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# GRE Math Challenge #46-If h > 0 and p is the only

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GRE Math Challenge #46-If h > 0 and p is the only [#permalink]  19 Sep 2014, 03:51
Expert's post
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Question Stats:

56% (01:07) correct 43% (02:07) wrong based on 23 sessions
If $$h > 0$$ and p is the only value of x for which eq: $$x^2 - h *x +16 = 0$$, then $$\frac{h}{p}$$ =

A. 1/4

B. 1/2

C. 1

D. 2

E. 4
[Reveal] Spoiler: OA

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Sandy
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Re: GRE Math Challenge #46-If h > 0 and p is the only [#permalink]  03 Dec 2018, 10:53
Expert's post
sandy wrote:
If $$h > 0$$ and p is the only value of x for which eq: $$x^2 - h *x +16 = 0$$, then $$\frac{h}{p}$$ =

A. 1/4

B. 1/2

C. 1

D. 2

E. 4

IMPORTANT HINT: When we read that the quadratic equation x² - hx + 16 = 0 has only 1 solution, our reaction should be "Hmmm, that's odd; quadratic equations usually have 2 solutions.
For example, the equation x² - 5x + 6 = 0 can be rewritten as (x - 3)(x - 2) = 0, which means the two solutions are x = 3 and x = 2

That said, there ARE times when a quadratic equation has 1 solution.
This occurs when the quadratic expression can be factored into a binomial times itself.
For example, the equation x² - 6x + 9 = 0 can be rewritten as (x - 3)(x - 3) = 0, which means there's exactly one solution: x = 3

From here, we might recognize that the equation x² - 8x + 16 = 0 can be rewritten as: (x - 4)(x - 4) = 0, which means there's exactly one solution: are x = 4

In the question, we're given the equation x² - hx + 16 = 0
Since the equation x² - 8x + 16 = 0 has ONE solution, we can conclude that h = 8
Also, if p is the only solution to the equation, then p = 4

So, h/p = 8/4 = 2

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

Re: GRE Math Challenge #46-If h > 0 and p is the only   [#permalink] 03 Dec 2018, 10:53
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