if b < 1 and 2x - b = 0

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.

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)!

Let's solve it using Co-ordinate Geometry.
We'll draw b and x axes.

Figure below shows the b < 1 region.



Drawing the line b = 2x.



Mark the point of intersection as shown below.



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.


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

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

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>