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08 Jul 2025, 08:00
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Difficulty:
65%
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Question Stats:
60% (01:36) correct
40%
(01:50)
wrong
based on 321
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Jacob, Yuki, and Stephen each took the same science test. If the total of their scores on the test was 90, was the average (arithmetic mean) of the 3 scores equal to the median of the 3 scores?
(1) Yuki's score was 20 greater than Stephen’s score.
(2) Jacob's score was 30.
(1) Yuki's score was 20 greater than Stephen’s score.
(2) Jacob's score was 30.
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08 Jul 2025, 08:30
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Bunuel
Experts' Global Explanation:
Let Jacob’s score be A.
Let Yuki’s score be B.
Let Stephen’s score be C.
Since the total of their scores on the test was 90, A + B + C = 90
The average of the 3 scores = (A + B + C)/3 = 90/3 = 30.
We need to find whether the median of the 3 scores is 30.
Statement (1)
B = 20 + C
Possibility 1: If A = 10, B = 50, and C = 30, then median = 30.
Possibility 2: If A = 40, B = 35, and C = 15, then median = 35.
It is NOT possible to determine with certainty whether the median of the 3 scores is 30. Hence, Statement (1) is insufficient.
Statement (2)
A = 30
Since the value of A is equal to the average of the 3 scores, maintaining the average requires that both B and C are either equal to 30, or one of them is greater than 30 while the other is less than 30. In either case, the median will be 30.
It is possible to determine with certainty that the median of the 3 scores is 30. Hence, Statement (2) is sufficient.
B is the correct answer choice.
General Discussion
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08 Jul 2025, 08:27
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First, we know the average is 90 ÷ 3 = 30.
Statement (1): Yuki's score was 20 greater than Stephen's score.
This gives us Y = S + 20, but we don't know what J is. Without knowing all three scores, we can't determine if the median equals 30. Statement (i) alone is insufficient.
Statement (2): Jacob's score was 30.
We know J = 30, but we don't know Y and S individually. Without knowing all three scores, we can't determine if the median equals 30. Statement (2) alone is insufficient.
Statements (1) and (2) combined:
From statement (1): Y = S + 20A
From statement (2): J = 30
We know J+ Y +S = 90, so 30 + (S+ 20) + S= 90
30 + 25 + 20 = 90
2S = 40
S= 20
Therefore, Y = S + 20 = 20 + 20 = 40
The three scores are 20, 30, and 40.
The median is 30, which equals the average.
Therefore, the correct answer is C) Both statements together are sufficient, but neither alone is sufficient.
Statement (1): Yuki's score was 20 greater than Stephen's score.
This gives us Y = S + 20, but we don't know what J is. Without knowing all three scores, we can't determine if the median equals 30. Statement (i) alone is insufficient.
Statement (2): Jacob's score was 30.
We know J = 30, but we don't know Y and S individually. Without knowing all three scores, we can't determine if the median equals 30. Statement (2) alone is insufficient.
Statements (1) and (2) combined:
From statement (1): Y = S + 20A
From statement (2): J = 30
We know J+ Y +S = 90, so 30 + (S+ 20) + S= 90
30 + 25 + 20 = 90
2S = 40
S= 20
Therefore, Y = S + 20 = 20 + 20 = 40
The three scores are 20, 30, and 40.
The median is 30, which equals the average.
Therefore, the correct answer is C) Both statements together are sufficient, but neither alone is sufficient.
