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07 Jun 2017, 21:58
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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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08 Jun 2017, 01:21
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quantumliner
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
\(z^2 + 2z + 4 = z^2 + 2z + 1 + 3 = (z + 1)^2 + 3\)
3 leaves remainder 3 when divided by 8, we need to know the remainder of \((z + 1)^2\).
(1) When \((z−3)^2\) is divided by 8, the remainder is 4
\(z^2 – 6z + 9 = z^2 + 2z + 1 – 8z + 8 = (z + 1)^2 – 8(z + 1)\)
\(8(z + 1)\) has remainder 0 when divided by 8, hence remainder 4 can be brought only by our expression \((z + 1)^2\). Sufficient.
(2) When 2z is divided by 8, the remainder is 2
2z has remainder 2, then z has remainder 1. Knowing the remainder of z we’ll get the remainder of the expression. Sufficient.
Answer D
08 Jun 2017, 02:11
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quantumliner
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
We need the remainder when \(z^2 + 2z + 4\) is divided by 8.
(1) When \((z-3)^2\) is divided by 8, the remainder is 4
\((z - 3)^2\)
\((z^2 - 6z + 9)\) gives remainder 4 when divided by 8
\((z^2 - 6z + 9 + 8z)\) will give remainder 4 when divided by 8 because 8z is divisible by 8 so there will be no extra remainder from the extra term.
This means \((z^2 + 2z + 5)\) is divisible by 8.
So \((z^2 + 2z + 4)\) will give remainder 7 when divided by 8.
Sufficient.
(2) When 2z is divided by 8, the remainder is 2.
2z = 8a + 2
z = 4a + 1
\(z^2 = 16a^2 + 8a + 1\)
Given: \(z^2 + 2z + 4\)
\(z^2\) leaves a remainder 1 when divided by 8.
2z leaves a remainder 2 when divided by 8.
4 leaves a remainder 4 when divided by 8.
So \(z^2 + 2z + 4\) leaves a remainder 7 when divided by 8.
Sufficient.
Answer (D)
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 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!
