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On Monday, 9 students each took a test with 100 questions. The average

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On Monday, 9 students each took a test with 100 questions. The average  [#permalink]

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New post 21 Jun 2019, 00:22
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Question Stats:

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On Monday, 9 students each took a test with 100 questions. The average (arithmetic mean) number of correct answers was 50, and the median number of correct answers was 40. With of the following statements must be true?

I. At least one student had more than 60 correct answers.
II. At least one student had more than 40 and less than 50 correct answers.
III. At least one student had less than 40 correct answers.

(A) I only
(B) II only
(C) III only
(D) I and III
(E) II and III

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Re: On Monday, 9 students each took a test with 100 questions. The average  [#permalink]

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New post 21 Jun 2019, 00:32
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Bunuel wrote:
On Monday, 9 students each took a test with 100 questions. The average (arithmetic mean) number of correct answers was 50, and the median number of correct answers was 40. With of the following statements must be true?

I. At least one student had more than 60 correct answers.
II. At least one student had more than 40 and less than 50 correct answers.
III. At least one student had less than 40 correct answers.

(A) I only
(B) II only
(C) III only
(D) I and III
(E) II and III


Data = 9*50=450 total correct questions.
I) Assume all students including median (5th student) had 40. So balance correct Ques = 450-200=250; Even if all 4 remaining students score 60 correct is 240 Ques only. So one scored more than 60 - Correct
II) Using the above it is not necessary to have between 40-50; remaining 4 students will have 250 among them which can call be greater than 60 - incorrect
III) Using I - Not nessary
So IMO A
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On Monday, 9 students each took a test with 100 questions. The average  [#permalink]

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New post 21 Jun 2019, 03:35
1
Bunuel wrote:
On Monday, 9 students each took a test with 100 questions. The average (arithmetic mean) number of correct answers was 50, and the median number of correct answers was 40. With of the following statements must be true?

I. At least one student had more than 60 correct answers.
II. At least one student had more than 40 and less than 50 correct answers.
III. At least one student had less than 40 correct answers.

(A) I only
(B) II only
(C) III only
(D) I and III
(E) II and III


How I approached this question-

I tried to negate an easy looking statement, I started with statement 2 and realized that I can also negate statement III in the process:

40*7 + 70 + 100 = 450,

So, 7 people got 40 (Median 40 :)), and one got 70 another one got 100 questions correct.
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On Monday, 9 students each took a test with 100 questions. The average   [#permalink] 21 Jun 2019, 03:35
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