## Is x less than 20? Ron? Stacey? Others?

Math questions from mba.com and GMAT Prep software
ells1986
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### Is x less than 20? Ron? Stacey? Others?

Question: Is x less than 20?
(St 1): The sum of x and y is less than 20.
(St 2): y is less than 20.

From GMAT prep software. OA is E. My problem is NOT seeing why E is correct. I can easily pick numbers and prove why that is so. The thing that has me baffled is why a straightforward algebraic approach doesn't work. I always thought you could add inequalities as long as the ineq symbol was pointed in the same direction. Also, if you look at the thread for the question "Is xy<20?" you'll see a suggestion that this is the case (from Ron P).

So, when I saw this question, I quickly wrote the question as "Is x<20." I then wrote statement 1 as "x+y < 20" and I wrote statement 2 as "y< 20." After quickly eliminating S1 & S2, I subtracted S2 from S1 and I got x < 0. If x<0, then x MUST BE less than 20. So I picked C and moved on, thinking I'd cracked it with no sweat. Where did I go wrong? What's the underlying principle I'm missing? I thought I'd shredded this one quickly and was surprised to see the result. It's got me questioning a tool I thought was a basic one for inequalities. Many thanks.
ells1986
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### Re: Is x less than 20? Ron? Stacey? Others?

Whups, slight correction to my earlier post: the prior forum question I was referring to (that Ron had commented on with the suggestion "add two inequalities if their signs are pointed in the same direction") was: "Is xy > 0?"
RonPurewal
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### Re: Is x less than 20? Ron? Stacey? Others?

your problem is that you are overextending rules.

here, you make an absolutely correct statement of the rule:

ells1986 wrote:I always thought you could add inequalities as long as the ineq symbol was pointed in the same direction.

(emphasis mine)

... but then you did this:
After quickly eliminating S1 & S2, I subtracted S2 from S1 and I got x < 0.

your rule DOES NOT allow you to subtract the inequalities; it allows you only to add them. so this is incorrect.

don't overextend rules! make sure that you know the boundaries of the rules -- specifically, to which operations they apply, and to which they don't.
ells1986
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### Re: Is x less than 20? Ron? Stacey? Others?

Many thanks. And a lesson I won't soon forget! (that's how it works, doesn't it.)
mschwrtz
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### Re: Is x less than 20? Ron? Stacey? Others?

We're glad that Ron could help.
wonuorah
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### Re: Is x less than 20? How is it E

I added the two statements and had x + 2y < 40. So what should we do next to conclude that E is the answer. Thanks
Last edited by wonuorah on Mon Jun 07, 2010 10:47 am, edited 1 time in total.
suneelv001
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### Re: Is x less than 20? Ron? Stacey? Others?

Hi wonuorah,

Statement1: X+Y < 20

Scenario 1: x = 25 , y= -8 , x+y = 17 ------> x> 20
Scenario 2: x = 15, y= 3, x+Y = 18 ------> x < 20

hence, INSUFFICIENT

Statement2: Y < 20

Clearly INSUFFICIENT

So, QA is E

Ron, please let me know if my approach is correct
wonuorah
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### Re: Is x less than 20? Ron? Stacey? Others?

Yes,
I am okay with knowing Aand B are insufficient, but how do you combine the two equations ( which must have made us strike out option C) before determining the answer is E.

Thanks
Last edited by wonuorah on Sun Jun 06, 2010 8:27 pm, edited 1 time in total.
suneelv001
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### Re: Is x less than 20? Ron? Stacey? Others?

Okay!!!!

Combining the two statements

x+y< 20 and y<20, take extreme values,

y= 18, x= 1, x+y = 19 then x < 20

y= -3, x= 22 then, x+y = 19 but x > 20

Hence it is E.
wonuorah
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### Re: Is x less than 20? Ron? Stacey? Others?

Thanks for the explanation.
RonPurewal
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### Re: Is x less than 20? How is it E

I added the two statements and had x + 2y < 40. So what should we do next to conclude that E is the answer. Thanks

be very careful when you do this sort of thing -- if you combine TWO equations into ONE equation, the resulting equation does not carry as much information as did the two original equations.
in other words, it's quite possible to add the inequalities together and arrive at one, combined inequality that is NOT sufficient to address the given question -- even though the two inequalities, taken together, ARE sufficient to address the given question.

for instance, consider the following problem (from GMAT PREP)
Is m + z > 0?
(1) z - 3m > 0
(2) 4m - z > 0
if you add these two inequalities together, you get m > 0, which by itself is not sufficient to address the question.
however, if you realize that the two original inequalities are still valid, then the observation that z > 3m (from statement 1), COMBINED with the combined inequality m > 0, lets you conclude that z is also positive -- which means m + z > 0. sufficient.

so, big takeaway here:
if you combine two or more equations/inequalities in a data sufficiency problem, DO NOT FORGET ABOUT THE ORIGINAL EQUATIONS/INEQUALITIES.