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

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Joined: 02 Sep 2009
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If b < 2 and 2x - 3b = 0, which of the following must be tru  [#permalink]

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13 Feb 2014, 02:20
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 92
Category: Algebra Inequalities
Page: 73
Difficulty: 600

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Re: If b < 2 and 2x - 3b = 0, which of the following must be tru  [#permalink]

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13 Feb 2014, 02:20
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SOLUTION

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

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

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Re: If b < 2 and 2x - 3b = 0, which of the following must be tru  [#permalink]

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13 Feb 2014, 05:44
1
2x-3LT2=0, where LT means 'Less Than'
2X-LT6=0
2x=LT6
x=LT6/2
x=LT3

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Re: If b < 2 and 2x - 3b = 0, which of the following must be tru  [#permalink]

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13 Feb 2014, 06:12
From 2x-3b=0 we have x = 3/2*b. Since b<2, it follows that x<3. If x<3, x is ALWAYS less than 2. Thus, the correct answer is B.
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Re: If b < 2 and 2x - 3b = 0, which of the following must be tru  [#permalink]

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13 Feb 2014, 06:48
@magneticlp : What about values between 2 and 3? Remember there are no integer restrictions on this question.

Also note that its a must be true question.
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Re: If b < 2 and 2x - 3b = 0, which of the following must be tru  [#permalink]

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13 Feb 2014, 11:57
1
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

Sol: given 2x-3b=0 or x =3b/2 and b<2

St 1: x>-3 lets consider possible value of b if b =-24 then x =-36 so x>-3 could be true but not must be true

St2: x<2 if b=1.9 the x= 3*1.9/2 or x> 2 so this condition could be true but not must be true

St3: x=3 for x =3 we need b=1 which is possible but again falls under could be true cause b can take any value
Less than 2

St4:x<3 -------> or 3b/2<3 we get

(3b-6)/2< 0 or 3b-6< 0
Or b< 2 which is same as the original given condition so we need not look beyond option D but for curiosity lets look at E as well

St 5: x> 3 or 3b/2>3 or (3b-6)/2 >0

3b-6>0 or b>2 clearly not true

Ans D

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Re: If b < 2 and 2x - 3b = 0, which of the following must be tru  [#permalink]

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13 Feb 2014, 18:15
1
X & B DO NOT HAVE TO BE INTEGERS

take a closely related number to $$2x=3b$$

$$2x=3(1.9)$$

$$\frac{(2x=5.7)}{2}$$

$$x=2.85$$

$$2.85< 3$$
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Re: If b < 2 and 2x - 3b = 0, which of the following must be tru  [#permalink]

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15 Feb 2014, 10:53
1
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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 => 2x/3 = b < 2
=> 2x/3 < 2
=> x < 3 - Option D)
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Re: If b < 2 and 2x - 3b = 0, which of the following must be tru  [#permalink]

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16 Feb 2014, 02:45
1
Option D.
We're given,
b<2
Multiply both sides with 3
3b<6
Given,3b=2x
2x<6
x<3
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Re: Inqualities QR2 PS 92  [#permalink]

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24 Apr 2016, 16:18
1
to solve this problem first you need to solve for b. You are given 2 facts, that b<2 and that 2x - 3b = 0

1) Solve for b

2x - 3b = 0 => -3b = -2x => b = -2x/-3 => b = 2x/3

2) then replace into b < 2 and solve for x

2x/3 < 2 => x < 6/2 => x < 3

3) x <3 is answer choice D!
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Re: If b < 2 and 2x - 3b = 0, which of the following must be tru  [#permalink]

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06 May 2016, 03:51
given equation -
2x - 3b = 0;
simplifying
2x = 3b
x = 3b/2
x = 3/(2/b)
now as b < 2
then denominator 2/b will always be greater than 1
so x will always be less than 3
hence
x< 3. correct option D.
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Re: If b < 2 and 2x - 3b = 0, which of the following must be tru  [#permalink]

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13 Feb 2018, 22:19
Hi All,

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
Eliminate B.

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Re: If b < 2 and 2x - 3b = 0, which of the following must be tru  [#permalink]

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15 Feb 2018, 11:06
1
Quote:

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

If b < 2, then multiplying the inequality by 3 yields 3b < 6

Manipulating the equation, we have 2x = 3b; thus:

2x < 6

x < 3

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Re: If b < 2 and 2x - 3b = 0, which of the following must be tru  [#permalink]

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19 Jul 2018, 10:06
From the question stem
--> 2x-3b=0 then
2x=3b.
Possible value of x=3 and b=2
BUT
b<2 THEN, x<3.
Anser choice D.
Re: If b < 2 and 2x - 3b = 0, which of the following must be tru &nbs [#permalink] 19 Jul 2018, 10:06
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