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The question is asking whether the mean = 30 is equal to the median score of three people
(1): We can do extreme test cases as following: If Stephen = 0 & Yuki = 20, then Jacob = 70 - the answer is NO (20#30)
- If Stephen = 10 & Yuki = 30, then Jacob = 50 - the answer is YES
This statement is NOT SUFFICIENT

(2): W/ Jacob's score = 30, we have S + Y = 60. Notice that w/ any test cases of S & Y, we still have Jacob's score as median, which is always equal to the mean - SUFFICIENT
- Choice (B) is the final answer
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Assume each score is j, y and s
S1 means y=s+20
meaning j+s+s+20=90= j+2s=90 From this we can have many values including 30,30,30 and 15,3540 hence insufficIent
S1 means of the two remaining values one is either more or less than 30 or equal to 30. In both the two cases mean will always be equal to median hence sufficient
ANS B
Bunuel
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.


 


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The correct answer choice is (E)

The question provides information that the total of the scores was 90 and that there were 3 scores. The mean can be calculated by adding all 3 (which is 90) and then dividing by 3, so the mean = 30. Then we need to check if the statements provide enough information to calculate the median.

Statement 1 - this gives us information about 2 of the 3 scores as a relationship but not enough to determine the exact 3 scores.

Statement 2 - this gives us information explicitly about 1 score, which also equals the mean. We know then that the other two scores need to be a similar distance away from 30 to keep the median of all 3 scores at 30. This coukd still mean the scores could be any pair that are a similar distance away from 30 but adding up to the 90 - 30 = 60. All 3 scores could also equal 30.

However when we look at both statements together, we can determine that if one score is 30 and the other two have a difference of 20, then the scores could be 10 above and 10 below 30. This would allow the mean and median to be the same. We still do not know if the scores could be 7 below and 13 above or some combination of that difference of 20. Therefore even together, the statements are not enough.

The correct answer is (E)
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Question Analysis: If total of scores is 90, then the average = 30. Then, the question wants to know if median is also 30.

I- Y = S + 20 -> We know nothing about J, so Y could be 55, S 35 and J 0. Y could also be 40, S 20 and J 30. So Not suf

II - We know nothing about other scores, so just like I, we could have different scores that would result in median = 30 or median ≠ 30 -> Not suf

Together: If J = 30, we know that S + Y = 60. Knowing that Y = S + 20, we find S = 20, J = 30 and Y = 40. So, Med = Avg = 30 -> Suf (C)

----------------
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.
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Given:
Total score = 90 → Average = 30
What to check: Is median = 30?
(1) Yuki = Stephen + 20
Not enough — scores can lead to median = 30 or not, depending on values.
Not sufficient

(2) Jacob = 30
Then, Yuki + Stephen = 60
No matter how Yuki and Stephen split 60, 30 is always the middle value
Sufficient

Statement (2) alone is sufficient. So, Correct answer choice is option B.
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Hi Bunuel, can i make combination of scores of J, Y and S as (68+21+1) and so on.. to make inference that statement 1 is Insufficient. Because i feel difficulty in making combinations randomly, i miss some combinations ??
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.
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shaliny
Hi Bunuel, can i make combination of scores of J, Y and S as (68+21+1) and so on.. to make inference that statement 1 is Insufficient. Because i feel difficulty in making combinations randomly, i miss some combinations ??

Hello Shaliny,

No you can't make that specific combination of 68,21,1 because statement 1 is about that one is greater Than other by 20.

You don’t need to form any combination here. Statement 1 only tells us that one student scored 20 more than the other. Under this condition, there can be multiple possible cases, and in some of them the answer is “yes,” while in others it is “no.” Whenever a statement allows for both outcomes, it is considered not sufficient.

Ex : Possibility 1: If A = 10, B = 50, and C = 30, then median = 30. Yes, because here median = mean
Possibility 2: If A = 40, B = 35, and C = 15, then median = 35. No because here median not equal to mean

There can be other possibilities too, However this two possibility is enough to say that statement 1 is not sufficient.

I hope this helps.
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statement 1 says the one is 20 more than other that's why i made cases of 1 and 21,68 so why it is not right
Gmat860sanskar

Hello Shaliny,

No you can't make that specific combination of 68,21,1 because statement 1 is about that one is greater Than other by 20.

You don’t need to form any combination here. Statement 1 only tells us that one student scored 20 more than the other. Under this condition, there can be multiple possible cases, and in some of them the answer is “yes,” while in others it is “no.” Whenever a statement allows for both outcomes, it is considered not sufficient.

Ex : Possibility 1: If A = 10, B = 50, and C = 30, then median = 30. Yes, because here median = mean
Possibility 2: If A = 40, B = 35, and C = 15, then median = 35. No because here median not equal to mean

There can be other possibilities too, However this two possibility is enough to say that statement 1 is not sufficient.

I hope this helps.
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shaliny
statement 1 says the one is 20 more than other that's why i made cases of 1 and 21,68 so why it is not right

Oh, My bad! I'm sorry. Yes this is a valid combination as 21 - 1 = 20. As, you can see there can ne multiple possibilities here. Please feel free to let me know, if you have any further query regarding this.
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