Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Thank's in advance for helping to solve the problem, the OA should be ( C ) , but I'm not sure 100% about it; a friend gave to me several GMAT exercises for training.

Re: If a ≠ b and |a-b| = b-a, which of the following statements [#permalink]
27 Mar 2013, 04:06

3

This post received KUDOS

Expert's post

If a ≠ b and |a-b| = b-a, which of the following statements must be true ?

I. a < 0 II. a + b < 0 III. a < b

(A) None (B) I only (C) III only (D) I and II (E) II and III

Absolute value properties:

When x\leq{0} then |x|=-x, or more generally when some \ expression\leq{0} then |some \ expression|={-(some \ expression)}. For example: |-5|=5=-(-5);

When x\geq{0} then |x|=x, or more generally when some \ expression\geq{0} then |some \ expression|={some \ expression}. For example: |5|=5;

Thus, according to the above, since |a-b| = b-a=-(a-b), then a-b\leq{0} --> a\leq{b}. Since we also know that a\neq{b}, then we have that a<b. So, III is always true.

As for the other options: I. a < 0 --> not necessarily true, consider a=1 and b=2. II. a + b < 0 --> not necessarily true, consider a=-2 and b=-1.

Re: If a ≠ b and |a-b| = b-a, which of the following statements [#permalink]
26 Mar 2013, 23:26

1

This post received KUDOS

The given conditions are : i) a is not equal to b ,i,e a-b is non zero. ii) |a -b | = b-a ,i,e -(a-b). So ,considering the above conditions, a - b < 0 => a < b. _________________

Re: If a b and |a-b| = b-a, which of the following statements [#permalink]
15 Jun 2013, 22:32

1

This post received KUDOS

WholeLottaLove wrote:

So, in other words,

I.) |a-b| = b-a II.) b-a is positive because it is equal to an absolute value III.) b must be greater than a because b-a is positive IV.) a-b must be negative V.) |a-b| = -(a-b) VI.) a-b ≤ 0 VII.) a ≤ b

Yes, perfect. Just remember that we are told that a\neq{b} so

VII)a<b _________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: If a b and |a-b| = b-a, which of the following statements [#permalink]
15 Jun 2013, 16:58

So, in other words,

I.) |a-b| = b-a II.) b-a is positive because it is equal to an absolute value III.) b must be greater than a because b-a is positive IV.) a-b must be negative V.) |a-b| = -(a-b) VI.) a-b ≤ 0 VII.) a ≤ b

Zarrolou wrote:

WholeLottaLove wrote:

Because |a-b| = b-a, could we say that b-a is positive (because it is equal to an abs. val.) and therefore, b must be greater than a?

Also, I first tired to solve this problems by:

|a-b| = b-a so:

a-b = b-a 2a = 2b a=b (which isn't true as the stem tells us it isn't)

OR

-a+b=b-a 0=0

But I'm not sure how to interpret that result. Is that a valid way to solve the problem?

The second result tells you that whatever value a and b have, that equation will always be true: 0=0 always.

0=0 means that that case will always hold, hence that case (b>a) will always be "true"

Re: If a b and |a-b| = b-a, which of the following statements [#permalink]
16 Jun 2013, 06:58

Ahh - I forgot about that. Thanks!

Zarrolou wrote:

WholeLottaLove wrote:

So, in other words,

I.) |a-b| = b-a II.) b-a is positive because it is equal to an absolute value III.) b must be greater than a because b-a is positive IV.) a-b must be negative V.) |a-b| = -(a-b) VI.) a-b ≤ 0 VII.) a ≤ b

Yes, perfect. Just remember that we are told that a\neq{b} so