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Is integer R positive?

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Is integer R positive? [#permalink]

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Is integer R positive?

(1) R^3 = R
(2) |R| = R
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Jul 2013, 06:38, edited 1 time in total.
Edited the question and added the OA

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Re: DS question [#permalink]

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New post 27 Dec 2010, 10:50
Fairness wrote:
Is integer R positive?

1. R^3=R
2. lRl=R


Is integer R positive?

(1) R^3=R --> \(r^3-r=0\) --> \(r(r^2-1)=0\) --> \(r(r-1)(r+1)=0\) --> \(r=0\), \(r=1\), or \(r=-1\). Not sufficient.

(2) |R|=R --> \(r\) is some non-negative integer, so \(r\) can be 0 or any positive integer. Not sufficient.

(1)+(2) \(r\) can be 0, so not a positive integer or 1, a positive integer, two different answers, hence not sufficient.

Answer: E.
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Re: DS question [#permalink]

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New post 28 Dec 2010, 04:06
Thanks, I missed the word " integer"

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Re: Is integer R positive? [#permalink]

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New post 28 Apr 2015, 20:15
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Hi All,

Certain DS questions are really just a test of your "thoroughness"; you don't have to be amazing at math to get the correct answer, but you DO have to "see" more than just the obvious solution to a given question.

Here, we're told that R is an integer. We're asked if it is POSITIVE. This is a YES/NO question. The phrasing of the prompt gets me thinking that R MIGHT be positive, but it also MIGHT be negative or even 0.

Fact 1: R^3 = R

Most Test Takers look at this and "see" that R = 1 is a solution....but is it the ONLY solution? With a bit more work (or even just 'playing around' with the prompt), you'll see that R= 0 and R = -1 are BOTH possible solutions....

IF...
R = 1 then the answer to the question is YES
R = 0 then the answer to the question is NO
R = -1 then the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: |R| = R

Again, most Test Takers would see that R = 1 is a solution, but R could be ANY positive integer and R = 0 is another solution worth noting.

IF....
R = 1 then the answer to the question is YES
R = 0 then the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we know...
R^3 = R
|R| = R

From our prior work, we already can see answers that fit both Facts:
IF....
R = 1 then the answer to the question is YES
R = 0 then the answer to the question is NO
Combined, INSUFFICIENT

Final Answer:
[Reveal] Spoiler:
E


The 'takeaway' from all of this is that, in many DS questions, you have to seek out the potential answers. There's ALWAYS at least one answer - it's just a matter of whether there's more than one or not.

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Is integer R positive? [#permalink]

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This was an excellent question! And, the low accuracy rates suggest that many students got stumped by it, probably because they failed to consider that the modulus function yields non-negative values, and not strictly positive values (in simpler words, the modulus function can also yield a value of zero)

Here is a similar question for you to further practice this very important point:

Is integer x negative?

(A) x is not equal to |x|
(B) x = -|y - 2|, where y is an integer


Please post your solution below. I'll provide the official answer and explanation soon. Till then, Happy Solving and wish you all the best! :)

Best Regards

Japinder
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Re: Is integer R positive? [#permalink]

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EgmatQuantExpert wrote:
This was an excellent question! And, the low accuracy rates suggest that many students got stumped by it, probably because they failed to consider that the modulus function yields non-negative values, and not strictly positive values (in simpler words, the modulus function can also yield a value of zero)

Here is a similar question for you to further practice this very important point:

Is integer x negative?

(A) x is not equal to |x|
(B) x = -|y - 2|, where y is an integer


Please post your solution below. I'll provide the official answer and explanation soon. Till then, Happy Solving and wish you all the best! :)

Best Regards

Japinder



Hello Japinder, thanks for interesting question )

1) \(x\) can be not equal to \(|x|\) only in case when \(x < 0\). Because if \(x >= 0\) when \(x\) will be equal to \(|x|\)
Sufficient

2) This statement give us two possible variants:
\(x = 0\) and \(y =2\) and then \(0 = -|2 - 2|\)
or \(x = -2\) and \(y = 4\) or \(y = 0\) then \(-2 = -|0-2|\) or \(-2=-|4-2|\)
So \(x\) can be negative or equal to \(0\)
Insufficient

Answer is A
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Re: Is integer R positive? [#permalink]

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Hi Japinder,

Here goes my approach:

Is integer x negative?

(A) x is not equal to |x|
(B) x = -|y - 2|, where y is an integer



Statement A - if X <> |X| then this implies that x is positive number - Sufficient
Statement B - this introduces another variable 'y' we know nothing about - Insufficient

Hence A is the correct option.





EgmatQuantExpert wrote:
This was an excellent question! And, the low accuracy rates suggest that many students got stumped by it, probably because they failed to consider that the modulus function yields non-negative values, and not strictly positive values (in simpler words, the modulus function can also yield a value of zero)

Here is a similar question for you to further practice this very important point:

Is integer x negative?

(A) x is not equal to |x|
(B) x = -|y - 2|, where y is an integer


Please post your solution below. I'll provide the official answer and explanation soon. Till then, Happy Solving and wish you all the best! :)

Best Regards

Japinder

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Re: Is integer R positive? [#permalink]

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New post 05 May 2015, 05:28
EgmatQuantExpert wrote:
This was an excellent question! And, the low accuracy rates suggest that many students got stumped by it, probably because they failed to consider that the modulus function yields non-negative values, and not strictly positive values (in simpler words, the modulus function can also yield a value of zero)

Here is a similar question for you to further practice this very important point:

Is integer x negative?

(A) x is not equal to |x|
(B) x = -|y - 2|, where y is an integer


Please post your solution below. I'll provide the official answer and explanation soon. Till then, Happy Solving and wish you all the best! :)

Best Regards

Japinder


The correct answer is Option A

The question statement just tells us that x is an integer.

This means,
either x is negative
or x = 0
or x is positive

Let's now see if the given statements help us eliminate some of these cases.

(1) x is not equal to |x|

This statement only holds true for x is negative

x = 0 and
x is positive violate Statement 1, and therefore can be ruled out.

Thus, Statement 1 is sufficient to confirm that x is negative.

(2) x = -|y - 2|, where y is an integer

Now, as I pointed out in the post quoted here, the modulus function yields non-negative values, and not strictly positive values (in simpler words, the modulus function can also yield a value of zero)

This means either
|y-2| > 0
(for example, for y = 3, -3 etc.)
and therefore, x = -(positive number) = negative integer

or |y-2| = 0 (for y = 2)
and therefore, x = 0

Thus, using Statement 2 alone, we get that x is either negative or equal to zero. So, it's not sufficient to confirm that x is negative.

Hope you enjoyed working on this question :-D

Japinder
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Re: Is integer R positive? [#permalink]

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New post 05 May 2015, 06:00
aimtoteach wrote:
Hi Japinder,

Here goes my approach:

Is integer x negative?

(A) x is not equal to |x|
(B) x = -|y - 2|, where y is an integer



Statement A - if X <> |X| then this implies that x is positive number - Sufficient
Statement B - this introduces another variable 'y' we know nothing about - Insufficient

Hence A is the correct option.


Dear aimtoteach

By going through the solution I've posted just now, you'll see that even though y is just a variable, we can deduce from Statement 2 that x is either negative or zero. Statement 2 is not sufficient only because the possibility of x = 0 also exists.

Suppose, the question had asked 'Is integer x positive?' instead. Then, the very same Statement 2 would have been sufficient to deduce that. :)
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Re: Is integer R positive?   [#permalink] 05 May 2015, 06:00
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