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If n is an integer and 3n/7 is a perfect square, the smallest possible
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11 Aug 2021, 01:08
11 Aug 2021, 01:08
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Question Stats:
86% (00:40) correct
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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) Edition
GRE - Math Book
(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) Edition
GRE - Math Book
Intern
Joined: 25 Oct 2020
Posts: 20
Given Kudos: 9
Location: India
Concentration: Strategy, Finance
Re: If n is an integer and 3n/7 is a perfect square, the smallest possible
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11 Aug 2021, 01:59
11 Aug 2021, 01:59
1
For the solution to be a perfect square we need n to be a multiple of 7 and also can be factored to form a perfect square.
Looking at the options all of B,C and D hold true. But the question asks for the smallest integer value
so if n=21 and n 21 can be written as 3*7. The equation now becomes (3*3*7)/7 which is equal to 9, perfect square.
The answer is C
Looking at the options all of B,C and D hold true. But the question asks for the smallest integer value
so if n=21 and n 21 can be written as 3*7. The equation now becomes (3*3*7)/7 which is equal to 9, perfect square.
The answer is C
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Joined: 10 Apr 2015
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Re: If n is an integer and 3n/7 is a perfect square, the smallest possible
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15 Jan 2022, 12:30
15 Jan 2022, 12:30
1
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) Edition
GRE - Math Book
(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) Edition
GRE - 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 A
B. If n = 7, we get: \(\frac{3n}{7}=\frac{3(7)}{7}=3\). Not a perfect square. Eliminate B
C. If n = 21, we get: \(\frac{3n}{7}=\frac{3(21)}{7}=9\). Perfect square!
Answer: C
