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A
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Difficulty:
45%
(medium)
Question Stats:
61% (01:56) correct
39%
(02:18)
wrong
based on 204
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If k is a positive integer, what is the remainder when k^2 is divided by 8?
(1) When k is divided by 2, the remainder is 1.
(2) When k is divided by 3, the remainder is 2.
(1) When k is divided by 2, the remainder is 1.
(2) When k is divided by 3, the remainder is 2.
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:
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Data Sufficiency Forum
01 Feb 2012, 19:14
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Smita04
It's possible to solve this problem algebraically bu simple number plugging would be better.
If k is a positive integer, what is the remainder when k² is divided by 8?
(1) When k is divided by 2, the remainder is 1 --> k=odd:
k=1 --> k^2=1 --> 1 divided by 8 yields remainder of 1;
k=3 --> k^2=9 --> 9 divided by 8 yields remainder of 1;
k=5 --> k^2=25 --> 25 divided by 8 yields remainder of 1;
k=7 --> k^2=49 --> 49 divided by 8 yields remainder of 1;
...
At this stage we can safely assume that all odd numbers when squared yield the remainder of 1. Sufficient.
(2) When k is divided by 3, the remainder is 2 --> k=3q+2: 2, 5, 8, ... each when squared yield different reminader upon division by 8. Not sufficient.
Answer: A.
