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Updated on: 25 Oct 2023, 23:59
Originally posted by 12922 on 15 Jun 2023, 00:48.
Last edited by gmatophobia on 25 Oct 2023, 23:59, edited 2 times in total.
Last edited by gmatophobia on 25 Oct 2023, 23:59, edited 2 times in total.
Renamed the topic.
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
70% (01:47) correct
30%
(01:59)
wrong
based on 777
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Kevin, Leo, and Max each received a monetary award for their work on project X. If the total of the 3 awards was $705, was the average (arithmetic mean) of the 3 awards equal to the median of the 3 awards?
(1) Kevin's award was $235.
(2) Leo's award was $70 greater than Max's award.
(1) Kevin's award was $235.
(2) Leo's award was $70 greater than Max's award.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
15 Jun 2023, 01:30
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Kevin, Leo, and Max each received a monetary award for their work on project X. If the total of the 3 awards was $705, was the average (arithmetic mean) of the 3 awards equal to the median of the 3 awards?
Since the total of the 3 awards was $705, the average was 705/3 = $235.
(1) Kevin's award was $235.
Since Kevin's award of $235 matches the average, then one of the remaining two awards must have been less than or equal to that amount, and the other must have been more than or equal to that amount. Consequently, the awards were {≤235, 235, ≥235}. Therefore, the median, which is the middle value, would also be equal to 235, and hence, to the average. Sufficient.
(2) Leo's award was $70 greater than Max's award.
The above is clearly insufficient. For instance consider: {0, 70, 635} and {200, 235, 270}.
Answer: A.
Since the total of the 3 awards was $705, the average was 705/3 = $235.
(1) Kevin's award was $235.
Since Kevin's award of $235 matches the average, then one of the remaining two awards must have been less than or equal to that amount, and the other must have been more than or equal to that amount. Consequently, the awards were {≤235, 235, ≥235}. Therefore, the median, which is the middle value, would also be equal to 235, and hence, to the average. Sufficient.
(2) Leo's award was $70 greater than Max's award.
The above is clearly insufficient. For instance consider: {0, 70, 635} and {200, 235, 270}.
Answer: A.
29 Jul 2023, 17:27
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12922
Kevin, Leo, and Max each received a monetary award for their work on project X. If the total of the 3 awards was $705, was the average (arithmetic mean) of the 3 awards equal to the median of the 3 awards?
(1) Kevin's award was $235.
(2) Leo's award was $70 greater than Max's award.
(1) Kevin's award was $235.
(2) Leo's award was $70 greater than Max's award.
average = 705/3 = 235
We need to answer the question:
Is average = median ?, which we can rephrase into:
Is median = 235 ?
Statement One Alone:
=> Kevin’s award was $235.
The sum of the deviations from the mean is always equal to zero. We see that Kevin’s award doesn’t differ from the mean. So, if one of the unknown awards is x above the mean (235 + x), then the other unknown award must be x below the mean (235 – x).
The list of awards in ascending order:
235 – x, 235, 235 + x
Regardless of the value of x, the median is 235. The answer to the rephrased question is a definite Yes.
Statement one is sufficient. Eliminate answer choices B, C, and E.
Statement Two Alone:
=> Leo’s award was $70 greater than Max’s award.
If the list of awards in ascending order is 200, 235, 270, then the median is 235. Whereas, if the ordered list is 195, 245, 265, then the median is 245.
Statement two is not sufficient.
Answer: A
