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If the average (arithmetic mean) exam score of Alice, Bob and Cindy is

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If the average (arithmetic mean) exam score of Alice, Bob and Cindy is [#permalink]

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New post 30 Oct 2017, 01:42
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[GMAT math practice question]

If the average (arithmetic mean) exam score of Alice, Bob and Cindy is 80, what is the median exam score of them?

1) Alice’s score is 75.
2) Cindy’s score is 80.
[Reveal] Spoiler: OA

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Re: If the average (arithmetic mean) exam score of Alice, Bob and Cindy is [#permalink]

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New post 30 Oct 2017, 03:01
MathRevolution wrote:
[GMAT math practice question]

If the average (arithmetic mean) exam score of Alice, Bob and Cindy is 80, what is the median exam score of them?

1) Alice’s score is 75.
2) Cindy’s score is 80.



Hi....

Average of 3 people is 80...

Let's see what each statement tells us..
1) A's score is 75..
Other 2 can be 75 and 90.. median is 75
Other 2 can be 80 and 85... Median is 80
Various other possibilities...
Insuff

2) C's score is 80
Median will always be 80 as Average is 80..
If A's score is less than 80, B's will be more than 80 to get the average to 80..
But in every case 80 will be the middle value
Sufficient

B
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Re: If the average (arithmetic mean) exam score of Alice, Bob and Cindy is [#permalink]

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New post 30 Oct 2017, 03:11
Mean = Sum/Number
240 = sum
median = ?

1) Alice = 75
Bob = 75
Cindy = 90

If Bob = 80
Cindy = 85

Insufficient, as median is changing.

2) Cindy = 80
Bob = 80
Alice = 80

if Bob = 75
Alice = 85
Median is constant at 80
=> Sufficient.

B is the answer.
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Re: If the average (arithmetic mean) exam score of Alice, Bob and Cindy is [#permalink]

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New post 31 Oct 2017, 12:53
MathRevolution wrote:
[GMAT math practice question]

If the average (arithmetic mean) exam score of Alice, Bob and Cindy is 80, what is the median exam score of them?

1) Alice’s score is 75.
2) Cindy’s score is 80.


This is one where if I was moving really fast, I might make a silly mistake and pick C. But I slowed myself down.

St1, still don't know much. All we know is that the other two scores must sum to 165. Insufficient.
St2, Cindy's score is the average of the group. Therefore, A and B must be equidistant from 80 which implies 80 is the median.

B
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Re: If the average (arithmetic mean) exam score of Alice, Bob and Cindy is [#permalink]

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New post 01 Nov 2017, 01:55
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Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations.

Assume A, B and C are exam scores of Alice, Bob and Cindy, respectively.
We have ( A + B + C ) / 3 = 80 or A + B + C = 240.
Since we have 3 variable and 1 equation, C is most likely to be the answer.

Conditions 1) and 2)
Since A = 75, C = 80 and A + B + C = 240, we have B = 85.
Then, the median is C = 80.
Since it is a statistics question, one of the key questions, according to CMT4(A), we should consider A or B if C is chosen too easily.

From the condition 1), A = 75, we can’t figure out the median.
From the condition 2), C = 80, we have A + B = 160.
If one of them is less than 80, the other one must be greater than 80 and C = 80 is the median.
Otherwise, A = B = C = 80 and the median is 80.
The condition 2) is sufficient.
Therefore, B is the answer.

Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore, C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer, hence using 1) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

Ans: B
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Re: If the average (arithmetic mean) exam score of Alice, Bob and Cindy is   [#permalink] 01 Nov 2017, 01:55
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