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01 Oct 2010, 09:01
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B
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45%
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70% (02:06) correct
30%
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If x, y, and n are positive integers, is \((\frac{x}{y})^n\) greater than 1,000 ?
(1) \(x = y^3\) and \(n > y\).
(2) \(x > 5y\) and \(n > x\).
(1) \(x = y^3\) and \(n > y\).
(2) \(x > 5y\) and \(n > x\).
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01 Oct 2010, 09:16
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If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ?
Question: is \((\frac{x}{y})^n>1,00\)
(1) x=y^3 and n>y --> \((\frac{x}{y})^n=(\frac{y^3}{y})^n=y^{2n}\), so the question becomes is \(y^{2n}>1,000\) --> y=1 and n=2 answer is NO but y=10 and n=11 answer is YES. Not sufficient.
(2) x>5y and n>x --> \(\frac{x}{y}>5\) also as \(x\), \(y\), and \(n\) are positive integers then the least value of \(x\) is 6 (for \(y=1\)) and the least value of \(n\) is 7 --> so we would have \((number \ more \ than \ 5)^{(at \ least \ 7)}\) which is more than 1,000 (5^7>1,000). Sufficient.
Answer: B.
Question: is \((\frac{x}{y})^n>1,00\)
(1) x=y^3 and n>y --> \((\frac{x}{y})^n=(\frac{y^3}{y})^n=y^{2n}\), so the question becomes is \(y^{2n}>1,000\) --> y=1 and n=2 answer is NO but y=10 and n=11 answer is YES. Not sufficient.
(2) x>5y and n>x --> \(\frac{x}{y}>5\) also as \(x\), \(y\), and \(n\) are positive integers then the least value of \(x\) is 6 (for \(y=1\)) and the least value of \(n\) is 7 --> so we would have \((number \ more \ than \ 5)^{(at \ least \ 7)}\) which is more than 1,000 (5^7>1,000). Sufficient.
Answer: B.
General Discussion
06 Oct 2010, 23:40
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HI Bunuel,
I have a small doubt here....Do positive integers include zero too? If so, we have an undefined value as the answer right? Kinly clarify
I have a small doubt here....Do positive integers include zero too? If so, we have an undefined value as the answer right? Kinly clarify
