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Difficulty:
15%
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Question Stats:
85% (02:05) correct
15%
(02:18)
wrong
based on 325
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Which of the following statements is equivalent to \(8 + 2X < 18 - 6X < 23 + 2X\)?
A. 4/5 < X < 2.5.
B. 4/5 < X < 8/5.
C. -5/8 < X < 5/4.
D. 2.5 < X < 3.5.
E. 5 < 8X < 12.
_________________
A. 4/5 < X < 2.5.
B. 4/5 < X < 8/5.
C. -5/8 < X < 5/4.
D. 2.5 < X < 3.5.
E. 5 < 8X < 12.
_________________
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Divyadisha
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Joined: 18 Oct 2014
Last visit: 01 Jun 2018
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GMAT 1: 660 Q49 V31
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GMAT 1: 660 Q49 V31
Posts: 659
Bunuel
\(8 + 2X < 18 - 6X < 23 + 2X\)
8<18-8x<23 (add -2x on all sides)
-10<-8x<5
10>8x>-5 (multiply by -1 on all sides)
5/4>x>-5/8
C is the answer
General Discussion
Posts: 1,776
Bunuel
8 + 2X < 18 - 6X < 23 + 2X
Taking one inequality at a time,
8 + 2X < 18 - 6X
8X < 10
X < 5/4 - (i)
18 - 6X < 23 + 2X
8X > -5
X > -5/8 - (ii)
Combining (i) and (ii),
-5/8 < X < 5/4
Correct Option: C
Bunuel
8+2X< 18 - 6X
2X + 6X < 18 - 8
8X < 10
X < (5/4)
Only C has this option.
C is the answer.
[Verify:
18-6X < 23+2X
18-23 < 8 X
-5 < 8X
X > - (5/8) .
Once again this is appearing only in option C]
Bunuel pls explain this sum, and i m not able to understand y in above explanations "add -2x on both sides" is done as x's sign is not stated ?
Rikhraj1
You can add or subtract a variable from both sides of an inequality regardless of its sign => https://gmatclub.com/forum/inequalities ... l#p2045931
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