If b

Question

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

Bunuel · Accepted Answer

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 . Answer: D.

TroyfontaineMacon · Answer

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

Cosmas · Answer

2x-3LT2=0, where LT means 'Less Than'
2X-LT6=0
2x=LT6
x=LT6/2
x=LT3

Answer is D

magneticlp · Answer

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.

Cosmas · Answer

@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.

WoundedTiger · Answer

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

Posted from my mobile device

kinjiGC · Answer

2x = 3b => 2x/3 = b < 2 => 2x/3 < 2 => x < 3 - Option D)

AKG1593 · Answer

Option D.
We're given,
b<2
Multiply both sides with 3
3b<6
Given,3b=2x
2x<6
x<3

lalania1 · Answer

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!

minhaz3333 · Answer

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.

EMPOWERgmatRichC · Answer

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 
2X = (about 6) 
X = (about 3) 
Eliminate B.

Final Answer:  D

GMAT assassins aren't born, they're made, 
Rich

ScottTargetTestPrep · Answer

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

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

2x < 6

x < 3

Answer: D

aborja87 · Answer

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.

msu6800 · Answer

Let, b=2
then, 2x-3*2=0
or,2x=6
So, x=3
Since, b<2, x also must be less than 3.
Ans: D

Posted from my mobile device

egmat · Answer

Great inequality question that tests whether you can connect algebraic manipulation with constraint application. Let me walk you through the core approach that'll help you crack this one.

Here's how to think about this:

Step 1: Solve for x in terms of b

You've got the equation \(2x - 3b = 0\). Let's isolate x to see how it relates to b.

\(2x - 3b = 0\)
\(2x = 3b\)
\(x = \frac{3b}{2}\)

So x is always three-halves times whatever b is. This relationship is your key to the whole problem.

Step 2: Apply the constraint on b

Now here's the critical insight: you know that \(b < 2\), and you've just found that \(x = \frac{3b}{2}\).

Since \(b < 2\), let's multiply both sides by \(\frac{3}{2}\):

\(\frac{3b}{2} < \frac{3(2)}{2}\)

\(\frac{3b}{2} < 3\)

Notice that \(\frac{3}{2}\) is positive, so the inequality direction stays the same (this is crucial - you don't flip the sign when multiplying by a positive number).

But remember, \(x = \frac{3b}{2}\), which means:

\(x < 3\)

Step 3: Match with answer choices

Looking at the options:

\(x > -3\): Could be true, but not necessarily for all values
\(x < 2\): Too restrictive - x could be 2.5, for example
\(x = 3\): Only true if b = 2, but we know \(b < 2\)
\(x < 3\): This is exactly what we derived!
\(x > 3\): Contradicts our finding

Answer: (D) \(x < 3\)

The key here was recognizing that the constraint on b translates directly to a constraint on x through their relationship. Since b must be less than 2, and x equals \(\frac{3b}{2}\), then x must be less than 3.

Want to master this question type systematically?

The complete solution on Neuron shows you the systematic framework for inequality constraint problems, including an alternative "smart numbers" approach and the common traps students fall into (like choosing option A instead of D). You'll also see how to spot when to flip inequality signs and when not to - a pattern that shows up across many GMAT questions. Check out Neuron's complete library of official questions with detailed solutions to build rock-solid fundamentals for test day.

totaltestprepNick · Answer

D https://www.youtube.com/watch?v=sy_p0FZrLfo Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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

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