One side of a certain triangle has length 7. Is the perimeter of the t

Question

One side of a certain triangle has length 7. Is the perimeter of the triangle greater than 20 ?

(1) On side of the triangle has length 9.
(2) On side of the triangle has length 3.

Bambi63 · Answer

1) 9-7 < 3rd side of triangle < 7+9
Hence perimeter can range from 19 to 31. Data is not sufficient. 
2) 7-3 < 3rd side of triangle < 7+3
Perimeter ranges from 14 to 19
Answer to the question stem is No
Therefore B is the answer.

Posted from my mobile device

gmatophobia · Answer

Statement 1

(1) On side of the triangle has length 9.

9 - 7 < third side < 9 + 7

2 < third side < 16

7+ 9 + 2 < Perimeter < 7+ 9 + 16

18 < Perimeter < 32

Hence, for some values of the third side, the perimeter can be greater than 20 or it can be less than 20.

The statement is not sufficient.

Statement 2

(2) On side of the triangle has length 3.

7 - 3 < third side < 7 + 3

4 < third side < 10

7+ 3 + 4 < Perimeter < 7+ 3 + 10

14 < Perimeter < 20

Hence, the perimeter is always less than 20.

Sufficient.

Option B

sahvdahvj654 · Answer

I don't understand, how B is the answer. The question asks if the perimeter is greater than 20, and none of the options conclusively proved that the perimeter is bigger than 20.

I understood the calculation but why option B?

why?why?why?

I think the answer should be E, which perfectly conveys that neither of the statements prove the perimeter to be above 20.

dvns · Answer

We are asked if the perimeter is greater than 20. We don't care what it is exactly, all that we are after is whether the information provided in the statements is enough to say "YES, it is greater than 20" or "NO, it is not greater than 20". If we can conclude that the information from statement 2 allows us to either say definitively YES or definitively NO, the statement will be sufficient to answer the target question.

From S2, we get:

4 < third side < 10.

So no matter what length the thirds side is, adding all side lengths will definitely NOT be greater than 20, and hence B is sufficient on its own. 
Hope this helps.

One side of a certain triangle has length 7. Is the perimeter of the t

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GMAT Data Sufficiency (DS) Questions

One side of a certain triangle has length 7. Is the perimeter of the t

Prep Toolkit

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