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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
If, a perfect square number, is divisible by 5, and q, an
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28 Oct 2020, 01:02
28 Oct 2020, 01:02
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Question Stats:
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53% (01:29) wrong based on 43 sessions
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If \(p^2\), a perfect square number, is divisible by 5, and q, an integer, is not divisible by 5, which of the following must be divisible by 10?
(A) \(pq + 5\)
(B) \(p + q\)
(C) \(2(p + 5q)\)
(D) \(2(5p + q)\)
(E) \(p^2 + 5q\)
(A) \(pq + 5\)
(B) \(p + q\)
(C) \(2(p + 5q)\)
(D) \(2(5p + q)\)
(E) \(p^2 + 5q\)
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If, a perfect square number, is divisible by 5, and q, an
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14 Nov 2020, 06:49
14 Nov 2020, 06:49
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GeminiHeat wrote:
If \(p^2\), a perfect square number, is divisible by 5, and q, an integer, is not divisible by 5, which of the following must be divisible by 10?
(A) \(pq + 5\)
(B) \(p + q\)
(C) \(2(p + 5q)\)
(D) \(2(5p + q)\)
(E) \(p^2 + 5q\)
(A) \(pq + 5\)
(B) \(p + q\)
(C) \(2(p + 5q)\)
(D) \(2(5p + q)\)
(E) \(p^2 + 5q\)
As with many Integer Properties question, we can solve this quickly by testing values that meet the given conditions.
GIVEN CONDITIONS: \(p^2\), a perfect square number, is divisible by 5, and q, an integer, is not divisible by 5
Let's test \(p = 5\) and \(q = 2\)
We get:
(A) \((5)(2) + 5 = 15\) NOT divisible by 10
(B) \(5 + 2 =7 \) NOT divisible by 10
(C) \(2(5 + 5(2))=30\) divisible by 10
(D) \(2(5(5) + 2)=54\) NOT divisible by 10
(E) \(5^2 + 5(2)=35\) NOT divisible by 10
Answer: C
Re: If, a perfect square number, is divisible by 5, and q, an
[#permalink]
17 Nov 2020, 03:37
17 Nov 2020, 03:37
3
here, p is divisible by 5, let it be 5a, where a= 1,2,3,4,.....
and a number to be divisible by 10 must contain 2 and 5 prime factors
in this regard, option C qualifies this: 2(p+5q)= 2(5a+5q)=2*5 (a+q)=10(a+q), which is divisible by 10 (C is the answer).
and no other options satisfy this.
and a number to be divisible by 10 must contain 2 and 5 prime factors
in this regard, option C qualifies this: 2(p+5q)= 2(5a+5q)=2*5 (a+q)=10(a+q), which is divisible by 10 (C is the answer).
and no other options satisfy this.
