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If ab < 0, which of the following must be true?
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16 Mar 2023, 01:24
16 Mar 2023, 01:24
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71% (00:36) correct
28% (00:37) wrong based on 28 sessions
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If \(ab < 0\), which of the following must be true?
\(a < 0\)
\(b > 0\)
\(\frac{a}{b} < 0\)
\(2a – 3b > 0\)
\(a + b > 0\)
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE INEQUALITIES
\(a < 0\)
\(b > 0\)
\(\frac{a}{b} < 0\)
\(2a – 3b > 0\)
\(a + b > 0\)
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE INEQUALITIES
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Joined: 20 Feb 2017
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Re: If ab < 0, which of the following must be true?
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08 Apr 2023, 04:19
08 Apr 2023, 04:19
2
Expert Reply
Based on the given information that ab < 0, where a and b are real numbers, we can deduce the following:
a < 0: This is not necessarily true. For example, if a = -2 and b = 3, then ab = (-2)(3) = -6 < 0, but a = -2 > 0.
b > 0: This is not necessarily true. For example, if a = 3 and b = -2, then ab = (3)(-2) = -6 < 0, but b = -2 < 0.
a/b < 0: This must be true. Since ab < 0, and a and b have opposite signs (one is positive and the other is negative), the quotient a/b will also have a different sign than ab. Therefore, a/b < 0 must be true.
2a - 3b > 0: This is not necessarily true. For example, if a = 1 and b = 1/3, then ab = (1)(1/3) = 1/3 > 0, but 2a - 3b = 2(1) - 3(1/3) = 2 - 1 = 1 > 0.
a + b > 0: This is not necessarily true. For example, if a = -1 and b = -2, then ab = (-1)(-2) = 2 > 0, but a + b = (-1) + (-2) = -3 < 0.
So, the only statement that must be true is a/b < 0.
Answer: C
a < 0: This is not necessarily true. For example, if a = -2 and b = 3, then ab = (-2)(3) = -6 < 0, but a = -2 > 0.
b > 0: This is not necessarily true. For example, if a = 3 and b = -2, then ab = (3)(-2) = -6 < 0, but b = -2 < 0.
a/b < 0: This must be true. Since ab < 0, and a and b have opposite signs (one is positive and the other is negative), the quotient a/b will also have a different sign than ab. Therefore, a/b < 0 must be true.
2a - 3b > 0: This is not necessarily true. For example, if a = 1 and b = 1/3, then ab = (1)(1/3) = 1/3 > 0, but 2a - 3b = 2(1) - 3(1/3) = 2 - 1 = 1 > 0.
a + b > 0: This is not necessarily true. For example, if a = -1 and b = -2, then ab = (-1)(-2) = 2 > 0, but a + b = (-1) + (-2) = -3 < 0.
So, the only statement that must be true is a/b < 0.
Answer: C
gmatclubot
Re: If ab < 0, which of the following must be true? [#permalink]
08 Apr 2023, 04:19
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