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20 May 2020, 00:54
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
61% (01:40) correct
39%
(01:53)
wrong
based on 59
sessions
History
Date
Time
Result
Not Attempted Yet
If x is a positive integer, what is the value of x?
(1) (6 - 2x)(6 - x) < 0
(2) (x - 5)(x + 7) < 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
Data Sufficiency Forum
20 May 2020, 03:02
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Solution
Step 1: Analyse Question Stem
- • x is a positive integer.
• We need to find the value of x.
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: (6 -2x)(6-x) < 0
- • The two critical points of the given inequality is x = 3 and x = 6.
- • From the above, we have \((6 -2x)(6-x) < 0 ⟹ 3< x < 6\)
• Therefore, x = 4 or 5
• We are not getting a unique value of x here.
Statement 2: (x -5)(x+7) < 0
- • The two critical points of the given inequality is x = 5 and x = -7.
- • From the above, we have \((x-5)(x+7) < 0 ⟹ -7 < x < 5\)
• Therefore, x can be 1, 2, 3, or 4.
• We are not getting a unique value of x here.
Step 3: Analyse Statements by combining.
From statement 1: x can be 4 or 5
From statement 2: x can be 1, 2, 3, or 4.
On combining both, we got, x = 4
Thus, the correct answer is Option C.
20 May 2020, 04:27
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x is a positive integer, what is the value of x?
(1) (6 - 2x)(6 - x) < 0
3 < x < 6
x = 4 or 5. We don't know which one.
NOT SUFFICIENT
(2) (x - 5)(x + 7) < 0
-7 < x < 5
x = -6, -5,..., 3, 4. We don't know which one.
COMBINED
Now we know that x=4.
SUFFICIENT
FINAL ANSWER IS (C)
Posted from my mobile device
(1) (6 - 2x)(6 - x) < 0
3 < x < 6
x = 4 or 5. We don't know which one.
NOT SUFFICIENT
(2) (x - 5)(x + 7) < 0
-7 < x < 5
x = -6, -5,..., 3, 4. We don't know which one.
COMBINED
Now we know that x=4.
SUFFICIENT
FINAL ANSWER IS (C)
Posted from my mobile device
