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Neat working out - laying out your workings

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Neat working out - laying out your workings

by jsl » Sat Jul 05, 2008 1:48 pm
Hiya,

Does anyone have any advice for laying out your working outs on the quant section? When it comes to "testing" several sets of numbers such as picking numbers to find out whether or not a specific DS question is sufficient or not, I sometimes get in a muddle.

For example, if a question is looking to test you on what happens to both x and y when you raise both to either the power of 2 and power of 3, how would you lay out your workings? In this example, you should test fractions, positives & negatives and combinations of all those. Thus, there would be a lot to lay out.

Example question...

From which of the following does it follow that x must be greater than y?
a. x^2 > y
b. x^2 > y^2
c. x^3 > y^2
d. x^2 > y^3
e. x^3 > y^3

Do you have any tips you could share?
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Re: Neat working out - laying out your workings

by Ian Stewart » Sun Jul 06, 2008 1:33 pm
jsl wrote:Hiya,

Does anyone have any advice for laying out your working outs on the quant section? When it comes to "testing" several sets of numbers such as picking numbers to find out whether or not a specific DS question is sufficient or not, I sometimes get in a muddle.

For example, if a question is looking to test you on what happens to both x and y when you raise both to either the power of 2 and power of 3, how would you lay out your workings? In this example, you should test fractions, positives & negatives and combinations of all those. Thus, there would be a lot to lay out.

Example question...

From which of the following does it follow that x must be greater than y?
a. x^2 > y
b. x^2 > y^2
c. x^3 > y^2
d. x^2 > y^3
e. x^3 > y^3

Do you have any tips you could share?
Considering how much work it could be to test many sets of numbers here, you wouldn't want to test haphazardly. It's clearly going to save time to rule out as many answer choices as possible, as quickly as possible, by understanding what the inequalities actually say.

Notice that if x is negative, x^2 will be positive. So if x = -1,000,000 (say), x^2 will be bigger than any power of y if y = 1 or 0, but x will not be bigger than y. A, B and D are out.

In C, the power on x is larger than the power on y. We should thus expect x^3 to be larger than y^2 sometimes, even if x is smaller than y. Take x = 3, y = 4, for example.

That leaves E.

Testing numbers is sometimes a good strategy on the GMAT- some DS questions, for example, really are a test of what combinations of numbers we can imagine. Often enough, however, testing numbers can lead us to spend more time than necessary on a question, or can lead us into GMAT traps if we don't test enough combinations. One can certainly learn to test numbers 'well'- that is, to learn what combinations of numbers are important to check for different types of questions. But the more mathematical understanding you can bring to the problem, the better off you'll be.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by notgoodinmath » Tue Jul 08, 2008 2:26 pm
Im sorry but why would the answer be E
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by Stacey Koprince » Tue Jul 22, 2008 7:55 am
The wording of this question is definitely confusing. If you do try some numbers, as Ian showed, this is what happens:

From which of the following does it follow that x must be greater than y?
a. x^2 > y
b. x^2 > y^2
c. x^3 > y^2
d. x^2 > y^3
e. x^3 > y^3

The goal is to find which answer choice leads to the result that you can ONLY choose an x that is greater than what you choose for y.

If x= -2 and y = 1, then x is NOT greater than y, right? So if any of the answer choices DO work with these two numbers, then that is NOT the right answer, because we're supposed to find something from which we could conclude that x is ALWAYS greater than y.

a) x^2 > y would be 4>1. That's true, so this is not the right answer (because you can choose numbers such that a smaller x will make this statement still true).

b) x^2 > y^2 would be 4 > 1. That's true, so this is not the right answer.

c) x^3 > y^2 would be -8 > 1. That's false. Leave this one in for now.

d) x^2 > y^3 would be 4 > 1. True, so not right.

e) x^3 > y^3 would be -8 > 1. That's false, so leave this one in.

Now we're down to C and E.
The next set of numbers Ian tried: x=3 and y=4. (Again, a pair in which x is smaller than y, which is what we DON'T want, so statements that work with this pair will be wrong answers.)

c) x^3 > y^2 would be 27 > 16. That's true, so this isn't right.

e) x^3 > y^3 would be 27 > 64. That's false, so leave this one in.

E is the only one left, so it must be the right answer.

One other thing, note that Ian used his knowledge of exponent number properties to decide how to set up this problem and to know which numbers would be likely to help him figure this out efficiently. If you are going to use numbers, do try to think about what you're doing as much as you can. It takes a lot longer if you just blindly pick numbers without knowing how useful they might be to the setup of this particular problem. Picking numbers can be a great technique as long as you're thoughtful about it.
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