GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
If ab < 0, which of the following must be true?
[#permalink]
16 Mar 2023, 01:24
16 Mar 2023, 01:24
1
Expert Reply
1
Bookmarks
00:00
Question Stats:
72% (00:35) correct
27% (00:37) wrong based on 29 sessions
Hide Show timer Statistics
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
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
Re: If ab < 0, which of the following must be true?
[#permalink]
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
Moderators:
