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07 Nov 2007, 09:53
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If X and Y are positive integers, what is the remainder of (XY)/4?
1. remainder of x/4 is 3
2. remainder of y/4 is 2
1. remainder of x/4 is 3
2. remainder of y/4 is 2
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07 Nov 2007, 10:14
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Statement 1 tells us that possible values of X are 3,7,11,15......Not Sufficient
Statement 2 tells us that possible values of Y are 2,6,10,14......Not Sufficient
Combining both the statements, we find that the product of any possible value of X and any possible value of Y leaves a remainder of 2 when divided by 4.....e.g: 3*2,11*14,...
Therefore, C is the answer.
A more conceptual approach is as follows:
X=4n+3
Y=4m+2
Therefore,
XY=(4n+3)(4m+2)
= 16nm+8n+12m+6
= 16nm+8n+12m+4+2
= 4(4nm+2n+3m+1) + 2
Therefore (XY)/4 will always leave a remainder of 2.
Statement 2 tells us that possible values of Y are 2,6,10,14......Not Sufficient
Combining both the statements, we find that the product of any possible value of X and any possible value of Y leaves a remainder of 2 when divided by 4.....e.g: 3*2,11*14,...
Therefore, C is the answer.
A more conceptual approach is as follows:
X=4n+3
Y=4m+2
Therefore,
XY=(4n+3)(4m+2)
= 16nm+8n+12m+6
= 16nm+8n+12m+4+2
= 4(4nm+2n+3m+1) + 2
Therefore (XY)/4 will always leave a remainder of 2.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
