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Difficulty:
5%
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Question Stats:
80% (01:04) correct
20%
(01:07)
wrong
based on 704
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Which of the following could be q if |4q – 5| < 1?
A. –1
B. 1/4
C. 1
D. 5/4
E. 0
_________________
A. –1
B. 1/4
C. 1
D. 5/4
E. 0
_________________
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GMAT 1: 640 Q48 V28
Posts: 369
|4q – 5| < 1
-1<4q-5<1 Add 5 to each section
4<4q<6 Divide by 4 each section
1<q<6/4
Answers A, B, C, E are less or equal to 1, only D is left
-1<4q-5<1 Add 5 to each section
4<4q<6 Divide by 4 each section
1<q<6/4
Answers A, B, C, E are less or equal to 1, only D is left
General Discussion
Abhishek009
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Joined: 11 Jun 2011
Last visit: 17 Dec 2025
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Posts: 5,879
Bunuel
Plug in the values ( From the options given ) of q and check , none but (D) satisfies, hence answer will definitely be (D)
_________________
Bunuel
You can open brackets the "long" way if you can't remember the compound expression format.*
Case 1: \(4q - 5 < 1\)
\(4q < 6\)
\(q < \frac{6}{4}\)
(Do not reduce this fraction. Two answers have 4 in the denominator.)
Case 2: \(- (4q - 5) < 1\)
Divide by -1 and flip the sign
\(4q - 5 > -1\)
\(4q > 4\)
\(q > 1\)
Write the range:
\(1 < q < \frac{6}{4}\)
Only D fits in the range.
Answer D
I have seen confusion about linear inequality setup. If sign is \(<\) or \(\leq\)? Compound inequality. If sign is \(>\) or \(\geq\)? TWO inequalities. Here is a review.
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JeffTargetTestPrep
Expert
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Joined: 04 Mar 2011
Last visit: 05 Jan 2024
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Affiliations: Target Test Prep
Expert reply
Posts: 2,973
Bunuel
Looking at our answer choices we can determine that only when q = 5/4 is the given inequality true.
|4(5/4) – 5| < 1
|5 - 5| < 1
0 < 1
Answer: D
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I don't understand this problem sloving at all. Please, Kindly explain it more easily.
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Which of the following could be q if |4q – 5| < 1?
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