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The question given below is a sample question in Numbers and operation. The question tests basic concepts in ratio and operations of numbers (LCM).

Question

The ratio between two numbers is 3 : 4. If their LCM is 192, what is the difference between the squares of the numbers?
A. 1792
B. 1790
C. 1798
D. 1796
E. 1794

Correct answer is 1792. Choice A.

Explanatory Answer

Let the two numbers be 3x and 4x.

Therefore, the LCM of these two numbers will be 3 * 4 * x = 12x.

We know that the LCM of these two numbers is 192.

Equating, we get 12x = 192

Or x = 16.

Hence, the two numbers are 3*16 and 4 * 16. i.e., 48 and 64

We have to find out the difference between the squares of the numbers = 64² - 48²

= (64 + 48) * (64 - 18) = 112 * 16 = 1792

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