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Data sufficiency

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by BTGmoderatorRO » Mon Sep 18, 2017 1:10 pm
Is w+h^4 positive?
1) h is positive
2) w is positive
OA is d

a. statement 1 and 2 are both sufficient
b. statement 1 is sufficient and statement 2 is not sufficient
c. none is sufficient
d. statement 1 is not sufficient and statement 2 is sufficient

Can you express this in mathematical language why the 2 statement are correct?
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon Sep 18, 2017 1:32 pm
Roland2rule wrote:Is w+h^4 positive?

1) h is positive
2) w is positive
The correct answers is B, not D

Target question: Is w + h^4 positive?

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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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