# Arithmetic Aptitude 5

• Last Updated : 21 May, 2019

 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? 4 5 6 None of these

Question 1-Explanation:

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: 34 62 43 26

Question 2-Explanation:
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 20 -4 -10 4

Question 3-Explanation:
```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? 30 28 34 32

Question 4-Explanation:
```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: 5 4 3 None of these

Question 5-Explanation:
```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) Only R1 is correct. Only R2 is correct. Both R1 and R2 are correct. Neither R1 nor R2 is correct.

Question 6-Explanation:
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.
There are 6 questions to complete.