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On the map above, \(2\) inches represent \(3\) miles. If the roads from \(O\) to \(P,\) from \(O\) to \(Q,\) and from
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A. \(3\)
B. \(\dfrac92\)
C. \(5\)
D. \(6\)
E. \(\dfrac{15}2\)
Answer: B
Source: GMAT Prep
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APPROACH #1: Apply Pythagorean theoremGmat_mission wrote: ↑Fri Feb 11, 2022 8:23 am1 (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
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

APPROACH #2: Identify Pythagorean triples
Before test day, students should memorize the following Pythagorean triples
345
51213
72425
(and maybe 81517)
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