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22 May 2023, 01:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
40% (01:38) correct
60%
(02:05)
wrong
based on 42
sessions
History
Date
Time
Result
Not Attempted Yet
If (x−2.5)(x+0.5)=4, what is the value of x?
(1) (x+1.5)(x−1.5)=0
(2) (x−3.5)(x+1.5)=0
(1) (x+1.5)(x−1.5)=0
(2) (x−3.5)(x+1.5)=0
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
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22 May 2023, 18:19
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(x−2.5)(x+0.5)=4
Solving this equation we get x = 3.5/-1.5
Any option which gives us either of these values but not both is the answer.
(1) (x+1.5)(x−1.5)=0
This gives us x=-1.5
Sufficient
(2) (x−3.5)(x+1.5)=0
This gives us both the values.
Hence, insufficient.
Solving this equation we get x = 3.5/-1.5
Any option which gives us either of these values but not both is the answer.
(1) (x+1.5)(x−1.5)=0
This gives us x=-1.5
Sufficient
(2) (x−3.5)(x+1.5)=0
This gives us both the values.
Hence, insufficient.
22 May 2023, 21:19
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Question: (x−2.5)(x+0.5)=4, x = ?
(1) (x+1.5)(x−1.5) = 0
--> x = 1.5 or x = -1.5
Backsolve: x = 1.5 --> (1.5 - 2.5)(1.5 + 0.5) < 0 --> rejected
x = -1.5 --> (-1.5 - 2.5)(-1.5 + 0.5) = (-4)(-1) = 4
Therefore, statement (1) is sufficient.
(2) (x−3.5)(x+1.5)=0
--> x = 3.5 or x = -1.5
Backsolve: x = 3.5 --> (3.5 - 2.5)(3.5 +0,5) = (1)(4) = 4 (valid)
x = -1.5 --> (-1.5 - 3.5)(-1.5 + 0.5) = (-4)(-1) = 4 (valid)
2 different values of x, hence not sufficient
Answer is (A).
(1) (x+1.5)(x−1.5) = 0
--> x = 1.5 or x = -1.5
Backsolve: x = 1.5 --> (1.5 - 2.5)(1.5 + 0.5) < 0 --> rejected
x = -1.5 --> (-1.5 - 2.5)(-1.5 + 0.5) = (-4)(-1) = 4
Therefore, statement (1) is sufficient.
(2) (x−3.5)(x+1.5)=0
--> x = 3.5 or x = -1.5
Backsolve: x = 3.5 --> (3.5 - 2.5)(3.5 +0,5) = (1)(4) = 4 (valid)
x = -1.5 --> (-1.5 - 3.5)(-1.5 + 0.5) = (-4)(-1) = 4 (valid)
2 different values of x, hence not sufficient
Answer is (A).
