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by mathewmithun » Thu May 17, 2012 12:25 am
Shalabh's Quants wrote:Dear Mithun,

See this one from Master GMAT.

https://www.beatthegmat.com/mba/2012/04/ ... perts-miss
thank you once again Shalabh. I think I can face must be true questions henceforth...

I would like to thank Aneesh, Mitch and others too...
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by Mo2men » Thu Jun 30, 2016 11:40 pm
GMATGuruNY wrote:
mathewmithun wrote:If x/lxl<x, which of the following must be true about x
(Note: Read lxl as modulus x)

A) x>1
B) x>-1
C) lxl<1
D) lxl = 1
E) lxl^2 > 1
An efficient approach is to COMPARE THE ANSWER CHOICES and to plug in values that are included in some ranges but not in others.

A: x > 1
B: x > -1

x=-1/2 is included in the range of answer choice B but not in the range of answer choice A.
Plugging x = -1/2 into x/lxl<x, we get:
(-1/2)/|1/2| < -1/2
-1 < -1/2.
This works.
Eliminate A and any other answer choice that does not include x=-1/2 within its range.
Eliminate A, D and E.

B: x > -1
C: |x| < 1.

x=2 is included in the range of answer choice B but not in the range of answer choice C.
Plugging x=2 into x/lxl<x, we get:
(2)/|2| < 2
1 < 2.
This works.
Eliminate C.

The correct answer is B.
Dear Mitch,

I understood the solution but I have a doubt about Choice B.

Choice B is: X>-1, does it mean that 0 included in the choice B, while X can't be 0 as it will make denumerator be 0.

Thanks
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by GMATGuruNY » Fri Jul 01, 2016 5:23 am
Mo2men wrote:Dear Mitch,

I understood the solution but I have a doubt about Choice B.

Choice B is: X>-1, does it mean that 0 included in the choice B, while X can't be 0 as it will make denominator be 0.

Thanks
I offer an alternate approach here:
https://www.beatthegmat.com/let-get-abso ... 27383.html

The alternate approach indicates two ranges that satisfy x/|x| < x:
-1<x<0 and x>1.
Question stem:
Which of the following must be true about x?
B: x>-1
Since both of the ranges in red are to the right of -1 on the number line, it must be true that x>-1.
Thus, answer choice B must be true about x.

The OA does not imply that EVERY value greater than -1 is a valid solution for x/|x|<x.
It implies the reverse:
That every valid solution for x/|x|<x is greater than -1.
Last edited by GMATGuruNY on Sun Jul 03, 2016 4:18 am, edited 1 time in total.
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by mjmehta81 » Sat Jul 02, 2016 7:41 pm
Hello Mitch,
I do not understand where I am wrong in my understanding below.

For option A.. let x=3, so 3/mod(3)=1. 1 less than 3. This is true for all value of x greater than 1. So why A is wrong option.
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by [email protected] » Sat Jul 02, 2016 9:56 pm
Hi mjmehta81,

When a question asks "which of the following must be true...", it's ultimately asking "which of the following is ALWAYS TRUE no matter how many different examples you come up with..."

With X = 3, three of the answer choices "appear" to be true (Answers A, B and E), but they can't all always be true, so you have to do a bit more work to eliminate two of the answer choices. If you try X = -1/2, you'll end up with....

(-1/2)/|-1/2| < -1/2
(-1/2)/(1/2) < -1/2
-1 < -1/2

Thus, X COULD be -1/2. With this solution, you can eliminate answers A and E, leaving just one option.

Final Answer: B

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by GMATGuruNY » Sun Jul 03, 2016 4:25 am
mjmehta81 wrote:Hello Mitch,
I do not understand where I am wrong in my understanding below.

For option A.. let x=3, so 3/mod(3)=1. 1 less than 3. This is true for all value of x greater than 1. So why A is wrong option.
Question stem:
What must be true about EVERY valid solution for x/|x|<x?
You have correctly determined that x=3 is a valid solution for x|x|<x.
But x=-1/2 is also a valid solution for x|x|<x.
Since it does NOT have to true that EVERY valid for solution x|x|<x is greater than 1, eliminate A.
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by Matt@VeritasPrep » Thu Jul 07, 2016 4:02 pm
In a nutshell, "x must be > -1" ≠ "any number > -1 is a possible value of x". (In GMAT terms, this is the difference between a NECESSARY condition and a SUFFICIENT condition.)
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