## absolute value

##### This topic has expert replies
Junior | Next Rank: 30 Posts
Posts: 17
Joined: 02 Jun 2008

### absolute value

by yakiraz » Mon Jun 30, 2008 7:00 pm

Master | Next Rank: 500 Posts
Posts: 132
Joined: 27 Apr 2008
Location: Portugal
Thanked: 7 times
by atlantic » Tue Jul 01, 2008 2:08 am
I got D. Is it the OA?

Post explanation later.

Junior | Next Rank: 30 Posts
Posts: 17
Joined: 02 Jun 2008
by yakiraz » Tue Jul 01, 2008 3:47 am
yep

Master | Next Rank: 500 Posts
Posts: 320
Joined: 13 Jan 2008
Thanked: 10 times
by ildude02 » Tue Jul 01, 2008 3:00 pm
can someone please explain the reasoning, appreciate it. I choose D as well but not sure if I used the best approach since I went about by picking numbers and backsolving. I assume there is an easier to solve it ?

Master | Next Rank: 500 Posts
Posts: 246
Joined: 19 May 2008
Location: Texaco Gas Station
Thanked: 7 times
by cubicle_bound_misfit » Wed Jul 02, 2008 7:11 am
Even I did the same and this is taking hell lot of time.
Can someone please discuss a better approach ?

regards,
Cubicle Bound Misfit

### GMAT/MBA Expert

GMAT Instructor
Posts: 2615
Joined: 02 Jun 2008
Location: Toronto
Thanked: 1090 times
Followed by:355 members
GMAT Score:780
by Ian Stewart » Wed Jul 02, 2008 10:55 am
Almost every difficult absolute value question on the GMAT is testing whether you understand that absolute value measures distance:

|c| is the distance, on the number line, from c to zero;
|c - d| is the distance, on the number line, between c and d.

The question tells us a < y < z < b. We know a is furthest to the left on the number line, b furthest to the right, and y is closer to a than z is. We can draw the points on the number line. The question asks:

Is |y - a| < |y - b|?

In words, using the distance interpretation above, this just asks "Is the distance between y and a less than the distance between y and b?" In other words, "Is y closer to a than it is to b?"

1) tells us that z is closer to a than to b. Well, y is even closer to a than z is, so y must be closer to a than to b. Sufficient.

2) tells us that y is closer to a than z is to b. Well, y is even further away from b than z is, so y must be closer to a than to b. Sufficient.

D.

It's a lot easier if you draw the number line and think about what the distance statements are telling you while looking at the picture.
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Master | Next Rank: 500 Posts
Posts: 443
Joined: 28 Jun 2008
Thanked: 5 times
by Vignesh.4384 » Mon Aug 25, 2008 8:57 pm
Ian Stewart wrote:Almost every difficult absolute value question on the GMAT is testing whether you understand that absolute value measures distance:

|c| is the distance, on the number line, from c to zero;
|c - d| is the distance, on the number line, between c and d.

The question tells us a < y < z < b. We know a is furthest to the left on the number line, b furthest to the right, and y is closer to a than z is. We can draw the points on the number line. The question asks:

Is |y - a| < |y - b|?

In words, using the distance interpretation above, this just asks "Is the distance between y and a less than the distance between y and b?" In other words, "Is y closer to a than it is to b?"

1) tells us that z is closer to a than to b. Well, y is even closer to a than z is, so y must be closer to a than to b. Sufficient.

2) tells us that y is closer to a than z is to b. Well, y is even further away from b than z is, so y must be closer to a than to b. Sufficient.

D.

It's a lot easier if you draw the number line and think about what the distance statements are telling you while looking at the picture.
Hi Ian,

As per your explanation .. i consider 4 point on the number line

a = -4
y = 1
z = 2
b = 3

This follows the rule a < y < z < b.

Here if u notice the distance between y and a is greater than y and b right ?

Could you please explain this ?

GMAT Instructor
Posts: 3225
Joined: 08 Jan 2008
Location: Toronto
Thanked: 1710 times
Followed by:613 members
GMAT Score:800
by [email protected] » Mon Aug 25, 2008 11:33 pm
Vignesh.4384 wrote:Hi Ian,

As per your explanation .. i consider 4 point on the number line

a = -4
y = 1
z = 2
b = 3

This follows the rule a < y < z < b.

Here if u notice the distance between y and a is greater than y and b right ?

Could you please explain this ?
The numbers you picked violate both statements, so are impermissable for this question.

1) tells us that z is closer to a than to b. In your example, z is closer to b than to a.

2) tells us that y is closer to a than z is to b. In your example, z is closer to b than y is to a.

Remember, there are 2 steps to picking numbers in data sufficiency:

1) Pick permissible numbers. The numbers you select MUST follow the rules given in the question stem and in the statement (or statements) that you're evaluating.

2) Plug the numbers you've chosen back into the original question to see what answer you get.

The numbers you've chosen don't pass the rule in step (1), so you have to discard them and pick new numbers.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for \$100 off a full course

Master | Next Rank: 500 Posts
Posts: 443
Joined: 28 Jun 2008
Thanked: 5 times
by Vignesh.4384 » Tue Aug 26, 2008 12:10 am
Thanks Stuart.
I guess i dint read the question properly

Legendary Member
Posts: 1578
Joined: 28 Dec 2008
Thanked: 82 times
Followed by:9 members
GMAT Score:720
by maihuna » Mon Apr 13, 2009 10:25 am
Ian,
You provided fantastic soln but can you elaborate please with an algebraic solution?

### GMAT/MBA Expert

GMAT Instructor
Posts: 2615
Joined: 02 Jun 2008
Location: Toronto
Thanked: 1090 times
Followed by:355 members
GMAT Score:780
by Ian Stewart » Mon Apr 13, 2009 2:52 pm
maihuna wrote:Ian,
You provided fantastic soln but can you elaborate please with an algebraic solution?
I wouldn't normally do this kind of question algebraically, but it is certainly possible. We need to use the fact that |x| = x if x is positive, and |x| = -x if x is negative.

Since we're given that a < y < z < b, we can easily work out whether the expressions in each absolute value are positive or negative. Note also that since y < z, then 2y < 2z must be true.

-- In the question itself, we're asked if |y-a| < |y-b|. Since y - a is positive, |y - a| = y - a. Since y - b is negative, |y - b| = b - y. So the question is just asking if y - a < b - y, or if 2y < a + b.

-- Statement 1 tells us that |z - a| < |z - b|. As above, z - a is positive and z - b is negative, so this really tells us that z - a < b - z, or 2z < a + b. Well since 2y < 2z, then 2y < a + b must be true. Sufficient.

-- Statement 2 tells us that |y - a| < |z - b|. As above, y - a is positive and z - b is negative, so this really tells us that y - a < b - z, or y + z < a + b. Now, since y < z, y + y must be less than y + z, so 2y must be less than a + b. So this statement is also sufficient.

As I said above, however, I wouldn't personally consider taking this approach to this question.
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Legendary Member
Posts: 1578
Joined: 28 Dec 2008
Thanked: 82 times
Followed by:9 members
GMAT Score:720
by maihuna » Tue Apr 14, 2009 10:40 am
Thank you very much Ian, for taking time out of your busy schedule and explaining it in great detail. Wonderful, thank you again.

I am struggling with absolute value questions a lot and may trouble you on some more questions, please bear with me.

Master | Next Rank: 500 Posts
Posts: 246
Joined: 19 May 2008
Location: Texaco Gas Station
Thanked: 7 times
by cubicle_bound_misfit » Tue Apr 14, 2009 11:36 am
maihuna,
for absolute value questions, u got the right guy to ask
Cubicle Bound Misfit

• Page 1 of 1