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If a + b < 0 and a + 2b = 3, then which of the following must be true?
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20 Mar 2023, 03:00
20 Mar 2023, 03:00
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If a + b < 0 and a + 2b = 3, then which of the following must be true?
a > 4
a < –4
a < –2
2 < a < 4
None of the above
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 > 4
a < –4
a < –2
2 < a < 4
None of the above
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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Posts: 2508
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Re: If a + b < 0 and a + 2b = 3, then which of the following must be true?
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08 Apr 2023, 04:24
08 Apr 2023, 04:24
1
Expert Reply
a > 4: This is not necessarily true. The given condition a + b < 0 does not provide enough information to determine the value of a.
a < –4: This is not necessarily true. The given condition a + b < 0 does not provide enough information to determine the value of a.
a < –2: This must be true. Since a + b < 0 is given, subtracting b from both sides of the inequality results in a < -b. Substituting a + 2b = 3 into this inequality, we get a < -b < 3. Since a and -b have opposite signs, and a + 2b = 3, which implies 2b > -3, we can deduce that a < -b < 3, which further implies a < -b < 2 < 3. Therefore, a must be less than -2.
2 < a < 4: This is not necessarily true. The given condition a + b < 0 does not provide enough information to determine the value of a.
None of the above: This is not the correct answer, as option 3 (a < -2) must be true based on the given conditions.
Therefore, the correct answer is: a < –2.
a < –4: This is not necessarily true. The given condition a + b < 0 does not provide enough information to determine the value of a.
a < –2: This must be true. Since a + b < 0 is given, subtracting b from both sides of the inequality results in a < -b. Substituting a + 2b = 3 into this inequality, we get a < -b < 3. Since a and -b have opposite signs, and a + 2b = 3, which implies 2b > -3, we can deduce that a < -b < 3, which further implies a < -b < 2 < 3. Therefore, a must be less than -2.
2 < a < 4: This is not necessarily true. The given condition a + b < 0 does not provide enough information to determine the value of a.
None of the above: This is not the correct answer, as option 3 (a < -2) must be true based on the given conditions.
Therefore, the correct answer is: a < –2.
Re: If a + b < 0 and a + 2b = 3, then which of the following must be true?
[#permalink]
07 Oct 2023, 05:48
07 Oct 2023, 05:48
GeminiHeat wrote:
a > 4: This is not necessarily true. The given condition a + b < 0 does not provide enough information to determine the value of a.
a < –4: This is not necessarily true. The given condition a + b < 0 does not provide enough information to determine the value of a.
a < –2: This must be true. Since a + b < 0 is given, subtracting b from both sides of the inequality results in a < -b. Substituting a + 2b = 3 into this inequality, we get a < -b < 3. Since a and -b have opposite signs, and a + 2b = 3, which implies 2b > -3, we can deduce that a < -b < 3, which further implies a < -b < 2 < 3. Therefore, a must be less than -2.
2 < a < 4: This is not necessarily true. The given condition a + b < 0 does not provide enough information to determine the value of a.
None of the above: This is not the correct answer, as option 3 (a < -2) must be true based on the given conditions.
Therefore, the correct answer is: a < –2.
a < –4: This is not necessarily true. The given condition a + b < 0 does not provide enough information to determine the value of a.
a < –2: This must be true. Since a + b < 0 is given, subtracting b from both sides of the inequality results in a < -b. Substituting a + 2b = 3 into this inequality, we get a < -b < 3. Since a and -b have opposite signs, and a + 2b = 3, which implies 2b > -3, we can deduce that a < -b < 3, which further implies a < -b < 2 < 3. Therefore, a must be less than -2.
2 < a < 4: This is not necessarily true. The given condition a + b < 0 does not provide enough information to determine the value of a.
None of the above: This is not the correct answer, as option 3 (a < -2) must be true based on the given conditions.
Therefore, the correct answer is: a < –2.
Boss, can you please show the steps for how you substituted a+2b in the a<-b eqn ??
