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by GMATGuruNY » Sat Oct 10, 2015 6:14 am
oquiella wrote:If b<2 and 2x-3b=0, which of the following must be true?

A. X> -3
B. X< 2
C. X= 3
D. X< 3
E. X> 3
2x - 3b = 0
2x = 3b
b = (2/3)x.

Substituting b = (2/3)x into b<2, we get:
(2/3)x < 2
2x < 6
x < 3.

The correct answer is D.
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by [email protected] » Sat Oct 10, 2015 8:46 am
Hi oquiella,

This question can be solved by TESTing VALUES, although you'll likely need more than one TEST to get to the solution.

We're told that B < 2 and 2X - 3B = 0. We're asked what MUST be true.

IF...
B = 0
2X - 3(0) = 0
2X = 0
X = 0
Eliminate C and E.

IF....
B = -10
2X - 3(-10) = 0
2X + 30 = 0
2X = -30
X = -15
Eliminate A.

Notice how similar Answers B and D are? On a fundamental level, any number that 'fits' Answer B ALSO fits Answer D (but D includes some solutions that are NOT in B). Since there can't be two correct answers, B cannot be correct. That having been said, here's how you can prove that D is the answer...

IF....
B = 1.99
2X - 3(1.99) = 0
2X - (about 6) = 0
2X = (about 6)
X = (about 3)
Eliminate B.

Final Answer: D

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