Arithmetic Aptitude 5

Question 1

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. 4
• B. 5
• C. 6
• D. None of these

Answer: (A)

Let the ten’s digit be x and the unit’s digit be y
Then (10x + y) – (10y + x) = 36
         9(x – y) = 36
           x – y = 4

Hence Option (A) is correct.

Question 2

A two-digit number is such that the product of the digits is 12. When 9 is subtracted from the number, the digits are reversed. The number is:

• A. 34
• B. 62
• C. 43
• D. 26

Answer: (C)

Let the tens digit of the number be a and ones digit be b.

Given:
ab = 12 ................(i) and,
(10a + b) - (10b + a) = 9
10a + b - 10b - a = 9
9a - 9b = 9
9(a-b) = 9
(a-b) = 1 .................(ii)

Factors of 12 = 1, 2, 3, 4, 6, 12. and from equation (ii), (a - b) = 1 So, a = 4 & b = 3. Required number = ab = 43.

Question 3

Find a positive number which when increased by 16 is equal to 80 times the reciprocal of the number

• A. 20
• B. -4
• C. -10
• D. 4

Answer: (D)

Let the number be x.
Then x + 16 = 80 * (1/x)
x2 + 16x – 80 = 0
x2 + 20x – 4x – 80 =0
(x + 20) (x -4)
Therefore x = 4

Question 4

What is the sum of two consecutive odd numbers, the difference of whose squares is 56?

• A. 30
• B. 28
• C. 34
• D. 32

Answer: (B)

Let the no. be x and (x +2).
Then (x + 2)2 – x2 = 56
4x + 4 = 56
x + 1 = 14
x = 13
Sum of numbers = x + (x +2) = 28

Question 5

The product of two numbers is 108 and the sum of their squares is 225. The difference of the number is:

• A. 5
• B. 4
• C. 3
• D. None of these

Answer: (C)

Let the numbers be x and y.
Then xy = 108 and x2 + y2 = 225
(x –y)2 = x2 + y2 – 2xy
(x –y)2 = 225 – 216
(x –y)2 = 9
Therefore (x –y) = 3

Question 6

Consider following two rules R1 and R2 in logical reasoning in Artificial Intelligence (AI) : R1 : From α ⊃ β and α/Inter β is known as Modus Tollens (MT) R2 : From α ⊃ β and ¬β/Inter ¬α is known as Modus Ponens (MP)

• A. Only R1 is correct.
• B. Only R2 is correct.
• C. Both R1 and R2 are correct.
• D. Neither R1 nor R2 is correct.

Answer: (D)

R1 : From α ⊃ β and α/Inter β is known as Modus Ponens (MP) R2 : From α ⊃ β and ¬β/Inter ¬α is known as Modus Tollens (MT) So, option (D) is correct.