GATE 2018 CE (CE2) – Question 3

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

For natural numbers a, b, n and m, the sum of n copies of a is $a^2b$, and the sum of m copies of b is $ab^2$. Find the product of the sum of n copies of m and the sum of m copies of n.

$2a^2b^2$
$a^4b^4$
$ab(a+b)$
$a^2+b^2$

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Correct answer: (B) $a^4b^4$

Explanation

The first repeated sum gives $na=a^2b$, so $n=ab$. The second gives $mb=ab^2$, so $m=ab$. Each requested sum equals $mn=a^2b^2$; their product is $a^4b^4$ (B).