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What is the perimeter of isosceles triangle MNP?

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sat Jun 22, 2019 5:00 am
BTGmoderatorDC wrote:What is the perimeter of isosceles triangle MNP?

(1) MN = 16
(2) NP = 20

OA E

Source: Official Guide
Target question: What is the perimeter of isosceles triangle MNP?

Statement 1: MN = 16
No idea about the other 2 sides
Statement 1 is NOT SUFFICIENT

Statement 2: NP = 20
No idea about the other 2 sides
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Since we have an ISOSCELES triangle, we know that two sides have the same length, but which two sides?
There are two possible cases:
Case a: The side lengths are 16, 16, 20. In this case, the answer to the target question is the perimeter = 16+16+20=52
Case b: The side lengths are 16, 20, 20. In this case, the answer to the target question is the perimeter = 16+20+20=56
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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by deloitte247 » Sat Jun 29, 2019 10:34 am
Isosceles has two equal sides.

Statement 1
MN = 16
Since the length of the other side is not given, statement 1 is NOT SUFFICIENT.

Statement 2
NP = 20
Since the length of the other side is not given, statement 2 is NOT SUFFICIENT.

Combining the two statements together.
We don't know which of the given length is of equal sides.
The perimeter can be
$$16+16+20=52$$
OR
The perimeter can be
$$16+20+20=56$$
Both statement together are INSUFFICIENT.
$$answer\ is\ Option\ E$$
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