Inequality ques???

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pardeep_10sharma: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Tue Mar 02, 2010 9:38 am; Location: India; Followed by:1 members; GMAT Score:540

Inequality ques???

by pardeep_10sharma » Fri Jun 18, 2010 5:22 am

If x and y are integers and x > 0, is y > 0?

(1) 7x - 2y > 0

(2) -y < x

By me Ans shoud be :- A as it fits all the parameters of being positive.

But ans given by test makers is :- E

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Source: Beat The GMAT — Data Sufficiency | Fri Jun 18, 2010 5:22 am

asamaverick: Master | Next Rank: 500 Posts; Posts: 106; Joined: Mon Sep 28, 2009 9:29 am; Location: Boston, MA; Thanked: 26 times; Followed by:2 members; GMAT Score:700

by asamaverick » Fri Jun 18, 2010 5:31 am

What made you go for a A?
(1) gives is 7x > 2y
Consider these x = 1, = 2. Yes y > 0
x = 2, y = -1. No y < 0

So A is not the right answer.

We can easily prove that (2) alone is not sufficient.

Combining the two:

7x -2y > 0
x + y > 0

Multiply second one by 2 and add. This gives.
9 x > 0
So all we know is x is positive. This still is not enough to say if y > 0. Hence E.

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tpr-becky: GMAT Instructor; Posts: 509; Joined: Wed Apr 21, 2010 1:08 pm; Location: Irvine, CA; Thanked: 199 times; Followed by:85 members; GMAT Score:750

by tpr-becky » Fri Jun 18, 2010 8:25 am

We are being asked if y is positive - given the parameters that x is positive and 7x-2y>0 this is an algebra inequality so we have to be careful about signs and may need to solve for actual values.

1 says 7x>2y - which means that 7/2(x)>y = so we know that some positive number is greater than y - this doesn't tell us whether y is positive or negative so it is insufficient. BCE

2. Says that -y<x - we know here that x is positive so we know that -y is less than a positive number. This still leaves both positive and negative options open - either y is negative so basically the positive value of y is less than another positive - or y is positive and teh negative value of y is less thana positive number - this isn't enough information.

if you put them together both statements allow for positive and negative values for y -and together they offer no new information - so the answer is E.

Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA

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jube: Master | Next Rank: 500 Posts; Posts: 186; Joined: Fri May 28, 2010 1:05 am; Thanked: 11 times

by jube » Fri Jun 18, 2010 8:30 am

asamaverick wrote: Combining the two:

7x -2y > 0
x + y > 0

Multiply second one by 2 and add. This gives.
9 x > 0
So all we know is x is positive. This still is not enough to say if y > 0. Hence E.

So why can't you multiply the 2nd equation by 7 which will give you:

7x - 2y > 0
7x + 7y > 0

and then subtract the 2 eqns which will give you -9y > 0 i.e. y HAS to be < 0 in which case the answer has to be C.

I'm guessing there's something I'm missing out when solving the 2 inequalities simultaneously. Can someone help me understand what it is? Should you NOT solve inequalities simultaneously? Thanks.

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asamaverick: Master | Next Rank: 500 Posts; Posts: 106; Joined: Mon Sep 28, 2009 9:29 am; Location: Boston, MA; Thanked: 26 times; Followed by:2 members; GMAT Score:700

by asamaverick » Fri Jun 18, 2010 12:03 pm

jube wrote:
So why can't you multiply the 2nd equation by 7 which will give you:

7x - 2y > 0
7x + 7y > 0

and then subtract the 2 eqns which will give you -9y > 0

As a general rule, you can add inequalities but not subtract them.
For example, consider:

6 > 4 and
4 > 1

we can add them and know that:

10 > 5

but we can't subtract them and get:

2 > 3