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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.
01 Feb 2012, 19:14
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Smita04
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.
(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.
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.
