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In the right triangle shown above, what is the value of a?

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In the right triangle shown above, what is the value of a?

by swerve » Mon Aug 06, 2018 9:45 am

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Source: Veritas Prep

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In the right triangle shown above, what is the value of a?

(1) C = 5.
(2) a < b.

The OA is E.

1. C = 5 => a^2+b^2 = 25 => (a,b) = (3,4) or (4,3).. those are the only 2 combinations. NS
2. a<b : this doesn't give any information. NS

combined: (a,b) = (3,4) => a = 3.

Hence, the answer should be C but this isn't the OA. Anyone help, please! Thanks!
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Source: — Data Sufficiency |
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by Brent@GMATPrepNow » Mon Aug 06, 2018 10:22 am

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swerve wrote: 1. C = 5 => a^2+b^2 = 25 => (a,b) = (3,4) or (4,3).. those are the only 2 combinations. NS
2. a<b : this doesn't give any information. NS

combined: (a,b) = (3,4) => a = 3.
Hence, the answer should be C but this isn't the OA. Anyone help, please! Thanks!
You're assuming that a and b are INTEGERS.
If that were the case, then C could be the correct answer.
Brent Hanneson - Creator of GMATPrepNow.com
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by Brent@GMATPrepNow » Mon Aug 06, 2018 10:27 am

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swerve wrote:Source: Veritas Prep

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In the right triangle shown above, what is the value of a?

(1) c = 5.
(2) a < b.
Target question: What is the value of a?
Let's jump straight too....

Statements 1 and 2 combined
Statement 1 tells us that c = 5.
Statement 2 tells us that a < b
There are several values of a, b and c that satisfy BOTH statements. Here are two cases:
Case a: a = 3, b = 4 and c = 5. Notice that the Pythagorean Theorem holds true: 3² + 4² = 5². In this case, the answer to the target question is a = 3
Case b: a = √11, b = √14 and c = 5. Notice that the Pythagorean Theorem still holds true: (√11)² + (√14)² = 5². In this case, the answer to the target question is a = √11
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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