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A rational number is such that when you multiply it by $52$ and add $23$ to the product, you get $− 712$ . What is the number?

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122

− 12 32

− 4 27

− 1 2

answer is D.

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Detailed Solution

It is given that the number is multiplied by

52

and

23

is added to the product, the result is

712

.
Let x be the rational number then the equation will be,

5 x 2 + 23 = − 712

Simplify the above equation,

5 x 2 = − 7 12 − 23

Taking LCM of

− 7 12

and

23

5 x 2 = − 7 − 2 × 4 12

5 x 2 = − 7 − 8 12

5 x 2 = − 15 12

Using crisscross multiplication,

x = − 15 12 × 25

x = − 3 6

Divide the factor by 2,

x = − 1 2

Hence, the rational number is

− 1 2

.
Correct option is 4.

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