On her annual road trip to visit her family in Seal Beach

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AAPL: Moderator; Posts: 2632; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Mon Apr 02, 2018 4:44 am

On her annual road trip to visit her family in Seal Beach, California, Traci stopped to rest after she traveled 1/3 of the total distance and again after she traveled 1/4 of the distance remaining between her first stop and her destination. She then drove the remaining 200 miles and arrived safely at her destination. What was the total distance, in miles, from Traci's starting point to Seal Beach?

A. 250
B. 300
C. 350
D. 400
E. 550

The OA is D.

Traci ran 1/3 of the total distance.

| - - - - - - - - - | - - - - - - - - - - - - - - - - - - - - - - - - - - - |
1/3 traveled 2/3 has not traveled

Traci then traveled 1/4 of the remaining distance meaning there is (3/4)(2/3)X left, X representing the distance of the total trip. If this equation equals 200 miles...

(3/4)(2/3)X = 200

X/2 = 200

X = 400. Option D.

Has anyone another strategic approach to solve this PS question? Regards!

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Source: Beat The GMAT — Problem Solving | Mon Apr 02, 2018 4:44 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Mon Apr 02, 2018 10:42 pm

AAPL wrote:On her annual road trip to visit her family in Seal Beach, California, Traci stopped to rest after she traveled 1/3 of the total distance and again after she traveled 1/4 of the distance remaining between her first stop and her destination. She then drove the remaining 200 miles and arrived safely at her destination. What was the total distance, in miles, from Traci's starting point to Seal Beach?

A. 250
B. 300
C. 350
D. 400
E. 550

The OA is D.

Traci ran 1/3 of the total distance.

| - - - - - - - - - | - - - - - - - - - - - - - - - - - - - - - - - - - - - |
1/3 traveled 2/3 has not traveled

Traci then traveled 1/4 of the remaining distance meaning there is (3/4)(2/3)X left, X representing the distance of the total trip. If this equation equals 200 miles...

(3/4)(2/3)X = 200

X/2 = 200

X = 400. Option D.

Has anyone another strategic approach to solve this PS question? Regards!

This can be solved taking smart numbers. Since we have to deal with 1/3 and 1/4, let's assume the distance = LCM of 3 and 4 = 12 miles

> 1st leg of journey = 1/3 of 12 = 4 miles
> 2nd leg of journey = 1/4 of (12 - 4) = 1/4 of 8 = 2 miles

Total distance covered = 4 + 2 = 6 miles = half of the total distance (= 12 miles)

Thus, half of the total distance is the 3rd leg of the journey

Since actual figure for the 3rd leg of the journey (half of the total distance) = 200 miles, the total distance would be 2*200 = 400 miles.

The correct answer: D

Hope this helps!

-Jay
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Manhattan Review GMAT Prep

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Jeff@TargetTestPrep: 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 Apr 05, 2018 4:22 pm

AAPL wrote:On her annual road trip to visit her family in Seal Beach, California, Traci stopped to rest after she traveled 1/3 of the total distance and again after she traveled 1/4 of the distance remaining between her first stop and her destination. She then drove the remaining 200 miles and arrived safely at her destination. What was the total distance, in miles, from Traci's starting point to Seal Beach?

A. 250
B. 300
C. 350
D. 400
E. 550

We can let the total distance = n, and create the equation:

(1/3)n + 1/4(2/3)n + 200 = n

n/3 + n/6 + 200 = n

Multiplying by 6, we have:

2n + n + 1200 = 6n

1200 = 3n

400 = n

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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

by deloitte247 » Sun Apr 15, 2018 1:43 pm

Let the total distance covered be 'x'
After one-third of x (i.e x/3 miles), she rested.
Distance left to be covered at this point $$=x-\frac{x}{3}=\frac{2x}{3}miles$$
After travelling one-fourth of 2x/3 (i.e 1/4 of 2x/3),
Distance left to be covered at this point $$=\frac{2x}{3}-\left(\frac{1}{4}\ of\ \frac{2x}{3}\right)$$
$$=\frac{2x}{3}-\frac{2x}{12}$$
$$=\frac{6x}{12}=\frac{x}{2}miles$$
But the distance left is given as 200 miles i.e
$$\frac{x}{2}=200\ miles$$
$$x=400\ miles\ \left(option\ D\right)$$

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