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# GRE prep Club test question

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GRE prep Club test question [#permalink]  26 Jun 2017, 10:12
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This is from Quant test#4 question ID: Q02-33

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
[Reveal] Spoiler: OA
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Re: GRE prep Club test question [#permalink]  26 Jun 2017, 15:11
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Expert's post
saumya17lc wrote:
This is from Quant test#4 question ID: Q02-33

If x^4=29x^2-100 , then which of the following is NOT a product of three possible values of x :
-50
25
50

a. I only
b. II only
c. III only
d. I and II only
e. I and III only

According to me the answer should be II only(b)

If you solve the expression $$x^4=29x^2 -100$$ or $$x^4-29x^2+100=0$$ or $$x^2= 25, 4$$

So $$x=5, -5, 2, -2$$.

You need to multiply 3 solutions. So clearly B is not possible!
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Re: GRE prep Club test question [#permalink]  27 Jun 2017, 10:45
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Expert's post
saumya17lc wrote:
This is from Quant test#4 question ID: Q02-33

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

At first, we might not recognize that the given equation is a quadratic equation in disguise.

To see this, you must notice that (x^2)^2 = x^4

Now, if we let u = x^2, then we can rewrite the given equation.
We get: u^2 = 29u - 100
Rearrange to get: u^2 - 29u + 100 = 0
Factor to get: (u - 4)(u - 25) = 0
So, either u = 4, or u = 25

At this point, we can replace u with x^2 to get:
Either x^2 = 4, or x^2 = 25

If x^2 = 4, then x = 2 or x = -2
If x^2 = 25, then x = 5 or x = -5

So, there are 4 possible values of x: 2, -2, 5, and -5

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

I. 50
(-2)(5)(-5) = 50
Since 50 is possible, we can eliminate A, D and E

III. -50
(2)(5)(-5) = 50
Since -50 is possible, we can eliminate C

NOTE: At this point, we need not examine statement II, since we have already eliminated answer choices A, C, D and E

[Reveal] Spoiler:
B

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Re: GRE prep Club test question [#permalink]  26 Jul 2017, 01:31
I am having trouble understanding the wording :
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

Based on the question we get x = -2 and + 2 and +4 and -4. Thus 50 and -50 is possible. While "NOT A PRODUCT" - 25 is not possible. Hence I chose B "II only"
Please do help with clarity of the question - as per OA option E, I and III is not a possible value - which is not true. Thank you!

a. I only
b. II only
c. III only
d. I and II only
e. I and III only
GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1606 [0], given: 375

Re: GRE prep Club test question [#permalink]  26 Jul 2017, 06:17
Expert's post
nancyjose wrote:
I am having trouble understanding the wording :
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

Based on the question we get x = -2 and + 2 and +4 and -4. Thus 50 and -50 is possible. While "NOT A PRODUCT" - 25 is not possible. Hence I chose B "II only"
Please do help with clarity of the question - as per OA option E, I and III is not a possible value - which is not true. Thank you!

a. I only
b. II only
c. III only
d. I and II only
e. I and III only

You are right we are correcting the test question.

Thank you for pointing out!
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Sandy
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Re: GRE prep Club test question   [#permalink] 26 Jul 2017, 06:17
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