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# If b < 2 and 2x - 3b = 0 which of the following must be true

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Manager
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If b < 2 and 2x - 3b = 0 which of the following must be true [#permalink]  25 Oct 2010, 04:42
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Question Stats:

62% (01:52) correct 38% (01:18) wrong based on 143 sessions
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
D. x > 3
[Reveal] Spoiler: OA
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Re: which of the following must be true.... [#permalink]  25 Oct 2010, 05:15
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Expert's post
pzazz12 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

$$2x-3b=0$$ --> $$b=\frac{2x}{3}<2$$ --> $$x<3$$.

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Re: which of the following must be true.... [#permalink]  26 Oct 2010, 09:48
good explanation Bunuel ...txs
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Re: which of the following must be true.... [#permalink]  29 Apr 2013, 20:14
1
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pzazz12 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
D. x>3

$$Given,$$ $$..........$$ $$b < 2$$ $$\Rightarrow$$ $$b = LT2$$ $$...........$$

$$&$$ $$2x - 3b = 0$$$$.....$$ $$Therefore$$ $$..........$$$$2x - 3 ( LT2 ) = 0$$

$$Therefore,$$ $$2x - LT6 = 0$$ $$\Rightarrow$$ $$2x = LT6$$ $$\Rightarrow$$ $$x=\frac{LT6}{2}$$

$$\Rightarrow$$ $$x = LT 3$$

$$\Rightarrow$$ $$x < 3$$ $$Hence,$$ $$Answer choice .. D$$
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Re: which of the following must be true.... [#permalink]  29 Apr 2013, 21:51
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2x - 3b = 0
Therefore, 2x = 3b
As, b<2
2x < 3(2)
i.e x < 3

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Re: If b < 2 and 2x - 3b = 0 which of the following must be true [#permalink]  26 Feb 2014, 16:13
As an alternative method, use optimization:

A. if x > -3, then x(100). If x(100) then b is not less than 2. Not true.
C. if x = 3, then x(3). If x(3), then b is 2. Not true.
E. if x > 3, then x(100). If x(100) then b is not less than 2. Not true.

Thus, both x<2 and x<3 are left.

D. If x<3, then x(2.5). If x(2.5), still b<2. Must be true.
(B. if x<2, then 2.5 missing from solution set. Thus, x<2 is not true.)
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Re: If b < 2 and 2x - 3b = 0 which of the following must be true   [#permalink] 26 Feb 2014, 16:13
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