Problem Solving

Ian Stewart wrote:

hemantsood wrote:That is the correct way.

I'd prefer to say "That is a correct way"!

The above solution is certainly correct, but as with most math problems, there is more than one solution. If you understand that |a - b| measures the distance between a and b on the number line, you can look at the problem as follows:

3 < |x-5| < 7

This is reallly two inequalities:

3 < |x-5|, so x is more than 3 away from 5, on the left or the right: x < 2 or x > 8.

|x-5| <7, so x is less than 7 away from 5, on the left or the right: x > -2, or x < 12.

Combining these, we have -2 < x < 2 or 8 < x < 12. If x is an integer, x can be -1, 0, 1, 9, 10 or 11. Drawing the number line makes this easier, of course.

If 3 < |x-5| < 7 , where x is an integer, how many possible values does x have?

If 3 < |x| < 7 , where x is an integer, how many possible values does x have?

Ian Stewart wrote:

Stuart Kovinsky wrote:My "too much math" alarm is sounding! I've always been a fan of the quick and dirty solution to GMAT questions.

If 3 < |x-5| < 7 , where x is an integer, how many possible values does x have?

That's all fine for this question, but what if you're asked:

What is the area of the region in the (x,y)-plane consisting of all points for which 3 <= |x-5| <= 7 and |y| <= 2 ?

Or:

What is the longest distance between two points which both satisfy:
3 <= |x-5| <= 7 and |y| <= 2

I think there's a lot of value in learning how to work out the values of x which satisfy the absolute value equation, at least if you're aiming for a top Quant score.

What I'm really saying is that if you're aiming for a 90th+ percentile in GMAT math, turn your 'too much math' alarm off- you're going to need to do some math. It's when the math would take longer than two minutes that you should look for another approach. I don't see at all how this question could take close to that long, so it's certainly not a question of 'too much math'. And if you want to do well on difficult absolute value questions, understand what absolute value measures: distance. Every high-level GMAT absolute value question I've seen is testing exactly that, and if you understand that well, these problems are not difficult.

ildude02 wrote:Ian, thanks for your response. I didn't mean this question was "too much" of math. I have been juggling around with too many concepts and doing lot of math lately, so that's what I was referring to. I'm trying to stick with the concepts that I'm strong at, but at the same time, I'm learning new concepts if I feel I'm weak in a particular area. So all your reponses are appreciated and I only wish I had more time before my exam, since I learn some new technique's every other day on this forum.

Ian Stewart wrote:

Stuart Kovinsky wrote:My "too much math" alarm is sounding! I've always been a fan of the quick and dirty solution to GMAT questions.

If 3 < |x-5| < 7 , where x is an integer, how many possible values does x have?

That's all fine for this question, but what if you're asked:

What is the area of the region in the (x,y)-plane consisting of all points for which 3 <= |x-5| <= 7 and |y| <= 2 ?

Or:

What is the longest distance between two points which both satisfy:
3 <= |x-5| <= 7 and |y| <= 2

I think there's a lot of value in learning how to work out the values of x which satisfy the absolute value equation, at least if you're aiming for a top Quant score.

What I'm really saying is that if you're aiming for a 90th+ percentile in GMAT math, turn your 'too much math' alarm off- you're going to need to do some math. It's when the math would take longer than two minutes that you should look for another approach. I don't see at all how this question could take close to that long, so it's certainly not a question of 'too much math'. And if you want to do well on difficult absolute value questions, understand what absolute value measures: distance. Every high-level GMAT absolute value question I've seen is testing exactly that, and if you understand that well, these problems are not difficult.

Ian Stewart wrote:

Stuart Kovinsky wrote:My "too much math" alarm is sounding! I've always been a fan of the quick and dirty solution to GMAT questions.

If 3 < |x-5| < 7 , where x is an integer, how many possible values does x have?

That's all fine for this question, but what if you're asked:

What is the area of the region in the (x,y)-plane consisting of all points for which 3 <= |x-5| <= 7 and |y| <= 2 ?

Or:

What is the longest distance between two points which both satisfy:
3 <= |x-5| <= 7 and |y| <= 2

I think there's a lot of value in learning how to work out the values of x which satisfy the absolute value equation, at least if you're aiming for a top Quant score.

What I'm really saying is that if you're aiming for a 90th+ percentile in GMAT math, turn your 'too much math' alarm off- you're going to need to do some math. It's when the math would take longer than two minutes that you should look for another approach. I don't see at all how this question could take close to that long, so it's certainly not a question of 'too much math'. And if you want to do well on difficult absolute value questions, understand what absolute value measures: distance. Every high-level GMAT absolute value question I've seen is testing exactly that, and if you understand that well, these problems are not difficult.