Problem Solving

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Fri Mar 26, 2021 9:44 am

GMAT Prep

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On the map above, 2 inches represents 3 miles. If the roads from O to P, from O to Q, and from P to Q are relatively flat and straight, approximately how many miles is it from P to Q?

A. 3
B. 9/2
C. 5
D. 6
E. 15/2

OA B

APPROACH #1: Apply Pythagorean theorem
Let x = the length of PQ
Apply the Pythagorean theorem to get: 4² + x² = 5²
Evaluate: 16 + x² = 25
Rewrite as: x² = 9
Solve: x = 3 or x = -3 (we can eliminate x = -3, since lengths can't be negative)

So, ON THE MAP, the length of PQ is 3 INCHES

Given: 2 inches represents 3 miles
In other words, 1 inch = 1.5 miles
So, 3 inches = 4.5 miles, since (3)(1.5) = 4.5

Answer: B
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APPROACH #2: Identify Pythagorean triples
Before test day, students should memorize the following Pythagorean triples
3-4-5
5-12-13
7-24-25
(and maybe 8-15-17)
Pythagorean triples sets of INTEGER values that could represent the three lengths of a right triangle

If we've memorized the Pythagorean triples, will instantly see that side PQ must have a length of 3 INCHES
Once we know that PQ = 3 INCHES (on the map), we can use the above technique to convert this to 4.5 miles

Answer: B

Cheers,
Brent