explanation:

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

Then, (10x + y) – (10y + x) = 36

9(x – y) = 36

x – y = 4.

Video Explanation: https://youtu.be/7QOJjAmGVx0

Question: A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:
[A].

3

[B].

5

[C].

9

[D].

11

Answer: Option D

Explanation:

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

Then, number = 10x + y.

Number obtained by interchanging the digits = 10y + x.

(10x + y) + (10y + x) = 11(x + y), which is divisible by 11.

Video Explanation: https://youtu.be/lytJE8GqRvM

Question:
In a two-digit, if it is known that its unit’s digit exceeds its ten’s digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:

[A].

24

[B].

26

[C].

42

[D].

46

Answer: Option A

Explanation:

Let the ten’s digit be x.

Then, unit’s digit = x + 2.

Number = 10x + (x + 2) = 11x + 2.

Sum of digits = x + (x + 2) = 2x + 2.

(11x + 2)(2x + 2) = 144

22×2 + 26x – 140 = 0

11×2 + 13x – 70 = 0

(x – 2)(11x + 35) = 0

x = 2.

Hence, required number = 11x + 2 = 24.

Question:
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

[C].

96

[D].

Cannot be determined

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.

Question:
What is the sum of two consecutive even numbers, the difference of whose squares is 84?

[A].

34

[B].

38

[C].

42

[D].

46

Answer: Option C

Explanation:

Let the numbers be x and x + 2.

Then, (x + 2)2 – x2 = 84

4x + 4 = 84

4x = 80

x = 20.

The required sum = x + (x + 2) = 2x + 2 = 42.

Question: Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:
[A].

9

[B].

11

[C].

13

[D].

15

Answer: Option D

Explanation:

Let the three integers be x, x + 2 and x + 4.

Then, 3x = 2(x + 4) + 3      x = 11.

Third integer = x + 4 = 15.

Video Explanation: https://youtu.be/_77C9YE321Y

Question:
The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:

[A].

20

[B].

23

[C].

169

[D].

None of these

Answer: Option B

Explanation:

Let the numbers be x and y.

Then, xy = 120 and x2 + y2 = 289.

(x + y)2 = x2 + y2 + 2xy = 289 + (2 x 120) = 529

x + y = 529 = 23.

Question: The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:

[A].

380

[B].

395

[C].

400

[D].

425

Answer: Option C

Explanation:

Let the numbers be x and y.

Then, xy = 9375 and	x	= 15.
	y

xy	=	9375
(x/y)		15

y2 = 625.

y = 25.

x = 15y = (15 x 25) = 375.

Sum of the numbers = x + y = 375 + 25 = 400.

Question:
The sum of two number is 25 and their difference is 13. Find their product.

[A].

104

[B].

114

[C].

315

[D].

325

Answer: Option B

Explanation:

Let the numbers be x and y.

Then, x + y = 25 and x – y = 13.

4xy = (x + y)2 – (x- y)2

   = (25)2 – (13)2

   = (625 – 169)

   = 456

xy = 114.

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

[A].

3

[B].

10

[C].

17

[D].

20

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.