Liam, Noah, and Olivia received their science project scores today.

Question

Liam, Noah, and Olivia received their science project scores today. If the average (arithmetic mean) of their three scores was 85, what is the median of the three scores?

(1) Liam scored an 80 on his project.

(2) Olivia scored an 85 on her project.

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Bunuel · Accepted Answer

Official Solution:

Liam, Noah, and Olivia received their science project scores today. If the average (arithmetic mean) of their three scores was 85, what is the median of the three scores? 
 
(1) Liam scored an 80 on his project.
 
We can distribute the other two scores in different ways to get different medians. For example, {80, 80, 95} would give a median of 80, while {80, 85, 90} would give a median of 85. Not sufficient.
 
(2) Olivia scored an 85 on her project.
 
Olivia scored exactly the same as the average score, which implies that one of the other two must have scored less than or equal to 85 and the other greater than or equal to 85, making Olivia’s score the middle score, and thus the median equal to 85. That’s because if both of the other two had scored more than 85, the average would have been greater than 85; if both had scored less than 85, the average would have been less than 85. Therefore, we must have had the case {a ≤ (Olivia’s 85) ≤ b}. Sufficient.

Answer: B

sachbash14 · Answer

(Liam + Noah + Olivia) / 3 = 85
 
L + N + O = 255

1) 80 + N + O = 255
N + O = 175
Insufficient

2) L + N + 85 = 255
L + N = 170
Insufficient

If we have both L and O, we can determine N by subtracting from 255 (although not necessary) since with all 3 values we know we can determine median.

Therefore Option (C).

manoj2025 · Answer

IMO B is sufficient. One of the score is equal to mean, that means other two numbers are either side of mean or all numbers are mean. So B would be sufficient

ODST117 · Answer

Liam's score = L , Noah's score = N , Olivia's score = O Given: \frac{L+N+O}{3} = 85 L+N+O = 255 Statement 1: Liam scored an 80 on his project. If L = 80 , then N+O=175 If N=O , then both N and O are 87.5 each. In that case, 87.5 would be the median. If N>O , say N=100 and O=75 , then 80 would be the median. If NN , say L=90 and N=80 , the median would still be 85 . If L

bekhzod23 · Answer

I approach more logical way.
By knowing the average is 85 and the score of the one of the candidates, we can assume that the two conditions: 
1. The rest two have at least 85 equally to have a mean of 85. In that case median score is 85.

2. If one of the rest two has a score lower than 85, the third has to have above 85. Again, there is a mean of 85 for these three.

Dereno · Answer

Three students Liam, Noah and Olivia received their science project scores.

Given average of three scores = 85

Median score. = ?

Statement 1:

(1) Liam scored an 80 on his project.

Since, Liam scored an 80. The total score of all three = 85*3 = 255

The other two scores add up to 175.

The scores can be:

80, 85, 90 median = 85.

75, 80, 100 median = 80.

Hence,  Insufficient.

Statement 2:

(2) Olivia scored an 85 on her project.

Since, Oliver score is 85 = average of the three.

Average is like a see saw. 85 being in the middle.

One value is less than 85 and another is greater than 85.

So, the median is 85.

Hence,  Sufficient.

Option B

gmatophobia · Answer

Statement 1

From Statement 1, we can infer that Liam's score is 5 below the mean. Knowing this information is not sufficient as we can have multiple possibilities

Case 1 :

80 85 90

The median in this case is 85

Case 2 :

80 84 91

The median in this case is 84

Hence, the statement alone is not sufficient to answer the question.

Statement 2

As Oliva's score is at the mean, the scores of the other two individuals can follow one of the two cases

Case 1: The score of one of the two is above mean by a certain point difference, and the score of the other is below mean by the same difference. 
 Case 2: The score of all three is at the mean.

In both the cases, the median is 85.

Statement 2 alone is sufficient to answer the question.

Option B

ravi1522 · Answer

Hello,
(1) Liam scored an 80 on his project.
This statement is not sufficient as we don"t anything about other score

Insufficient .

2)Olivia scored an 85 on her project.
 either all be 85 as average is 85 so median will be 85
or either on will bw more than mean and other will be higher then mean then also median will be 85

This statement is sufficient

Hence option B is correct .

I hope it helps

Liam, Noah, and Olivia received their science project scores today.

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Liam, Noah, and Olivia received their science project scores today.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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745 with Only Self-Prep and GMAT Club

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Perfect 805 Score Debrief by Julia

My Rewards