On the map above, 2 inches represents 3 miles. If the roads from O to

Question

https://gmatclub.com/forum/download/file.php?id=54681 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 PS21253 1.png

GMATinsight · Answer

2 inch = 3 miles

PQ  = √5^2 - 4^2 = 3  inch

but 3 inch = (3/2)*3 = 4.5 miles

Answer: Option B

Abhishek009 · Answer

PQ = 3 ( From Pythagorean Triplet)

So, Actual Length is  3*\frac{3}{2 }=\frac{9}{2} , Answer must be (B)

BrentGMATPrepNow · Answer

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
-----------------------
  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

NitishJain · Answer

B.

In triangle OPQ , using pythagoras theorem;
5^2 = 4^2 + PQ^2
==> PQ = 3

Using the unitary method

2 inches = 3 miles
1 inch = 3/2 miles
3 inches = 3* (3/2) = 9/2 miles

naveenban · Answer

Option B.

By Pythagoras Theorem, PQ = 3 Inch.
1 Inch = 3/2 Miles
3 Inches = 9/2 Miles

bumpbot · Answer

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On the map above, 2 inches represents 3 miles. If the roads from O to

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On the map above, 2 inches represents 3 miles. If the roads from O to

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