Carcass wrote:
If n is an integer and \(\frac{3n}{7}\) is a perfect square, the smallest possible value of n is
(A) 3
(B) 7
(C) 21
(D) 42
(E) 147
Kudos for the right answer and explanation
Question part of the project GRE Quant/Math Extreme Challenge Daily (2021) EditionGRE - Math Book STRATEGY: As with all GRE Problem Solving questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices.
In most cases, we should then give ourselves about 20 seconds to identify a faster approach. However, in this case, the numbers are nice and small. So, testing shouldn't take more than 30 seconds...
We'll begin with the smallest number test answers choices in ascending value...
A. If n = 3, we get: \(\frac{3n}{7}=\frac{3(3)}{7}=\frac{9}{7}\).
Not a perfect square. Eliminate AB. If n = 7, we get: \(\frac{3n}{7}=\frac{3(7)}{7}=3\).
Not a perfect square. Eliminate BC. If n = 21, we get: \(\frac{3n}{7}=\frac{3(21)}{7}=9\). Perfect square!
Answer: C
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