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

Expert replies

Previous Topic Next Topic

BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Mon May 06, 2019 3:42 pm

Timer

00:00

Answers

Stats

Difficulty—

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

Like this post

Source: Beat The GMAT — Data Sufficiency | Mon May 06, 2019 3:42 pm

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Sun May 12, 2019 10:19 pm

$$A=\frac{2}{3}of\ B$$
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.

Like this post

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Mon May 13, 2019 4:13 am

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.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review