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Algebra Question

by sanaa.rizwan » Mon May 06, 2013 7:44 am
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

here is how I am solving this question

if b<2 then b = {1,0,-1,-2...}

solving for x

2x - 3b = 0
2x = 3b
x = 3/2b or 1.5 b

since the highest possible value of b = 1, then highest possible value of x = 1.5 hence x<2 which is B

Correct answer is D

Can you explain how, Am I suppose to take b = {1.9, 1.8,1.7....} to solve these type questions or only integer values
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by Brent@GMATPrepNow » Mon May 06, 2013 7:55 am
sanaa.rizwan 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

here is how I am solving this question

if b<2 then b = {1,0,-1,-2...}

solving for x

2x - 3b = 0
2x = 3b
x = 3/2b or 1.5 b

since the highest possible value of b = 1, then highest possible value of x = 1.5 hence x<2 which is B

Correct answer is D

Can you explain how, Am I suppose to take b = {1.9, 1.8,1.7....} to solve these type questions or only integer values
Aside: When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

Your approach assumes that b is an integer but there's nothing in the question to suggest that this is the case. To solve this question for all possible (integer and non-integer values) try this approach:

Given: 2x = 3b [solve for b]
So, (2/3)x = b

We know that b < 2, so replace b with (2/3)x to get . . .
(2/3)x < 2
Multiply both sides by 3: 2x < 6
Divide both sides by 2: x < 3

Answer = D

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by GMATGuruNY » Mon May 06, 2013 10:58 am
sanaa.rizwan 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
An alternate approach is to show that four of the five answer choices DON'T have to be true.

Answer choice A: x > -3.
Test a value LESS than -3.
If we substitute x=-4 into 2x=3b, we get:
2(-4) = 3b
-8/3 = b.
Since b=-8/3 satisfies the constraint that b<2, it's possible that x=-4.
Eliminate A, C, and E, none of which includes x=-4 within its range.

Answer choice B: x < 2
Answer choice D: x < 3
Test a value BETWEEN 2 and 3.
If we substitute x=2.5 into 2x=3b, we get:
2(2.5) = 3b
b = 5/3.
Since b=5/3 satisfies the constraint that b<2, it's possible that x=2.5.
Eliminate B, which does not include x=2.5 within its range.

The correct answer is D.
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by Blue_Skies » Mon May 06, 2013 12:19 pm
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

here is how I am solving this question

if b<2 then b = {1,0,-1,-2...}

solving for x

2x - 3b = 0
2x = 3b
x = 3/2b or 1.5 b

since the highest possible value of b = 1, then highest possible value of x = 1.5 hence x<2 which is B

Correct answer is D

Can you explain how, Am I suppose to take b = {1.9, 1.8,1.7....} to solve these type questions or only integer values

Hi Sanna,
I wouldn't try to plug values and check for the answers in my first attempt for such questions.
This can be easily solved as the experts have solved it without plugging in answers.
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