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if b < 1 and 2x - b = 0

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if b < 1 and 2x - b = 0

by redng » Wed May 02, 2012 3:20 pm
If b<1 and 2x-b=0, which of the following must be true?
  • A. x > -1
    B. x < -2
    C. x = 2
    D. x < 3
    E. x > 3
OA: D

source: Kaplan GMAT Diagnostic Quiz

I though it was B, can someone explain? thanks
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by karthikchandru » Wed May 02, 2012 7:25 pm
It pretty much boils down to x<1/2 because b<1 and b=2x.
Now, answer choice B says that x<-2. However, x can be -1 in which case this statement doesn't hold true. But, with answer choice D: x<3, if x=-1 it would still hold true. Moreover, x cannot be, say, 1 because it is given that x<1/2.
Hope this helps.
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by Stuart@KaplanGMAT » Wed May 02, 2012 11:31 pm
redng wrote:If b<1 and 2x-b=0, which of the following must be true?
  • A. x > -1
    B. x < -2
    C. x = 2
    D. x < 3
    E. x > 3
OA: D

source: Kaplan GMAT Diagnostic Quiz

I though it was B, can someone explain? thanks
Hi! Like many GMAT questions, we should start by simplifying the question itself.

We know that b < 1 and that 2x-b=0. We can rewrite the equation as:

2x = b

Putting the two statements together:

2x = b < 1
2x < 1
x < 1/2

Now we need to find the answer that MUST be true, given that x < 1/2.

A) x > -1. Nope! If x = -100, then x < 1/2 and (A) is false.
B) x < -2. Nope! If x = 0 then x < 1/2 and (B) is false.
C) x = 2. Nope, if x < 1/2 it can't be equal to 2.
D) x < 3. YES! If x is less than a number smaller than 3, it's always going to be less than 3 as well. Choose (D)!
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by aneesh.kg » Wed May 02, 2012 11:47 pm
Let's solve it using Co-ordinate Geometry.
We'll draw b and x axes.

Figure below shows the b < 1 region.

Image

Drawing the line b = 2x.

Image

Mark the point of intersection as shown below.

Image

In the figure shown: if x < 0.5, x will surely be smaller than 3 in our favourable part of the line (shown in purple). None of the other options are a certainty.
Image

Option [spoiler](D) [/spoiler]is true.

See another problem solved easily with the help of Co-ordinate Geometry:
https://www.beatthegmat.com/if-y-0-is-y- ... tml#469314
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hi

by Jeff@TargetTestPrep » Mon Feb 26, 2018 10:26 am
redng wrote:If b<1 and 2x-b=0, which of the following must be true?
A. x > -1
B. x < -2
C. x = 2
D. x < 3
E. x > 3
Manipulating the equation we have 2x = b, thus:

2x < 1

x < 1/2

Thus, x must be less than 3.

Note that the correct answer x < 3 may be confusing. Here's the logic: we determined algebraically that x must be less than 1/2. Thus, some possible values for x are 1/4 , 0, -2/3, -5, and so on. Note that each of these values is, indeed, less than 3 (which is answer choice D). In fact, any value of x that satisfies x < 1/2 will ALSO satisfy x < 3. Hence, answer choice D is correct.

Answer: D

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TTT

by deloitte247 » Sat Mar 03, 2018 1:26 pm
If 2x-b=0
b=2x
Also , b<1
or 2x<1
Divide through by 2
we obtain x< 1/2...
The answer is x< 1/2...
Based on my understanding, i am convince that none of these options given are right<i class="em em-scream"></i><i class="em em-confused"></i>
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by [email protected] » Sun Mar 04, 2018 4:16 pm
Hi redng,

We're told that B < 1 and 2(X) - B = 0. We're asked which of the following MUST be true (which really means "which of the following is ALWAYS true no matter how many different examples we come up with)." We can answer this question by TESTing VALUES.

Since B < 1, let's start with B = 0....
IF... B=0, then 2X - 0 = 0 means that X = 0
Eliminate Answers B, C and E.

Next, let's look for something NEGATIVE....
IF... B = -2, then 2X - (-2) = 0 means that 2X + 2 = 0 and X = -1
Eliminate Answers A

Final Answer: D

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