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|k^2-4|=|k^2-9|
[#permalink]
04 Sep 2026, 16:14
04 Sep 2026, 16:14
Expert Reply
00:00
Question Stats:
66% (00:48) correct
33% (01:12) wrong based on 6 sessions
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\(|k^2-4|=|k^2-9|\)
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.
Quantity A |
Quantity B |
\(k^2+k \) |
\(9\) |
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.
- Part of the project: GRE Daily Quant Challenge ALL 4 CORE QUANT AREAS
- Also replying to the unanswered questions
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2932
Given Kudos: 1268
GPA: 3.39
Re: |k^2-4|=|k^2-9|
[#permalink]
08 Sep 2026, 10:03
08 Sep 2026, 10:03
1
Expert Reply
Solution
\(∣k^2-4∣=∣k^2-9∣\)
Use the property \((|A|=|B|)\)
This means either:
\(k^2-4=k^2-9\)
which is impossible, or
\(k^2-4=-(k^2-9)\)
So:
\(k^2-4=-k^2+9\)
\(2k^2=13\)
\(k^2=\frac{13}{2}\)
Compare the quantities
Quantity A:
\(k^2+k=\frac{13}{2}+k\)
Since
\(k=\pm\sqrt{\frac{13}{2}},\)
there are two possible values for Quantity A.
If (k>0, A is greater than 9.
If (k<0, A is less than 9.
Therefore, the relationship cannot be determined.
Answer: D
\(∣k^2-4∣=∣k^2-9∣\)
Use the property \((|A|=|B|)\)
This means either:
\(k^2-4=k^2-9\)
which is impossible, or
\(k^2-4=-(k^2-9)\)
So:
\(k^2-4=-k^2+9\)
\(2k^2=13\)
\(k^2=\frac{13}{2}\)
Compare the quantities
Quantity A:
\(k^2+k=\frac{13}{2}+k\)
Since
\(k=\pm\sqrt{\frac{13}{2}},\)
there are two possible values for Quantity A.
If (k>0, A is greater than 9.
If (k<0, A is less than 9.
Therefore, the relationship cannot be determined.
Answer: D
gmatclubot
Re: |k^2-4|=|k^2-9| [#permalink]
08 Sep 2026, 10:03
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