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05 Oct 2019, 02:02
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
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Question Stats:
33% (02:15) correct
67%
(02:42)
wrong
based on 89
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TOUGH QUESTION
If x is an integer, is |2x - 5| + |3x - 10| = 5 - x ?
(1) x is divisible by 2
(2) x is positive
05 Oct 2019, 02:18
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Bunuel
Either you solve or apply logic...
|2x - 5| + |3x - 10| = 5 - x ..
Now, \(5-x\geq{0}....x\leq{5}\)
If x is a negative integer, the right hand side will increase by ONE time, while left hand side will increase by FIVE (2x+3x) times as all terms within mod on LHS get added.
So x can be 0, 1, 2, 3, 4, 5..
A quick check by substituting 0, 1, 2, 3,4 ,5 in equation |2x - 5| + |3x - 10| = 5 - x tells us that x can be only 3..
\(|2*3 - 5| + |3*3 - 10| = 5 - 3......|6-5|+|9-10|=21+1=2 ..\)
So, the question is finally IS x=3
(1) x is divisible by 2
So ans is No...
(2) x is positive
x can be 2, 3 or so on
A..
Other way would be to solve for equation
05 Oct 2019, 02:35
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|2x—5| + |3x—10|= 5–x
1) x<=5/2
-2x+ 5–3x+10=5–x
—4x =—10
x= 5/2 ( satisfies the equation)
2) 5/2< x <10/3
2x—5 —3x +10=5–x
0=0
3) x>=10/3
2x—5 +3x—10=5–x
6x=20
x= 10/3 (satisfies the equation)
The question is that Are x=5/2 and x=10/3 ???
Statement1: x is divisible by 2.
—> both values of x are not divisible by 2.
—> The answer is Always No.
Sufficient
Statement2: x is positive.
Yes. Both answers are positive numbers.
Sufficient
The answer is D.
Posted from my mobile device
1) x<=5/2
-2x+ 5–3x+10=5–x
—4x =—10
x= 5/2 ( satisfies the equation)
2) 5/2< x <10/3
2x—5 —3x +10=5–x
0=0
3) x>=10/3
2x—5 +3x—10=5–x
6x=20
x= 10/3 (satisfies the equation)
The question is that Are x=5/2 and x=10/3 ???
Statement1: x is divisible by 2.
—> both values of x are not divisible by 2.
—> The answer is Always No.
Sufficient
Statement2: x is positive.
Yes. Both answers are positive numbers.
Sufficient
The answer is D.
Posted from my mobile device
