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Automobile A is traveling at two-thirds the speed that Autom

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Automobile A is traveling at two-thirds the speed that Autom

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Automobile A is traveling at two-thirds the speed that Automobile B is traveling. How fast is Automobile A traveling?

(1) If both automobiles increased their speed by 10 miles per hour, Automobile A would be traveling at three-quarters the speed that Automobile B would be traveling.

(2) If both automobiles decreased their speed by 10 miles per hour, Automobile A would be traveling at half the speed that Automobile B would be traveling

OA D

Source: Princeton Review

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$$A=\frac{2}{3}of\ B$$
How fast is Automobile A travelling

Statement 1
If both automobiles increased their speed by 10 miles per hour, Automobile A would be travelling at three - quarter the speed that automobile B will be travelling.
$$A+10=\frac{3}{4}of\ \left(B+10\right)$$
From question
$$A=\frac{2}{3}B$$
$$\frac{2}{3}B+10=\frac{3}{4}B+\frac{80}{4}$$
$$\frac{2}{3}B-\frac{3}{4}B=\frac{30}{4}-10$$
$$\frac{8B-9B}{12}=\frac{30-40}{4}$$
$$-\frac{B}{12}=-\frac{10}{4}$$
$$-\frac{4B}{4}=-\frac{120}{4}$$
$$b=30$$
$$Since\ A=\frac{2}{3}of\ B$$
statement 1 is INSUFFICIENT.
$$\frac{2}{3}\cdot30=20$$

Statement 2
If both automobile reduce their speed by 10 mph
Automobile A will be travelling a 1/2 the speed of that B would be travelling.

Therefore,
$$A-10==\frac{1}{2}\left(B-10\right)where\ A=\frac{2}{3}B$$ $$\frac{2}{3}B-10=\frac{1}{2}B-5$$ $$\frac{2}{3}B-\frac{1}{2}B=-5+10$$ $$\frac{4B-3B}{6}=5$$ $$b=6\cdot5=30mph$$ $$where\ A=\frac{2}{3}of\ B$$ $$where\ A=\frac{2}{3}of\ 30$$ $$where\ A=20mph$$
Statement 2 is also SUFFICIENT.

$$Answer\ is\ Option\ D$$
Both statement alone are SUFFICIENT.

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Each Statement gives the same type of relationship between the two speeds, so the answer will be C, D or E. If we let a and b be the two speeds of the cars, we know that a = 2b/3.

Using Statement 1 alone, you might be able to see by inspection that the speeds are 20 and 30. Or we can use algebra:

a + 10 = (3/4)(b + 10) = (3b/4) + 7.5

Substituting for a, we have

(2b/3) + 10 = (3b/4) + 7.5

which is an equation we can clearly solve for b, and thus we can find a. Statement 2 will produce a similar equation, so the answer is D.

_________________
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

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