If $a = 2^{2} .3 . x$ and $b = {2.3}^{2} . y$ ; $L C M = 2^{2} {.3}^{2} {.5}^{2}$ and HCF = 2.3.5, which of the following is true?

xy = 25

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x + y = 30

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x – y = 0

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x = 5

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Solution

The correct option is B
x + y = 30

Since product of two numbers = LCM x HCF
$(2^{2} .3 . x) \times ({2.3}^{2} . y) = 2.3.5 \times 2^{2} {.3}^{2} {.5}^{2}$ which gives $x y = {5.5}^{2}$
So, x and y can alternate between the values 5 and 25 and we can not tell which is which. But, we can say that the sum is always 25 + 5 = 30.

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