# Arithmetic Aptitude 5

1
 Question 1
The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 45. What is the difference between the two digits of that number?
 A 5 B 7 C 6 D None of these
Arithmetic Aptitude 5    Numbers
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Question 1 Explanation:
Let the ten’s digit be x and unit’s digit be y
Then (10x + y) – (10y + x) = 45
9(x – y) = 45
x – y = 5
 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
Arithmetic Aptitude 5    Numbers
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Question 2 Explanation:
Let the ten’s and unit’s digit be x and y.

Then 10x + - 9 = 10 x + x

10x2 + 12 -9x = 120 + x2
9x2 – 9x – 108 = 0
x2 –x – 12 = 0
x2 –4x + 3x – 12 = 0
(x – 4) (x + 3) = 0
Therefore x = 4
Hence the required no. is 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
Arithmetic Aptitude 5    Numbers
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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?
 A 30 B 28 C 34 D 32
Arithmetic Aptitude 5    Numbers
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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:
 A 5 B 4 C 3 D None of these
Arithmetic Aptitude 5    Numbers
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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
There are 5 questions to complete.
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