Is x > 0?

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uptowngirl92: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 19, 2009 9:08 pm; Location: Kolkata,India; Thanked: 7 times; GMAT Score:670

Is x > 0?

by uptowngirl92 » Fri Oct 23, 2009 5:31 pm

Is x > 0?

(1) |x + 3| = 4x - 3

(2) |x + 1| = 2x - 1

...................................

The question stem asks is x>0??

Stmt 1: |x + 3| = 4x - 3
Two cases:
a. x+3=4x-3 ,x=0
b. -(x+3)=4x-3 ,x=0.

Both cases gives us x=0 hence SUFF.

Stmt 2: |x + 1| = 2x - 1
Again two cases:
a.x+1=2x-1
x-2x=-1-1
x=2

b. -(x+1)=2x-1
x=0
Both case gives us diff. values hence insuff.

IMO: A

Please point out my flaw.

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Source: Beat The GMAT — Data Sufficiency | Fri Oct 23, 2009 5:31 pm

Harbinder: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Fri Oct 23, 2009 5:59 pm; Thanked: 2 times

by Harbinder » Fri Oct 23, 2009 6:25 pm

I think u did a calculation mistake in calculating first case of the stmt 1 , x should be 2. So both statements give the same result which is x=0 or 2 so answer should be E

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uptowngirl92: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 19, 2009 9:08 pm; Location: Kolkata,India; Thanked: 7 times; GMAT Score:670

by uptowngirl92 » Fri Oct 23, 2009 6:39 pm

Yes!I did!Thasnk you for pointing it out!
How is the answer D in tht case??

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uptowngirl92: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 19, 2009 9:08 pm; Location: Kolkata,India; Thanked: 7 times; GMAT Score:670

by uptowngirl92 » Fri Oct 23, 2009 6:43 pm

oh got it..you have to put back the values and only 2 will hold:)

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Harbinder: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Fri Oct 23, 2009 5:59 pm; Thanked: 2 times

by Harbinder » Fri Oct 23, 2009 7:30 pm

I think we are supposed to put the answers back into the equation to see which one works and in this case only x=2 works for both statements so it gives us a definte answer....
x =0 gives 3 = -3 in first stmt and 1=-1 in second stmt...

even I didn't think of it when I tried this the first time but I guess that's how we should be approaching this problem...

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sudeeparies: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Thu Sep 27, 2007 6:22 am

by sudeeparies » Fri Oct 23, 2009 7:42 pm

so is the OA C or E? If we combine statement A and B we get a definite 2, so shouldnt the answer be C

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uptowngirl92: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 19, 2009 9:08 pm; Location: Kolkata,India; Thanked: 7 times; GMAT Score:670

by uptowngirl92 » Fri Oct 23, 2009 7:57 pm

OA IS D

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sudeeparies: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Thu Sep 27, 2007 6:22 am

by sudeeparies » Fri Oct 23, 2009 8:16 pm

sorry, my mistake. we still cannot arrive at a conclusion by combining A and B. So, the answer should be E, it cannot be D. Which OG is this from?

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

Re: Is x > 0?

by Stuart@KaplanGMAT » Fri Oct 23, 2009 8:40 pm

uptowngirl92 wrote:Is x > 0?

(1) |x + 3| = 4x - 3

(2) |x + 1| = 2x - 1

Let's think this question through instead of doing it purely algebraically.

In both statements, we know that the the left side is equal to or greater than 0 (since it's absolute value). Therefore, the right side must also be greater than or equal to 0.

So, for (1) we know that:

4x - 3 >= 0
4x >= 3
x >= 3/4

If x is greater than or equal to 3/4, is it always going to be greater than 0? YES!

We can reason through statement (2) the same way to get:

2x - 1 >= 0
2x >= 1
x >= 1/2

If x is greater than or equal to 1/2, is it always going to be greater than 0? YES!

So, each statement confirms on its own that x must be greater than 0: choose (D).