Problem Solving

BTGmoderatorLU wrote:Source: Economist GMAT



In the figure above, what is the distance from point P to point Q?

$$A.\ \sqrt{2}$$
$$B.\ 1.52-1$$
$$C.\ \sqrt{1.52-1}$$
$$D.\ \frac{\sqrt{2}}{2}$$
$$E.\ 0.5$$

The OA is D.

Since the formula for finding the distance between two points is the Cartesian plane is not within the scope of the GMAT, let's do it differently.

Pl. see this self-explanatory image.



The correct answer: D

Hope this helps!

-Jay
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BTGmoderatorLU wrote:Source: Economist GMAT



In the figure above, what is the distance from point P to point Q?

$$A.\ \sqrt{2}$$
$$B.\ 1.52-1$$
$$C.\ \sqrt{1.52-1}$$
$$D.\ \frac{\sqrt{2}}{2}$$
$$E.\ 0.5$$

Once we create our right triangle with sides 1/2, 1/2 and x (the hypotenuse), we can apply the Pythagorean Theorem to get: (1/2)² + (1/2)² = x²
Expand: 1/4 + 1/4 = x²
So, 1/8 = x²
This means x = √(1/8)
Check the answer choices. . . .√(1/8) is not there. Looks like we need to simplify √(1/8)

First off, √(a/b) = (√a)/(√b)
So, √(1/8) = (√1)/(√8)
= 1/(√8)
= 1/(2√2)
Check the answer choices. . . .1/(2√2) is not there.

Take: 1/(2√2)
Multiply top and bottom by √2 to get: √2/4
Check the answer choices. . . .
Answer: D

Cheers,
Brent