On a Trolley Ride Around an Amusement Park, a Child GMAT Data Sufficiency

Question: On a trolley ride around an amusement park, a child travelled from one signpost to a second signpost at a constant speed of 125 meters per minute. Was the distance that the child travelled from the first signpost to the second signpost greater than 0.8km? (1km = 1,000meters)

1) It took less than 450 seconds for the child to travel from the first signpost to the second signpost
2) It took more than 400 seconds for the child to travel from the first signpost to the second signpost

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

“On a trolley ride around an amusement park, a child”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide". 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.

Solution and Explanation:
Approach Solution 1:
(distance) = (time)*(rate)

800 = (time)*125

(time) = 800/125 = 6.4 minutes = 384 seconds.

So, the question basically asks whether the time taken was greater than 384 seconds.

1) It took less than 450 seconds for the child to travel from the first signpost to the second signpost. Not sufficient.
2) It took more than 400 seconds for the child to travel from the first signpost to the second signpost. Sufficient.

Correct Answer: B

Approach Solution 2:
Since the statements are in terms of seconds, convert the given distance -- 0.8 km -- to seconds:

0.8−km/1 ∗ 1000−metres/1−km ∗ 1−minute/125−metres ∗ 60−seconds/1−minute= 800∗60/125= 384

Thus, 0.8 km is the equivalent of 384 seconds.
Implication:
To travel MORE THAN 0.8 km, the time must be MORE THAN 384 SECONDS.
Question stem, rephrased:
Is t > 384?

Statement 1: t < 450
If t = 300. The answer to the rephrased question stem is NO.
If t = 400. The answer to the rephrased question stem is YES.
Since the answer is NO in the first case but YES in the second case, INSUFFICIENT.

Statement 2: t > 400
Thus, the answer to the rephrased question stem is YES.
SUFFICIENT.

Correct Answer: B

Approach Solution 3:
Given: speed = 125m/min

Required: Distance > 0.8m?

Since both the statements are given in the form of time, it is better to convert the question in the form of time.

Distance = speed*time
(125/60)*t>800?
Or t > 384?

Statement 1: t < 450
Possible values of t:
t < 384
384 < t <450
Not Sufficient

Statement 2: t > 400
SUFFICIENT

Correct Answer: B

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