Aptitude Problems on Numbers Test Paper 2

16) The product of two numbers is 300, and the sum of their squares is 625. What are the numbers?

1025
1125
1225
1325

Answer: C

Explanation:

Let the numbers be x and y.
As per the question:

xy = 300
x² + y² = 625

So, (x+y)² = x² + y² + 2xy
                  = 625 + 2 * 300
                  = 625 + 600
                  = 1225

17) The difference between a two-digit number and the number obtained by interchanging the position of the digits is 45. What is the difference between digits of that number?

6
5
7
Data inadequate.

Answer: B

Explanation:

Let the number be = xy
so the ten's digit = x
Unit's digit = y
So, the number is = 10x +y
Number obtained by interchanging the digits = 10y + x
According to the question:
(10x + y) - (10y + x) = 45
10x + y - 10y - x = 45
9x - 9y = 45
9(x - y) = 45
X - Y = 5
∴The difference between the digits of the numbers: (x - y) = 5

18) When the numerator of a certain fraction is increased by 1 and the denominator by 2, it changes to Apti Problems on Numbers ; but when the numerator is increased by 5 and the denominator by 1, the value of the fraction changes to . What is the original fraction?

Apti Problems on Numbers

Answer: C

Explanation:

Let the fraction be Apti Problems on Numbers .

As per the question:
Apti Problems on Numbers
3x + 3 = 2y + 4
3x - 2y = 1 ..... (i)

As per the question:
Apti Problems on Numbers
4x + 20 = 5y + 5
4x - 5y = - 15 ..... (2)

Solving equation ((1) and (2), we get:

-x + 3y = 16 So, -x = 16 - 3y or x = -16 + 3y

Put the value of x in equation (i)

3 (-16 + 3y) - 2y = 1
- 48 + 9y - 2y = 1
-48 + 7y = 1
7y = 1 + 48
7y = 49
y = 7

Now, put the value of Y in equation (i)

3x - 2 * 7 = 1
3x = 1 + 14
3x =15
x = 5
X = 5, y = 7
So, the required fraction is Apti Problems on Numbers

19) The difference between a two-digit number and the number obtained by changing the positions of its digits is 36. What is the difference between the two digits of that number?