Three numbers on the number line

[gander123]

Hey guys,

Here comes the problem:

QDS08429 Official Prep Software pack:

" <-----a------b------->

If a,b and c are three numbers on the number line shown above, is c between a and b?

(1) b < 0

(2) a - b > c

Correct answer: E

Official Answer explanation:

Determine if c lies between a and b on the number line.

(1) It is given that b < 0, but nothing is known about a and c; NOT Sufficient.

(2) Given that a - b > c, it is possible that c lies between a and b (for example, a = 0, b = -2, and c = -1) and it is possible that c does not lie between a and b (for example, a = 0, b = -2, and c = 1). NOT Sufficient.

Given both (1) and (2) together, the examples given in (2) above show that both statements together are not NOT sufficient to determine if c lies between a and b."

Thats why I think the answer explanation is seriously flawed:

Statement one: fully agree with.

Statement two: From my point of view, a point b right to a point a on the number line cannot be smaller than that point a. However, since b = -2 is smaller than a = 0 the authors of the test seem to disagree with my standpoint (see the boldfaced portions of the official answer explanation). Do I need enlightenment ?!

Nevertheless, since the reasoning seems fine, I would suggest picking the following values:

Statement 2: c can lie between a and b for the values a = - 4 , b = -2 and c = -3, then a - b = -2 > - 3 and c lies between a and b. On the other hand c can lie outside range a and b for the values a = -2 b = -1 c = -3, then a-b = -1 > - 3 and c does not lie between a and b.

Since both the values introduced in Statement two also satisfy the constraint in (1) E would still be the appropriate answer choice.

What do you guys come up with ?

Kind regards,

Tobi

[Brent@GMATPrepNow]

Hey guys,

Here comes the problem:

QDS08429 Official Prep Software pack:

" <-----a------b------->

If a,b and c are three numbers on the number line shown above, is c between a and b?

(1) b < 0

(2) a - b > c

Correct answer: E

Official Answer explanation:

Determine if c lies between a and b on the number line.

(1) It is given that b < 0, but nothing is known about a and c; NOT Sufficient.

(2) Given that a - b > c, it is possible that c lies between a and b (for example, a = 0, b = -2, and c = -1) and it is possible that c does not lie between a and b (for example, a = 0, b = -2, and c = 1). NOT Sufficient.

Given both (1) and (2) together, the examples given in (2) above show that both statements together are not NOT sufficient to determine if c lies between a and b."

Thats why I think the answer explanation is seriously flawed:

Statement one: fully agree with.

Statement two: From my point of view, a point b right to a point a on the number line cannot be smaller than that point a. However, since b = -2 is smaller than a = 0 the authors of the test seem to disagree with my standpoint (see the boldfaced portions of the official answer explanation). Do I need enlightenment ?!

Nevertheless, since the reasoning seems fine, I would suggest picking the following values:

Statement 2: c can lie between a and b for the values a = - 4 , b = -2 and c = -3, then a - b = -2 > - 3 and c lies between a and b. On the other hand c can lie outside range a and b for the values a = -2 b = -1 c = -3, then a-b = -1 > - 3 and c does not lie between a and b.

Since both the values introduced in Statement two also satisfy the constraint in (1) E would still be the appropriate answer choice.

What do you guys come up with ?

Kind regards,

Tobi

You're absolutely correct, Tobi (unless you've transcribed the question incorrectly ).
In the number line diagram, we're told that a < b, but both examples in the solution (e.g., a = 0, b = -2, and c = -1) break that given condition.

Having said that, the correct answer is still E. Here's my solution:

Target question: is c between a and b?

Statement 1: b < 0
No information about c, so statement 1 is NOT SUFFICIENT

Statement 2: a - b > c
There are several sets of numbers that meet this condition. Here are two:
Case a: a = -3, b = -1 and c = -2.5 in which case c is between a and b
Case b: a = -3, b = -1 and c = -5 in which case c is not between a and b
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
There are still several sets of numbers that meet this condition. Here are two:
Case a: a = -3, b = -1 and c = -2.5 in which case c is between a and b
Case b: a = -3, b = -1 and c = -5 in which case c is not between a and b
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

[gander123]

Hey Brent,

this was the second time that the two of us recognized a mistake in the prep software answer explanations... We're getting good at it. Honestly, the solutions need some revision... It was only a minor mistake, sure, but I wouldn't have posted the problem to receive positive feedback, had the explanations been 100 per cent correct...

Thanks anyway....

Cheers,

Tobi