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Bob leaves point \(A\) and drives due west to point \(B.\) From point \(B,\) he drives due south to point \(C.\) How far

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Bob leaves point \(A\) and drives due west to point \(B.\) From point \(B,\) he drives due south to point \(C.\) How far

by M7MBA » Sat Jul 25, 2020 3:08 pm

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Bob leaves point \(A\) and drives due west to point \(B.\) From point \(B,\) he drives due south to point \(C.\) How far is Bob from his original location?

(1) Point \(A\) is 24 miles from point \(B.\)

(2) Point \(B\) is 18 miles from point \(C.\)

[spoiler]OA=C[/spoiler]

Source: Princeton Review
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Source: — Data Sufficiency |
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Re: Bob leaves point \(A\) and drives due west to point \(B.\) From point \(B,\) he drives due south to point \(C.\) How

by deloitte247 » Tue Jul 28, 2020 11:34 pm

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.Bob leaves point A and drives due west to point B.
From point B, Bob drives due south to point C.
Target question => How far is Bob from his original position.
Plotting the bearing of Bob's journey gives a right-angle triangle in which AB = base, BC = height, and CA = hypotenuse.
Find CA = hypotenuse

Statement 1: Point A is 24 miles from point B. i.e AB = 24 miles; the value of BC is unknown. So, the target question cannot be evaluated. Therefore, statement 1 is NOT SUFFICIENT.

Statement 2: Point B is 18 miles from point A. i.e BC = 18 miles; the value of AB is unknown. So, the target cannot be evaluated. Therefore, statement 2 is NOT SUFFICIENT.

Combining both statements together:
AB = 24 miles and BC = 18 miles
Using Pythagoras theorem;
$$CA=\sqrt{\left(AB\right)^2+\left(BC\right)^2}$$
$$CA=\sqrt{24^2+18^2}$$
$$CA=\sqrt{576+324}$$
$$CA=\sqrt{900}=30\ miles$$
From the above result, the combination of both statements shows it is SUFFICIENT. Therefore, the correct answer to this question is answer choice C.
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