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08 Jul 2025, 11:57
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J+Y+S=90
Is the median of (J,Y,S) equal to 30?
(1) Yuki’s score was 20 greater than Stephen’s score
Y=S+20
J+(S+20)+S=90
J+2S=70
we have two unknowns. Insufficient.
(2) Jacob’s score was 30
J=30.
Then:
30+Y+S=90 => Y+S=60
But without knowing how Y and S compare to 30, the median could be below, equal to, or above 30:
Therefor, statement (2) alone is sufficient to guarantee median = 30.
B) Statement 2 alone is sufficient.
Is the median of (J,Y,S) equal to 30?
(1) Yuki’s score was 20 greater than Stephen’s score
Y=S+20
J+(S+20)+S=90
J+2S=70
we have two unknowns. Insufficient.
(2) Jacob’s score was 30
J=30.
Then:
30+Y+S=90 => Y+S=60
But without knowing how Y and S compare to 30, the median could be below, equal to, or above 30:
- If (Y,S)=(35,25) , the list is (25, 30, 35) => median = 30.
- If (Y,S)=(50,10), the list is (10, 30, 50) => median = 30.
- If (Y,S)=(55,5), still median = 30.
Therefor, statement (2) alone is sufficient to guarantee median = 30.
B) Statement 2 alone is sufficient.
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08 Jul 2025, 12:16
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Solution:
Let the score of Jacob be J, Yuki be Y, and Stephen be S. The total of their scores on the test was 90. The question asked us whether the average of the 3 scores was equal to the median of the three scores.
Average = 30.
Is the average of the three scores equal to the median of the three scores?
(1) Yuki's score was 20 greater than Stephen’s score. Insufficient
Y= 20 + S
So, we put together, we get 20+S + S + J = 90---> 2S + Y = 70
(2) Jacob's score was 30. Insufficient
But if we combine both statements, we get
2S + 30 = 70
S = 20, Y is 40, and J is 30. So, we get the answer NO.
Hence, Option C
Let the score of Jacob be J, Yuki be Y, and Stephen be S. The total of their scores on the test was 90. The question asked us whether the average of the 3 scores was equal to the median of the three scores.
Average = 30.
Is the average of the three scores equal to the median of the three scores?
(1) Yuki's score was 20 greater than Stephen’s score. Insufficient
Y= 20 + S
So, we put together, we get 20+S + S + J = 90---> 2S + Y = 70
(2) Jacob's score was 30. Insufficient
But if we combine both statements, we get
2S + 30 = 70
S = 20, Y is 40, and J is 30. So, we get the answer NO.
Hence, Option C
Bunuel
08 Jul 2025, 13:16
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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?
Let J = Jacob, Y = Yuki, S = Stephen
If the total score is 90 then average is 90/3 = 30.
Rephrasing the question: "is median = 30?"
(1) Yuki's score was 20 greater than Stephen’s score.
With only this information we cannot define. It can be (example: J = 30, Y = 40, S = 20) and can be not (example: J = 70, Y = 20, S = 0).
Eliminate answer choices A and D.
(2) Jacob's score was 30.
Since J = 30, we have Y + S = 60.
If Y = S, then we will have the three values = 30 -> that will give us a median = 30.
If Y is not equal S, then we will have a value greater than 30 and another value lower than 30. J will be the median, with a value of 30.
In any scenario we can answer "Yes, the average is equal to the median".
Therefore:
Answer = B Statement 2 alone is sufficient but statement 1 alone is not
Let J = Jacob, Y = Yuki, S = Stephen
If the total score is 90 then average is 90/3 = 30.
Rephrasing the question: "is median = 30?"
(1) Yuki's score was 20 greater than Stephen’s score.
With only this information we cannot define. It can be (example: J = 30, Y = 40, S = 20) and can be not (example: J = 70, Y = 20, S = 0).
Eliminate answer choices A and D.
(2) Jacob's score was 30.
Since J = 30, we have Y + S = 60.
If Y = S, then we will have the three values = 30 -> that will give us a median = 30.
If Y is not equal S, then we will have a value greater than 30 and another value lower than 30. J will be the median, with a value of 30.
In any scenario we can answer "Yes, the average is equal to the median".
Therefore:
Answer = B Statement 2 alone is sufficient but statement 1 alone is not
