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1. The sum of four numbers is 64. If you add 3 to the first number, 3 is subtracted from the second number, the third is multiplied by 3 and the fourth is divided by 3, then all the results are equal. What is the difference between the largest and the smallest of the original numbers ?

A. 21

B. 27

C. 32

D. Cannot be determined

Solution:

Let the four numbers be , A, B, C and D
Let A + 3 = B - 3 = 3C =

\frac{D}{3}

= x
Then,
A = x - 3
B = x + 3
C =

\frac{x}{3}

D = 3x

\begin{aligned} \Leftrightarrow A + B + C + D = 64 \\ \Leftrightarrow (x - 3) + (x + 3) + \frac{x}{3} + 3 x = 64 \\ \Leftrightarrow 5 x + \frac{x}{3} = 64 \\ \Leftrightarrow 16 x = 192 \\ \Leftrightarrow x = 12 \end{aligned}

Thus, the numbers are 9, 15, 4 and 36
∴ Required difference :
= (36 - 4)
= 32

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