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GMAT Club Olympics 2025 (Day 7): Jacob, Yuki, and Stephen each took

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sanya511

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Total score = 90. Average = 90/3 = 30
Is mean = Median?
(1) stephen's score = x. Yuki's score = 20 + x. let jacob's score = y
y + 2x + 20 = 90.
y + 2x = 70.
Not sufficient.

(2) Jacob's score was 30.
If jacob's score was 30 then Yuki's and Stephen's score was either, equally distant from his score on both sides, or both of their scores was 30. In either cases, median = 30.
Sufficient.

Option B.

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Manu1995

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Each gift bag contains magnets, postcards, bookmarks, and keychains in the fixed ratio 2 : 3 : 4 : 5 — that means:

Every gift bag must have 2k, 3k, 4k, and 5k items for some constant value of k (same for all bags),

So if x bags were packed, total items = Magnets:2kx
Postcards:3kx
Bookmarks:4kx
Keychains:5kx

Let’s denote the total number of bags as x, and per-bag item counts as:

Magnets per bag:2k
Postcards per bag:3k
Bookmarks per bag:4k
Keychains per bag:5k

Then total items packed becomes:
Magnets per bag:2kx
Postcards per bag:3kx
Bookmarks per bag:4kx
Keychains per bag:5kx

From Statement(I):
Magnets = 24, Postcards = 36, Bookmarks = 48,Keychains = 60
So:
2kx=24 → kx=12
3kx=36 → kx=12
4kx=48 → kx=12
5kx=60 → kx=12

Number of bags x= 12/k
But since X and k must be positive integers, and we know x must be greater than 5, we need integer solutions of kx=12 such that x>5

Now, possible integer factor pairs of 12 and x>5
(k=1,x=12)
(k=2,x=6)

The combined data doesn't uniquely determine the number of bags.

Option (E)

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Bunuel

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Total score = 90
Mean = 90/3 = 30
Median = a

Is a = 30?

(1) Yuki's score was 20 greater than Stephen’s score.
Yuki = Stephen + 20

Let say
Jacob = 20
Yuki = 45
Stephen = 25
Invalid as 25 is not equal to 30

Jacob = 20
Yuki = 30
Stephen = 40
Valid as 30 is equal to 30

Insufficient

(2) Jacob's score was 30
Jacob = 30
=> Yuki +Stephen = 60
In any scenario Jacob's score stays the mean as
Case 1
Yuki < Jacob, then Stephen > Jacob
Mean score = Jacob

Case 2
Stephen < Jacob, then Yuki > Jacob
Mean score = Jacob

Case 1
Yuki = Jacob, then Stephen = Jacob
Mean score = Jacob

Hence mean will always be equal to median
Sufficient

Option B

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Bunuel

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Score of Jacob + Yuki + Stephen = 90

Average score = 30 = Median ?

1. Yuki = Stephen + 20 , We don't know the score of Jacob or whether the Yuk's score is lowest or note - Insufficient

2. Jacob Score is 30, Yuki + Stephen = 60, In any cases whether Yuki and Stephen has same score or either of them scores more than the other, Median will always be equal to 30 or Jacob's score - Sufficient B.

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Sum of three scores = 90
Average score = 30

Q - is the median 30?

S1
Y = 20 + S

Case 1
S-Y-J
0-20-70
Median is not 30

Case 2
S-J-Y
20-30-40
Median is 30

Not sufficient

S2
If Jacob scored 30, then the other two scores are either the same as his, or on either side of his (one greater than and one lower than him, by equal magnitude). In both cases, 30 will be the median.

Sufficient

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We are given:

Y+S+J=90 $\to$ mean = 30
Ask if median = mean?

(1) Y=S+20

If S=10, Y=30 $\to$ J=50, median = 30 = mean
If S=5, Y=25 $\to$ J=60, median = 25 <> mean

$\implies$ Insufficient

(2) J=30 $\to$ S+Y=60
3 possible cases:

S = Y = 30
S<30 & Y>30
S>30 & Y<30

In any case median = 30 = mean (YES)
$\implies$ Sufficient

Answer: B

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1) we cant etermine median NS
2) in this either all 3 scores are 30 or one is less than 30 and the other greater than 30 so average= median
suff

Ans B

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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.

If the total score is 90 and 3 students took the test. The mean = 30

Statement 1: Let Yuki=Y
Stephen =S
Y=20+S
Jacob=J= 90-(S+20+S)
=70-2S

The values are S, 20+S, 70-S

However, we dont know the arrangement of these values . Hence statement 1 is insufficient.

Statement 2

J=30

Y+S= 60

The values can be (1,59)(2,58),( 10,50).

Thus Jacob's score is the median and is equal to the mean. Statement 2 is sufficient.

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Basically, we need median score is 30 or not?

S1 : We don't know whether the lowest score is 20 or not? [NS]

S2 : If one score is 30 other two score has to be addition up to 60. [S]

B

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total of scores=90 and three people, average=90/3=30

(1)
Possibilities:
Stephen 10, Yuki 30, Jacob 50: median 30 equal to 30
Jacob 20, Stephen 25, Yuki 45: median 25 not equal to 30

Statement (1) alone is insufficient.

(2)
Jacob=30

As Jacob's score is equal to average, the other two scores (Stephen and Yuki) must be around that average, all the three equal to 30 or one less than 30 and the other more than 30 in the same amount. In any case, median is 30.

Statement (2) alone is sufficient.

Answer is B

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Total, T = 90
Given, average, A = (j + y + s)/3 = 30;

Statement 1,
Yuki's score was 20 greater than Stephen’s score.
Y = S + 20; substituting in total, T = 90
2S + J = 70
This is not sufficient to answer the question.

Statement 2,
Jacob's score was 30.
With the score of J provided as 30 which is also the average, the other two scores can be either 30, in which case we can say that the median is 30. The only other cases are where the sum of S + Y = 60.
In any of these cases the number 30, which has to be the average is the Median. So this statement alone is sufficient.

Correct option is Option B

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Average=90/3=30

Median=30?

(1)
Median=30 example:
Jacob=50
Yuki=30
Stephen=10

Median!=30 example:
Jacob=0
Yuki=55
Stephen=35

Insufficient

(2)
Jacob=30 and Average=30
Yuki+Stephen=60

If Yuki=Stephen then their score must be 30 too and Median=30.
If Yuki!=Stephen then Median is Jacob=30.

Sufficient

Correct answer is B

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Jacob + Yuki + Stephen = 90
Mean = 90/3 = 30

The question is if median=30

(1)
Yuki = Stephen + 20

(Stephen, Jacob, Yuki) can be (20, 30, 40) -> yes
(Stephen, Yuki, Jacob) can be (5, 25, 60) -> no

Statement is insufficient

(2)
If one of the three scores is 30=average, then all the other two can be both equal to 30 or one of them must be less than 30 and the other greater than 30.
In both cases median=30=average

Statement is sufficient

The right answer is B

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J+Y+S=90
Average=90/3=30

Is median=30?

(1)
Y=S+20

If S=10, Y=30, J=50 the answer is yes
If S=15, Y=35, J=40 the answer is no

INSUFFICIENT

(2)
J=30 -> S+Y=90-30=60

If S=Y=30 the answer is yes.
And if S!=Y then J is in the middle of S and Y, so 30 is the median and the answer is yes too.

SUFFICIENT

IMO B

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Total Score : 90 ; Avg = 90/3 = 30 ; Median = M
We want to check if M = 30

Statement 1 : Yuki's score was 20 greater than Stephen’s score.
-> Y = S + 20, so J = 90 – (S + Y)
-> J = 90 – (S + S + 20)
-> J = 70 – 2S
If S = 0, scores are 0, 20, 70 ; M = 20, which is not equal to avg
If S = 20, scores are 20, 30, 40 ; M = 30, which is equal to avg
Insufficient

Statement 2: Jacob's score was 30.
J = 30 -> So Y + S = 60.
No matter how we split 60, median will always be 30, which is equal to avg
Sufficient.

Answer: B.

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Total = J + Y + S = 90

is Average = Median ? or is Median = 30 ?

(1) Y = S + 20 , possible case 1 : J = 0, Y = 35 , S = 55 (median = 35 => no)
possible case 2: J=10, Y = 50, S = 30 (median = 30 => yes)
INSUFFICIENT

(2) J= 30 => Y+S = 60. for any combination of Y and S, median would be 30.

SUFFICIENT

B is the answer

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B. If one score is given to be 30, that would only be the median, when sum is 90, be it any no.s the rest. Hence sufficient. About the 1st there cant be any conclusion.

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Given -> $J+Y+S = 90$
To determine -> Median=Mean?

Statement 1 -> Yuki's score was $20$ greater than Stephen’s score.
$Y = S+20$
$J+S+20+S=90$
$J+2S=70$
If $S=20$ and $J=30$, then $Y=40$. The median is $30$ and the mean is $30$.
If $S=1$ and $J=68$, then $Y=21$. The median is $21$ and the mean is $30$.
Two different answers with Statement 1. Not sufficient.

Statement 2 -> Jacob's score was $30$.
$J+Y+S=90$
$30+Y+S=90$
$Y+S=60$
If $Y=30$ and $S=30$, the median is $30$ and the mean is $30$.
If $Y>S$, then $Y>30$ and $S<30$. In this case, the median is $30$ and the mean is also $30$.
If $Y<S$, then $Y<30$ and $S>30$. In this case, the median is $30$ and the mean is also $30$.
All cases give us the same answer.
Therefore, Statement 2 is sufficient.

Answer - B

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09 Jul 2025, 06:11

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J+Y+S = 90
Mean = 90/3 = 30
Q: Is median = mean = 30?

St1: Y= S+20 => Y>S
J + S+20+S = 90
J + 2S = 70
If S = 10,
J=50, Y = S+20 = 30
Scores would be: 10,30,50 which gives Median as 30
If S=15
J=40, Y = 35
Scores would be: 15,35,40 which gives Median as 35
Two different answers. Insufficient.

St2: J=30
Y+S = 90-30 = 60
One of Y and S will always be greater than 30 and the other less than 30 or Y=S. In both cases, J will be in the middle and Median = 30
Let’s understand by using examples:
If Y = 25, S = 35,
Scores would be 25,30,35 giving Median as 30
If Y= 45, S = 15
Scores would be 15,30,45 giving Median as 30
If Y= 30, S = 30
Scores would be 30,30,30 giving Median as 30
St2 is sufficient.
Option B

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Given:

Jacob (J), Yuki (Y), Stephan (S) and total of their score was 90

Question:

Is mean=Median?

Average score can be calculated as 90/3=30

So we can also say is median= 30?

Lets analyse the statements:

Statement 1.:Yuki's score was 20 greater than Stephen’s score.

From this we can say Y=S+20

We can also say,

Y+S+J=90
S+20+S+J=90
2S+J=70

Case1: S can be 10 then J will be 50

So median in this case will be 30, (10,30,50) So yes

Case 2: S can be 5 Then J will be 60

So median in this case will be 5, 25, 60 (Median is 25)

We cant definitely say that mean=median or not. So Not sufficient.

Statement 2: Jacob's score was 30.

When Jacob is 30

So, Y+J+S=90
Y+30+S=90
Y+S=90-30=60

Case 1: Y=10

So, S will be 50
Median is 30 (10,30,50)

Case 2: Y=20, S will be 40

Median is 30 ) (20,30,40)

We can test for any value median will always be 30.

So we can say median=Means

This statement is sufficient.

Answer B

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