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Mary and three other students took a math test. Each of their scores w

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Mary and three other students took a math test. Each of their scores w  [#permalink]

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New post 16 May 2019, 03:20
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Mary and three other students took a math test. Each of their scores was a non-negative integer. The teacher announced that the average score (of the 4 students) was 20. Mary immediately knew that all of the other three students scored below average. What is the minimum score that Mary could have gotten to be certain of the above situation?

A. 40
B. 41
C. 60
D. 61
E. 80
Director
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Re: Mary and three other students took a math test. Each of their scores w  [#permalink]

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New post 16 May 2019, 20:20
Mary immediately knew that all of the other three students scored below average, hence Mary score must be greater than 60.

The minimum score that Mary could have gotten to be certain of the above situation=61( Maximum score that any other student can get is 19 which is smaller than the average)
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Re: Mary and three other students took a math test. Each of their scores w  [#permalink]

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New post 11 Jun 2019, 07:01
nick1816 wrote:
Mary immediately knew that all of the other three students scored below average, hence Mary score must be greater than 60.

The minimum score that Mary could have gotten to be certain of the above situation=61( Maximum score that any other student can get is 19 which is smaller than the average)


Can you please explain this.

TIA
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Re: Mary and three other students took a math test. Each of their scores w  [#permalink]

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New post 12 Jun 2019, 15:07
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Karmesh wrote:
nick1816 wrote:
Mary immediately knew that all of the other three students scored below average, hence Mary score must be greater than 60.

The minimum score that Mary could have gotten to be certain of the above situation=61( Maximum score that any other student can get is 19 which is smaller than the average)


Can you please explain this.

TIA


1. We know, that average is 20.
2. Mary give information, that no one of other 3 student don't get more than 20

Let's say that we have Mary, student a, student b and student c

THE ONLY VARIANT , when we are sure , that no one of students a,b and c get more than 20 each is when the SUM of
their results is no more than 20

a + b + c < 20

Why is it so?

Let's imagine variant:
a+b+c = 30
So, 2 possibilities exist:
1. variant
Student a get 10
b get 10
c get 10
10+10+10=30
2. variant
a get 28
b get 1
c get 1
28+1+1=30

As we know Mary dont know results of 3 other students, but she KNOW that
NO ONE of them get result more than 20.
So, we have the only variant when a + b + c < 20

Next we calculate Mary result:
We know that
a+b+c = 19

(19+M)/4 = 20

M = 61

Answ D
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Re: Mary and three other students took a math test. Each of their scores w   [#permalink] 12 Jun 2019, 15:07
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