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Is the perimeter of a certain triangle less than 24 inches?

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Is the perimeter of a certain triangle less than 24 inches?

by BTGmoderatorDC » Tue Jul 23, 2019 5:31 pm

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Is the perimeter of a certain triangle less than 24 inches?

(1) The shortest side of the triangle is 8 1/4 inches.
(2) The triangle is isosceles and the longest side is 1 inch longer than each of the other sides.

OA A

Source: Princeton Review
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Wed Jul 24, 2019 10:26 pm

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BTGmoderatorDC wrote:Is the perimeter of a certain triangle less than 24 inches?

(1) The shortest side of the triangle is 8 1/4 inches.
(2) The triangle is isosceles and the longest side is 1 inch longer than each of the other sides.

OA A

Source: Princeton Review
Let's take each statement one by one.

(1) The shortest side of the triangle is 8 1/4 inches.

Since the shortest side of the triangle is 8 1/4 inches, the other two would be at least 8 1/4 inches; thus, perimeter ≥ [3*(8 1/4) = 24 3/4] > 24. The answer is no. Sufficient.

(2) The triangle is isosceles and the longest side is 1 inch longer than each of the other sides.

Case 1: Say the three sides are 2, 2 and 3. Thus, perimeter = 7 < 24. The answer is yes.
Case 2: Say the three sides are 12, 12 and 13. Thus, perimeter = 37 > 24. The answer is no. No unique answer. insufficient.

The correct answer: A

Hope this helps!

-Jay
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