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Re: GRE prep Club test question [#permalink]
27 Jun 2017, 10:45

3

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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

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

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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