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16 Sep 2014, 00:19
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If \(x^2 < 81\) and \(y^2 < 25\), what is the largest prime number that can be equal to \(x - 2y\)?
A. 3
B. 7
C. 11
D. 13
E. 17
A. 3
B. 7
C. 11
D. 13
E. 17
16 Sep 2014, 00:19
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Official Solution:
If \(x^2 < 81\) and \(y^2 < 25\), what is the largest prime number that can be equal to \(x - 2y\)?
A. 3
B. 7
C. 11
D. 13
E. 17
It is important to note that we are not given that \(x\) and \(y\) are integers.
\(x^2 < 81\) implies that \(-9 < x < 9\), and \(y^2 < 25\) implies that \(-5 < y < 5\). Now, since the largest value of \(x\) is slightly less than 9 and the largest value of \(-2y\) is slightly less than 10 (for instance, if \(y=-4.9\)), the largest value of \(x - 2y\) is slightly less than \(9 + 10 = 19\). This means that the largest prime number that can be equal to \(x - 2y\) is 17. For example, if \(x = 8\) and \(y = -4.5\), then \(x - 2y = 17\).
Answer: E
If \(x^2 < 81\) and \(y^2 < 25\), what is the largest prime number that can be equal to \(x - 2y\)?
A. 3
B. 7
C. 11
D. 13
E. 17
It is important to note that we are not given that \(x\) and \(y\) are integers.
\(x^2 < 81\) implies that \(-9 < x < 9\), and \(y^2 < 25\) implies that \(-5 < y < 5\). Now, since the largest value of \(x\) is slightly less than 9 and the largest value of \(-2y\) is slightly less than 10 (for instance, if \(y=-4.9\)), the largest value of \(x - 2y\) is slightly less than \(9 + 10 = 19\). This means that the largest prime number that can be equal to \(x - 2y\) is 17. For example, if \(x = 8\) and \(y = -4.5\), then \(x - 2y = 17\).
Answer: E
swanidhi
Joined: 11 Oct 2013
Last visit: 14 Jul 2023
Posts: 66
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Concentration: Marketing, General Management
Schools: Tepper MISM '17 (A) SPJ PGPM"16 (A)
GMAT 1: 600 Q41 V31
08 Dec 2015, 05:16
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Great question. Revolves around the fact that the question has not explicitly mentioned if x and y are integers. So if you presume them as integers, you'll mark the wrong answer!
