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a < b
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20 Mar 2023, 10:13
20 Mar 2023, 10:13
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Expert Reply
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Question Stats:
73% (01:07) correct
26% (00:36) wrong based on 45 sessions
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\(a < b\)
A Quantity A is greater.
B Quantity B is greater.
C The two quantities are equal.
D The relationship cannot be determined from the information given.
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
Quantity A |
Quantity B |
\( |a+b\)| |
\(|a-b|\) |
A Quantity A is greater.
B Quantity B is greater.
C The two quantities are equal.
D The relationship cannot be determined from the information given.
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
Re: a < b
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10 Apr 2023, 11:23
10 Apr 2023, 11:23
Expert Reply
a-b<0
so we do know that a-b is NEGATIVE
however, we could thin conceptually on the number line which is tedious and cumbersome but still effectively
Or we can think about the two numbers a and b
The two quantities will be always positive but we do not know anything about a and b which is greater and their magnitude
D is the answer
PS: testing different numbers and will see on your own
so we do know that a-b is NEGATIVE
however, we could thin conceptually on the number line which is tedious and cumbersome but still effectively
Or we can think about the two numbers a and b
The two quantities will be always positive but we do not know anything about a and b which is greater and their magnitude
D is the answer
PS: testing different numbers and will see on your own
Re: a < b
[#permalink]
22 May 2023, 17:11
22 May 2023, 17:11
1
Given the inequality a < b, we can evaluate Quantities A and B.
Quantity A: |a + b|
Since a and b are on the number line and a < b, their sum (a + b) will also be positive. Hence, |a + b| equals (a + b).
Quantity B: |a - b|
Since a is less than b (a < b), their difference (a - b) is negative. When you take the absolute value of a negative number, you get a positive number. Hence, |a - b| equals (b - a).
So, we now compare (a + b) and (b - a).
Because a < b, we can infer that a + b < b + b, or a + b < 2b.
But from |a - b|, we have b - a. This would be less than 2b - a, which we just found to be less than a + b. Therefore, b - a < a + b.
Hence, Quantity B (b - a) is less than Quantity A (a + b).
So, Option A: Quantity A is greater, is the correct answer.
Quantity A: |a + b|
Since a and b are on the number line and a < b, their sum (a + b) will also be positive. Hence, |a + b| equals (a + b).
Quantity B: |a - b|
Since a is less than b (a < b), their difference (a - b) is negative. When you take the absolute value of a negative number, you get a positive number. Hence, |a - b| equals (b - a).
So, we now compare (a + b) and (b - a).
Because a < b, we can infer that a + b < b + b, or a + b < 2b.
But from |a - b|, we have b - a. This would be less than 2b - a, which we just found to be less than a + b. Therefore, b - a < a + b.
Hence, Quantity B (b - a) is less than Quantity A (a + b).
So, Option A: Quantity A is greater, is the correct answer.
