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Confusion about the concept

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by Param800 » Fri Jan 04, 2013 8:22 pm
Hello Everyone,

Can anyone help me to understand this concept ?

Q. Is x < y ?
(1) The ratio of x to y is 7/9.
(2) xy > 0

OA E

First of all I understand that St 2 by its own is insufficient to solve this question as it [spoiler]doesn't[/spoiler] tell us any relation between x and y.

My main question is : When I solved this question, I choose A because, I did this :-

x/y = 7/9 < 1 ...so we can say x<y

But, after giving a second thought I noted that both x and y could both be negative and still the ratio would be 7/9... which will yield x>y.. and thus we will choose E

So, how do we know which method to choose basic algebra or method of substitution ? Or is it just a matter of practice?

Thank You
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Source: — Data Sufficiency |
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by GMATGuruNY » Sat Jan 05, 2013 5:33 am
Param800 wrote:Hello Everyone,

Can anyone help me to understand this concept ?

Q. Is x < y ?
(1) The ratio of x to y is 7/9.
(2) xy > 0

OA E

First of all I understand that St 2 by its own is insufficient to solve this question as it [spoiler]doesn't[/spoiler] tell us any relation between x and y.

My main question is : When I solved this question, I choose A because, I did this :-

x/y = 7/9 < 1 ...so we can say x<y

But, after giving a second thought I noted that both x and y could both be negative and still the ratio would be 7/9... which will yield x>y.. and thus we will choose E

So, how do we know which method to choose basic algebra or method of substitution ? Or is it just a matter of practice?

Thank You
I wouldn't worry about this problem.
Almost all GMAT problems about RATIOS involve a REAL-WORLD relationship: the ratio of teachers to students, the ratio of dogs to cats, etc.
The result is that ratio problems on the actual GMAT seem to be restricted to POSITIVE VALUES.

The following is a list of OG13 problems that use the word ratio:

PS: 11, 56, 66, 82, 98, 105, 113, 115, 125, 179, 200
DS: 23, 43, 47, 77, 81, 114, 148

In EVERY case, the problem is restricted to positive values.
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by ceilidh.erickson » Sat Jan 05, 2013 7:58 am
I agree that "ratio" wording is restricted to positive values in the OG.

But to your question about whether to pick values or solve algebraically... I find that with inequality problems, it's most helpful to think conceptually about the information given, before picking values or solving algebraically. Any time you see an inequality on DS, think about positives and negatives (unless a constraint is given specifying one or the other). Essentially, what statement (1) is saying is that x/y > 0. This means that they could both be positive or both be negative - they have the same sign. Statement (2) also tells us that they have the same sign, so in terms of positives and negatives, they're giving us the same information. There's no need to pick values to see that it would be insufficient.
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