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What is the value of h?

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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What is the value of h?

by VJesus12 » Tue Jul 17, 2018 12:50 am
What is the value of h?

(1) h^2 = 36
(2) h^2 + 12h = -36

The OA is the option B.

Why is the second statements sufficient but the first one isn't? Could anyone give me some help here? Please.
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by Vincen » Tue Jul 17, 2018 1:53 am
Hello Vjesus12.

Let's take a look at your question.

We need to find the value of h.


First statement
(1) h^2 = 36
From here, we can get $$h^2=36\ \ \Rightarrow\ \ h=\pm\ 6.$$ Since we got two different answers, this statement is not sufficient.

Second statement
(2) h^2 + 12h = -36


From the given equation we get $$h^2+12h=-36$$ $$h^2+12h +36=0$$ $$h^2+2\cdot h\cdot6+6^2=0$$ $$\left(h+6\right)^2=0$$ $$h+6=0$$ $$h=-6.$$ Therefore, the value of h is 6. So, this statement is sufficient.

This is why the correct answer is the option B.

I hope this can help you. <i class="em em-smiley"></i>
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by Scott@TargetTestPrep » Mon Jul 23, 2018 5:30 pm
VJesus12 wrote:What is the value of h?

(1) h^2 = 36
(2) h^2 + 12h = -36
Statement One Alone:

h^2 = 36

If we take the square root of both sides of the equation, we have:

|h| = 6

We see that h can be 6 or -6. Statement one alone is not sufficient.

Statement Two Alone:

h^2 + 12h = -36

If we add 36 to both sides of the equation, we have:

h^2 + 12h + 36 = 0

(h + 6)^2 = 0

h + 6 = 0

h = -6

We see that h = -6. Statement two alone is sufficient.

Answer: B

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by fskilnik@GMATH » Mon Aug 27, 2018 1:18 pm
VJesus12 wrote:What is the value of h?

(1) h^2 = 36
(2) h^2 + 12h = -36
? = h

(1) Insufficient: h = 6 or h = -6

(2) There is at least one solution (examiner´s burden when "what is the value..." is at stake), and in a second-degree equation (in the variable-focus) we have at most TWO (real) distinct solutions.
Who gives the number of roots? "Delta"!

Considering h^2 + 12h+36 = 0 , we have Delta = b^2 - 4ac = (12)^2 - 4(1)(36) = 144-144 = 0.

Hence h is unique (two equal real roots for the equation, if you prefer), hence Sufficient.

The above follows the notations and rationale taught in the GMATH method.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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