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16 Jan 2022, 08:46
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E
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30% (01:46) correct
70%
(02:07)
wrong
based on 135
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If \(xy ≠ 0\), is \(x < y\)?
(1) \(x^8 < y^8\)
(2) \(x^{(-9)} < y^{(-9)}\)
FRESH GMAT CLUB TETS' QUESTION
(1) \(x^8 < y^8\)
(2) \(x^{(-9)} < y^{(-9)}\)
FRESH GMAT CLUB TETS' QUESTION
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26 Jan 2022, 06:19
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Bunuel
(1) \(x^8 < y^8\)
\(x=2 , y=3 \) Yes to the stem
\(x=2 , y=-3 \) NO to the stem.
(2) \(x^{(-9)} < y^{(-9)}\)
\(x=-3 , y=2 \) Yes to the stem
\(x=3 , y=2 \) No to the stem
\(1+2 \)
\(x= - \frac {1}{3}\) \(y= \frac{1}{2}\) Yes to the stem
\(x=- \frac {1}{3}\) \(y= -\frac{1}{2}\) No to the stem
Ans E
27 Apr 2023, 03:58
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Official Solution:
If \(xy ≠ 0\), is \(x < y\)?
(1) \(x^8 < y^8\)
Taking the 8th root of the inequality above yields \(|x| < |y|\). This implies that \(y\) is farther from 0 than \(x\). However, this information alone is insufficient to determine whether \(x < y\).
(2) \(x^{(-9}) < y^{(-9)}\)
Taking the 9th root of the inequality above yields \(x^{(-1)} < y^{(-1)}\), which can be rewritten as \(\frac{1}{x} < \frac{1}{y}\). If \(x\) and \(y\) have the same sign, this would imply that \(y < x\) (in this case, cross-multiplying would involve multiplying by two negative or two positive values, so the inequality sign remains the same). However, if \(x\) and \(y\) have different signs, this would imply that \(y > x\) (in this case, cross-multiplying would involve multiplying by one negative value and one positive value, so the inequality sign reverses). Not sufficient.
(1)+(2) The information that \(|x| < |y|\) from (1) does not help us determine whether \(x\) and \(y\) have the same sign or not. Therefore, we cannot definitively conclude from \(\frac{1}{x} < \frac{1}{y}\) whether \(y < x\) or \(y > x\). For example, consider \(x = -1\) and \(y = -2\); in this case, \(y < x\). However, if \(x = -1\) and \(y = 2\), we have \(y > x\). Not sufficient.
Answer: E
If \(xy ≠ 0\), is \(x < y\)?
(1) \(x^8 < y^8\)
Taking the 8th root of the inequality above yields \(|x| < |y|\). This implies that \(y\) is farther from 0 than \(x\). However, this information alone is insufficient to determine whether \(x < y\).
(2) \(x^{(-9}) < y^{(-9)}\)
Taking the 9th root of the inequality above yields \(x^{(-1)} < y^{(-1)}\), which can be rewritten as \(\frac{1}{x} < \frac{1}{y}\). If \(x\) and \(y\) have the same sign, this would imply that \(y < x\) (in this case, cross-multiplying would involve multiplying by two negative or two positive values, so the inequality sign remains the same). However, if \(x\) and \(y\) have different signs, this would imply that \(y > x\) (in this case, cross-multiplying would involve multiplying by one negative value and one positive value, so the inequality sign reverses). Not sufficient.
(1)+(2) The information that \(|x| < |y|\) from (1) does not help us determine whether \(x\) and \(y\) have the same sign or not. Therefore, we cannot definitively conclude from \(\frac{1}{x} < \frac{1}{y}\) whether \(y < x\) or \(y > x\). For example, consider \(x = -1\) and \(y = -2\); in this case, \(y < x\). However, if \(x = -1\) and \(y = 2\), we have \(y > x\). Not sufficient.
Answer: E
