## 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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### On the map above, $$2$$ inches represent $$3$$ miles. If the roads from $$O$$ to $$P,$$ from $$O$$ to $$Q,$$ and from

by Gmat_mission » Fri Feb 11, 2022 8:23 am

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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 $$P$$ 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. $$\dfrac{15}2$$

Source: GMAT Prep

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### Re: On the map above, $$2$$ inches represent $$3$$ miles. If the roads from $$O$$ to $$P,$$ from $$O$$ to $$Q,$$ and fro

by [email protected] » Sat Feb 12, 2022 6:04 am
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. $$\dfrac{15}2$$

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

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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