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

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.
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X & B DO NOT HAVE TO BE INTEGERS

take a closely related number to \(2x=3b\)

\(2x=3(1.9)\)

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

\(x=2.85\)

\(2.85< 3\)

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

Answer is D

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

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
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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!

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.

@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.

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

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
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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

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.

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:

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

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.

b<2
x=3b/2<3

IMO D

Posted from my mobile device

Cosmas This is beautiful and elegant and I MUST know why this works!

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