GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 06 Dec 2019, 03:02

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Train A leaves New York and is heading towards Boston at a constant

Author Message
TAGS:

### Hide Tags

Manager
Joined: 20 Jun 2018
Posts: 81
Location: Japan
Concentration: Strategy, Finance
GMAT 1: 660 Q49 V31
WE: Analyst (Energy and Utilities)
Train A leaves New York and is heading towards Boston at a constant  [#permalink]

### Show Tags

Updated on: 24 Nov 2019, 01:44
3
00:00

Difficulty:

55% (hard)

Question Stats:

50% (01:54) correct 50% (02:11) wrong based on 18 sessions

### HideShow timer Statistics

Train A leaves New York and is heading towards Boston at a constant speed, at the same time train B leaves Boston and is traveling to New York in the opposite direction on a parallel track at a constant speed. Train A is traveling faster than train B, and the distance between New York and Boston is 140 miles. When train A reaches Boston, how far is train B from the point at which the two trains passed each other?

(1) Train A is traveling 15 miles per hour faster than train B.
(2) Train B is traveling at a speed that is one-fourth less than that of Train A’s speed.

Source: GMAT Quantum

Originally posted by akash7gupta11 on 23 Nov 2019, 23:51.
Last edited by Bunuel on 24 Nov 2019, 01:44, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Aug 2009
Posts: 8284
Re: Train A leaves New York and is heading towards Boston at a constant  [#permalink]

### Show Tags

24 Nov 2019, 00:33
Train A leaves New York and is heading towards Boston at a constant speed, at the same time train B leaves Boston and is traveling to New York in the opposite direction on a parallel track at a constant speed. Train A is traveling faster than train B, and the distance between New York and Boston is
140 miles. When train A reaches Boston, how far is train B from the point at which the two trains passed each other?

We just require the ratio of speed of two or actual speeds of both

(1) Train A is traveling 15 miles per hour faster than train B.
Say B is travelling at 1 and B at 16 and now compare it with A travelling at 115 and B at 100.
Clearly the answers will be different, as A’s speed is way higher than B’s 16 times while the speed in second case is comparable

(2) Train B is traveling at a speed that is one-fourth less than that of Train A’s speed.
Here we know the ratio so we can find the answer.
Suff

B

Now let us find the solution.
So B=3/4 of A.
A:B =4:3 and the distance covered will be in ratio 3:4=60:80..
Now after meeting each other A has to travel 60, so B will travel 3/4 of 60 in that time ..
_________________
Manager
Joined: 04 Apr 2015
Posts: 249
GMAT 1: 650 Q49 V31
GPA: 3.59
Re: Train A leaves New York and is heading towards Boston at a constant  [#permalink]

### Show Tags

24 Nov 2019, 04:54
1
chetan2u wrote:
Train A leaves New York and is heading towards Boston at a constant speed, at the same time train B leaves Boston and is traveling to New York in the opposite direction on a parallel track at a constant speed. Train A is traveling faster than train B, and the distance between New York and Boston is
140 miles. When train A reaches Boston, how far is train B from the point at which the two trains passed each other?

We just require the ratio of speed of two or actual speeds of both

(1) Train A is traveling 15 miles per hour faster than train B.
Say B is travelling at 1 and B at 16 and now compare it with A travelling at 115 and B at 100.
Clearly the answers will be different, as A’s speed is way higher than B’s 16 times while the speed in second case is comparable

(2) Train B is traveling at a speed that is one-fourth less than that of Train A’s speed.
Here we know the ratio so we can find the answer.
Suff

B

Now let us find the solution.
So B=3/4 of A.
A:B =4:3 and the distance covered will be in ratio 3:4=60:80..
Now after meeting each other A has to travel 60, so B will travel 3/4 of 60 in that time ..

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Train A leaves New York and is heading towards Boston at a constant  [#permalink]

### Show Tags

24 Nov 2019, 10:41
akash7gupta11 wrote:
Train A leaves New York and is heading towards Boston at a constant speed, at the same time train B leaves Boston and is traveling to New York in the opposite direction on a parallel track at a constant speed. Train A is traveling faster than train B, and the distance between New York and Boston is 140 miles. When train A reaches Boston, how far is train B from the point at which the two trains passed each other?

(1) Train A is traveling 15 miles per hour faster than train B.
(2) Train B is traveling at a speed that is one-fourth less than that of Train A’s speed.

Source: GMAT Quantum

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Assume $$v_a$$ and $$v_b$$ are speeds of the train A and B, respectively, and $$t$$ is the time the train takes to reaches Boston.
Then $$v_a \cdot t = 140$$.
And the question asks the value of $$140 - v_b \cdot t = v_a \cdot t - v_b \cdot t = (v_a - v_b)t$$.

Since we have $$v_b = \frac{1}{4}v_b$$ from condition 2).
$$v_b \cdot t = \frac{1}{4} v_a \cdot t = \frac{140}{4} = 35$$.
$$140 - v_b \cdot t = 140 - 35 = 105$$.
Condition 2) is sufficient.

Condition 1)
We have $$v_a - v_b = 15$$ from condition 1), but we don't any information about $$t$$.
We can't determine the value of $$140 - v_b \cdot t = v_a \cdot t - v_b \cdot t = (v_a - v_b)t = 15t$$.

Since condition 1) does not yield a unique solution, it is not sufficient.

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Re: Train A leaves New York and is heading towards Boston at a constant   [#permalink] 24 Nov 2019, 10:41
Display posts from previous: Sort by