Problem Solving

Gmat_mission wrote: ↑

Fri Feb 11, 2022 8:23 am

1 (1).png

On the map above, \(2\) inches represent \(3\) 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. \(\dfrac92\)

C. \(5\)

D. \(6\)

E. \(\dfrac{15}2\)

Answer: B

Source: GMAT Prep

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