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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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53% (01:29) wrong based on 43 sessions
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If p2, 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) p2+5q
(A) pq+5
(B) p+q
(C) 2(p+5q)
(D) 2(5p+q)
(E) p2+5q
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Joined: 10 Apr 2015
Posts: 6218
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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 p2, 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) p2+5q
(A) pq+5
(B) p+q
(C) 2(p+5q)
(D) 2(5p+q)
(E) p2+5q
As with many Integer Properties question, we can solve this quickly by testing values that meet the given conditions.
GIVEN CONDITIONS: p2, 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) 52+5(2)=35 NOT divisible by 10
Answer: C
Re: If, a perfect square number, is divisible by 5, and q, an
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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.
