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15 Sep 2021, 07:00
Kudos
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A
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Difficulty:
45%
(medium)
Question Stats:
66% (01:58) correct
34%
(02:12)
wrong
based on 182
sessions
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If p is a positive integer and r is the remainder when p^2-1 is divided by 8, what is the value of r ?
(1) When p is divided by 4, the remainder is zero.
(2) When p is divided by 8, the remainder is not zero.
(1) When p is divided by 4, the remainder is zero.
(2) When p is divided by 8, the remainder is not zero.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
15 Sep 2021, 10:36
Kudos
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Bunuel
(1) When p is divided by 4, the remainder is zero.
p=4 , p^2-1 is divided by 8, we get 7 as remainder
p=16 , p^2-1 is divided by 8 , we get 7 as remainder
p=8 , p^2-1 is divided by 8 , we get same remainder
Therefore clearly sufficient
(2) When p is divided by 8, the remainder is not zero.
The possibilities are endless and the remainder could be anything
Clearly insufficient
Therefore IMO A
18 Sep 2021, 08:03
Kudos
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Bunuel
Statement 1:
p is a multiple of 4. Then \(p^2\) is a multiple of 16. We know \(p^2\) must be divisible by 8, then \(\frac{p^2 - 1 }{ 8}\) will always result in a remainder of 7.
Statement 2:
p = 3 and p = 4 would result in different remainders for \(\frac{p^2 - 1 }{ 8}\). Insufficient.
Ans: A
