Buster Leaves the Trailer at Noon and Walks Towards the Studio GMAT Data Sufficiency

bySayantani Barman Experta en el extranjero

Question: Buster leaves the trailer at noon and walks towards the studio at constant rate B miles per hour. 20 minutes later, Charlie leaves the same studio and walks towards the same trailer at a constant rate of C miles per hour along the same route as Buster. Will Buster be closer to the trailer than to the studio when he passes Charlie?

Charlie gets to the trailer in 55 minutes.
Buster gets tot eh studio at the same time as Charlie gets to the trailer.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

“Buster leaves the trailer at noon and walks towards the studio at constant rate B miles per hour. 20 minutes later, Charlie leaves the same studio and walks towards the same trailer at a constant rate of C miles per hour along the same route as Buster. Will Buster be closer to the trailer than to the studio when he passes Charlie?” – is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken f0rom the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Answer

Approach Solution 1

(1) Charlie gets to the trailer in 55 minutes. No info about Buster.

Hence, this statement is not sufficient.

(2) Buster gets to the studio at the same time as Charlie gets to the trailer. Charlie needed 20 minutes less than Buster to cover the same distance, which means that the rate of Charlie is higher than that of Buster. Since after they pass each other they need the same time to get to their respective destinations (they get at the same time to their respective destinations) then Buster had less distance to cover ahead (at lower rate) than he had already covered (which would be covered by Charlie at higher rate).

Hence, this statement is sufficient.

Correct option: B

Approach Solution 2

Given: Speed of B = B miles per hour

Speed of C = C miles per hour and C started the journey after 20 minutes

(1) C took 55 minutes

This statement is not giving us any information regarding time taken by B so we can’t compare their speeds.

Hence, this statement is not sufficient.

(2) B and C reached at the same time.

Let us assume

Distance D = 100 miles and time taken by B = 100 minutes

Therefore, time taken by C = 80 minutes

Hence, speed of B = 1 mile per min and C = \(\frac{10}{8}\)mile per min

C started the journey after 20 minutes

So in 20 minutes, B covered 20 miles… remaining distance 80 miles

Now, Relative speed concept: They both are travelling in opposite directions

So relative speed = 1 + \(\frac{10}{8}\) = \(\frac{10}{8}\) miles per min

Time taken to cover 80 miles with this relative speed = \(\frac{80}{18}\) * 8 = 35

This is the time when they cross each other

B already covered 20 miles and in 35. Something times s/he will cover = 35 miles total = 55 miles

This means C covered 100 – 55 = 45 miles.

Correct option: B

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Buster Leaves the Trailer at Noon and Walks Towards the Studio GMAT Data Sufficiency

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