BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

The distance between Alice’s house and Bob's is 120 miles.

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times
by Max@Math Revolution » Wed May 02, 2018 1:54 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

[GMAT math practice question]

The distance between Alice's house and Bob's is 120 miles. Alice and Bob travel in opposite directions along the same road, starting at the same time. They meet at a place that is 40 miles away from Alice's house. If Alice's velocity is x miles per hour, what is Bob's velocity in terms of x?

A. (1/3)x
B. (1/2)x
C. x
D. 2x
E. 3x
Last edited by Max@Math Revolution on Thu May 03, 2018 11:14 am, edited 1 time in total.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Wed May 02, 2018 2:50 am
Max@Math Revolution wrote:[GMAT math practice question]

The distance between Alice's house and Bob's is 120 miles. Alice and Bob travel in opposite directions along the same road, starting at the same time. They meet at a place that is 40 miles away from Alice's house. If Alice's velocity is x miles per hour, what is Bob's velocity in terms of x?

A. (1/3)x
B. (1/2)x
C. x
D. 2x
E. 3x
Total distance between Alice and Bob =120 miles.
Since Alice travels 40 miles from her home to meet Bob, Bob travels the remaining 80 miles.
Since Bob travels twice as far as Alice, his rate is twice Alice's rate.
Since Alice's rate = x miles per hour, Bob's rate = 2x miles per hour.

The correct answer is D.

Alternate approach:

As noted above:
Total distance between Alice and Bob =120 miles.
Since Alice travels 40 miles from her home to meet Bob, Bob travels the remaining 80 miles.

Let x=40, implying that Alice's rate = 40 mph.
Since Alice's rate = 40 mph, the time for her to travel 40 miles from her home to meet Bob = d/r = 40/40 = 1 hour.
In this same 1 hour, Bob travels the remaining 80 miles from his home to meet Alice, implying that Bob's rate = d/t = 80/1 = 80 mph.

The question stem asks for Bob's rate: 80 mph.
Now plug x=40 into the answers to see which yields the target value of 80.
Only D works:
2x = 2*40 = 80.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Wed May 02, 2018 10:43 am
The correct answer is showing up as B
Upon re-reading the question, we can see that it's somewhat ambiguous, because it doesn't specify where Alice and Bob are when they begin their journeys (although I also assumed that Alice started at her own house and Bob started at his own house).

If each person started at his/her own house (and started walking to the other person's house), then the correct answer is D.
If each person started at the OTHER person's house (and started walking home), then the correct answer is B.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members
Location: New York, NY
Thanked: 39 times

by Jeff@TargetTestPrep » Thu May 03, 2018 3:27 pm
Max@Math Revolution wrote:[GMAT math practice question]

The distance between Alice's house and Bob's is 120 miles. Alice and Bob travel in opposite directions along the same road, starting at the same time. They meet at a place that is 40 miles away from Alice's house. If Alice's velocity is x miles per hour, what is Bob's velocity in terms of x?

A. (1/3)x
B. (1/2)x
C. x
D. 2x
E. 3x
The distance between Alice's house and Bob's is 120 miles, and the meeting place is 40 miles away from Alice's house. Therefore, Alice must have traveled 40 miles, and Bob must have traveled 80 miles. We see that Bob has traveled twice the distance Alice has traveled. Since they start at the same time, Bob must be traveling twice as fast as Alice in order to cover the distance that is twice as long. Since we are given that Alice is traveling at x mph, Bob must be traveling at 2x mph.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times

by Max@Math Revolution » Thu May 03, 2018 11:34 pm
=>

Let v be Bob's speed, and let t be the time they take to reach their meeting point. Then
xt = 40 and vt = 120 - 40 = 80.

Bob travels 80 miles in the time it takes Alice to travel 40 miles.
Thus, Bob's speed is twice Alice's speed.
In terms of x, this is 2x.

Therefore, the answer is D.

Answer : D
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Mon May 07, 2018 10:10 am
The duo met 40miles away from Alice house.
Alice has covered distance of 40miles
Bob has cover distance of 120-40
= 80miles
Alice velocity = x miles per hour
Given that they met at some time but cover different distance means their velocity id different.
Bob cover's most of the distance, this means Bob's velocity is twice that of Alice to cover twice the distance Alice was able to cover (40
: 80)
$$\frac{40}{x\ }\ =\ \frac{80}{y}$$
$$\frac{40y}{40}\ =\ \frac{80x}{40}$$
y = 2x
Option D is the correct answer
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1