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niteshwaghray
29 Jul 2017, 20:13
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If z is a positive integer and r is the remainder when \(z^2\) + 2z + 4 is divided by 8, what is the value of r?
(1) When \((z-3)^2\) is divided by 8, the remainder is 4
(2) When 2z is divided by 8, the remainder is 2
(1) When \((z-3)^2\) is divided by 8, the remainder is 4
(2) When 2z is divided by 8, the remainder is 2
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29 Jul 2017, 20:54
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niteshwaghray
If z is a positive integer and r is the remainder when \(z^2\) + 2z + 4 is divided by 8, what is the value of r?
(1) When \((z-3)^2\) is divided by 8, the remainder is 4
(2) When 2z is divided by 8, the remainder is 2
(1) When \((z-3)^2\) is divided by 8, the remainder is 4
(2) When 2z is divided by 8, the remainder is 2
Hi..
lets check the statements..
(1) When \((z-3)^2\) is divided by 8, the remainder is 4
so \((z-3)^2=z^2-6z+9\) is divided by 8, REMAINDER is 4...
this means \(z^2-6Z+9-4 = z^2-6z+5=(z-5)(z-1)\) is div by 8..
For this z has to be of the form of 4k+1, where k is a non negative integer..
example k = 1, z=4k+1=4*1+1=5......(5-5)(5-1)=0 div by 8..
k=2, z=4*2+1=9......(9-5)(9-1)=4*8, div by 8..
substitute value of z in main equation..
\(z^2\) + 2z + 4 .......\((4k+1)^2+2(4k+1)+4=16k^2+8k+1+8k+2+4=16k^2+16k+7\)...
when this is div by 8 ONLY term 7 is left..
so remainder = 7
sufficient
(2) When 2z is divided by 8, the remainder is 2
so 2z=8a+2 or z=4a+1 where a is non negative integer..
now we have same value as in statement I, so again remainder will come as 7
sufficient
D
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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 Data Sufficiency (DS) 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!
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