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.
What is the value of h?
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Hello Vjesus12.
Let's take a look at your question.
We need to find the value of h.
First statement
Second statement
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>
Let's take a look at your question.
We need to find the value of h.
First statement
From here, we can get $$h^2=36\ \ \Rightarrow\ \ h=\pm\ 6.$$ Since we got two different answers, this statement is not sufficient.(1) h^2 = 36
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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- Scott@TargetTestPrep
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Statement One Alone:VJesus12 wrote:What is the value of h?
(1) h^2 = 36
(2) h^2 + 12h = -36
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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? = hVJesus12 wrote:What is the value of h?
(1) h^2 = 36
(2) h^2 + 12h = -36
(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)
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