Is w + h^4 positive?
(1) h is positive
(2) w is positive
Official Guide question
Answer: B
Is w + h^4 positive?
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Target question: Is w + h^4 positive?jjjinapinch wrote:Is w + h^4 positive?
(1) h is positive
(2) w is positive
Official Guide question
Answer: B
Statement 1: h is positive
Let's TEST some values.
There are several values of w and h that satisfy statement 1. Here are two:
Case a: w = 1 and h = 1. In this case, w + h^4 = 1 + 1^4 = 2. So, w + h^4 IS positive
Case b: w = -3 and h = 1. In this case, w + h^4 = -3 + 1^4 = -2. So, w + h^4 is NOT positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: w is positive
Important concept: (any number)^(even integer) = a value greater than or equal to 0
Statement 2 tells us that w is some positive number
We can write: w + h^4 = (some positive number) + ( a value greater than or equal to 0)
We can see that w + h^4 positive is definitely positive
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
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Hi jjjinapinch,
This question is built around some Number Property Rules, so you can either TEST VALUES or use those NP rules to get to the correct answer.
We're asked if (W + H^4) is positive. This is a YES/NO question.
Before we get to the two Facts, it's worth noting that H^4 can NEVER be negative (it can be 0 when H=0, but in all other situations, H^4 will be POSITIVE). Thus, this question really comes down to the value of W....
1) H is positive
Fact 1 tells us that H is POSITIVE, so H^4 will be POSITIVE. However, it does NOT tell us anything about the value of W.
IF... H=1, W=1, then (H+W^4) = 2 and the answer to the question is YES.
IF... H=1, W= -2, then (H+W^4) = -1 and the answer to the question is NO.
Fact 1 is INSUFFICIENT
2) W is positive
Since W is POSITIVE, and we know that H^4 is >= to 0, then we know that (W+H^4) MUST be POSITIVE and the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
This question is built around some Number Property Rules, so you can either TEST VALUES or use those NP rules to get to the correct answer.
We're asked if (W + H^4) is positive. This is a YES/NO question.
Before we get to the two Facts, it's worth noting that H^4 can NEVER be negative (it can be 0 when H=0, but in all other situations, H^4 will be POSITIVE). Thus, this question really comes down to the value of W....
1) H is positive
Fact 1 tells us that H is POSITIVE, so H^4 will be POSITIVE. However, it does NOT tell us anything about the value of W.
IF... H=1, W=1, then (H+W^4) = 2 and the answer to the question is YES.
IF... H=1, W= -2, then (H+W^4) = -1 and the answer to the question is NO.
Fact 1 is INSUFFICIENT
2) W is positive
Since W is POSITIVE, and we know that H^4 is >= to 0, then we know that (W+H^4) MUST be POSITIVE and the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
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We need to ensure whether (w + h^4) positive.jjjinapinch wrote:Is w + h^4 positive?
(1) h is positive
(2) w is positive
Official Guide question
Answer: B
Since the exponent of h is 4, an even number, whether h is positive or negative, h^4 is positive.
Thus, (w + h^4) is positive, if
1. w is positive, or
2. w is negative, but |w| < h^4
(w + h^4) is NOT positive, if
w is negative, and |w| ≥ h^4
Statement 1: h is positive.
We already know the nature of h^4, we are not interested in the nature of h. Insufficient.
Statement 2: w is positive.
We already deduced that if w is positive, (w + h^4) is positive. Sufficient.
The correct answer: B
Hope this helps!
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We need to determine whether w+h^4 is positive. First, we know that h^4 is always non-negative.jjjinapinch wrote:Is w + h^4 positive?
(1) h is positive
(2) w is positive
Let's look at the 2 possibilities for the value of w+h^4:
1) If w is positive, then (w + h^4) will be positive.
2) If w is negative, then h^4 must be greater than |w| in order for (w + h^4) to be positive. For example if w = -4, then h^4 must be greater than 4 in order for (w + h^4) to be positive.
Statement One Alone:
h is positive
Since we already know that h^4 is positive and do not have any information about w, we do not have enough information to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
w is positive
Since we know that h^4 is non-negative, also knowing that w is positive is enough information to determine that w + h^4 is positive. Statement two is sufficient to answer the question.
Answer: B
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since h^4 will always be positive, we only need to determine the sign of w.jjjinapinch wrote: ↑Thu Jul 27, 2017 12:12 pmIs w + h^4 positive?
(1) h is positive
(2) w is positive
Official Guide question
Answer: B
So statement 2) alone is sufficient.
Hence option B is correct.