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# M28-13

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Math Expert
Joined: 02 Sep 2009
Posts: 49303

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16 Sep 2014, 01:28
2
2
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Difficulty:

65% (hard)

Question Stats:

60% (01:56) correct 40% (01:40) wrong based on 35 sessions

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If $$x^4 = 29x^2 - 100$$, then which of the following is NOT a product of three possible values of $$x$$?
I. -50

II. 25

III. 50

A. $$I$$ only
B. $$II$$ only
C. $$III$$ only
D. $$I$$ and $$II$$ only
E. $$I$$ and $$III$$ only

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Math Expert
Joined: 02 Sep 2009
Posts: 49303

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16 Sep 2014, 01:28
Official Solution:

If $$x^4 = 29x^2 - 100$$, then which of the following is NOT a product of three possible values of $$x$$?
I. -50

II. 25

III. 50

A. $$I$$ only
B. $$II$$ only
C. $$III$$ only
D. $$I$$ and $$II$$ only
E. $$I$$ and $$III$$ only

Re-arrange and factor for $$x^2$$: $$(x^2-25)(x^2-4)=0$$.

So, we have that $$x=5$$, $$x=-5$$, $$x=2$$, or $$x=-2$$.

$$-50=5*(-5)*2$$;.

$$50=5*(-5)*(-2)$$;

Only 25 is NOT a product of three possible values of $$x$$

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Intern
Joined: 16 Sep 2013
Posts: 2
Concentration: Accounting, Finance
GMAT 1: 510 Q29 V21
GMAT 2: 460 Q33 V19
GPA: 3.95

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17 Feb 2015, 13:25
I think this question is poor.
it is 29 in the question ,but factoring shows 25!!!
Math Expert
Joined: 02 Sep 2009
Posts: 49303

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17 Feb 2015, 13:29
Viktorijakm wrote:
I think this question is poor.
it is 29 in the question ,but factoring shows 25!!!

You are wrong.

Did you try to expand (x^2 - 25)(x^2 - 4) = 0? You'll get x^4 - 29x^2 + 100 = 0, which is the same as x^4 = 29x^2 - 100.
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Joined: 21 May 2015
Posts: 16

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22 Aug 2017, 12:25
I think this is a high-quality question and I agree with explanation.
Manager
Joined: 04 Jun 2018
Posts: 230
Location: Germany
Concentration: General Management, Finance
GPA: 3.6
WE: Analyst (Transportation)

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06 Jul 2018, 09:23
Viktorijakm wrote:
I think this question is poor.
it is 29 in the question ,but factoring shows 25!!!

The factoring is correct though, as you are looking for numbers which add to -29 and multiply to 100 respectively.

I think the question is of high quality and similar to stuff I have seen on the GMAC prep tests.
_________________

A couple of things that helped me in verbal:
https://gmatclub.com/forum/verbal-strategies-268700.html#p2082192

Gmat Prep CAT #1: V42, Q34, 630
Gmat Prep CAT #2: V46, Q35, 660
Gmat Prep CAT #3: V41, Q42, 680

On the mission to improve my quant score, all help is appreciated!

Intern
Joined: 23 May 2017
Posts: 1
GMAT 1: 640 Q48 V29

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28 Aug 2018, 08:17
I think this is a high-quality question.
Re M28-13 &nbs [#permalink] 28 Aug 2018, 08:17
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# M28-13

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