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01 Jul 2023, 09:23
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On a recent test taken by 21 students, each student’s test score was between 0 and 100, inclusive.
Was the average (arithmetic mean) of the 21 scores on the test greater than 75 ?
(1) The median of the 21 test scores was 80.
(2) The minimum of the 21 test scores was 70.
Was the average (arithmetic mean) of the 21 scores on the test greater than 75 ?
(1) The median of the 21 test scores was 80.
(2) The minimum of the 21 test scores was 70.
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01 Jul 2023, 09:53
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houston1980
Given
- The test was taken by 21 students
- Each student scored between 0 and 100, inclusive
Question Is the average of the 21 scores greater than 75 ?
If we arrange the scores in ascending order, the 11th score is the median score. We might not need this immediately, but its good to keep the information handy.
Attachment:
SC1.jpg [ 17.76 KiB | Viewed 30380 times ]
Statement 1
(1)The median of the 21 test scores was 80
Case 1: Let's assume that all the students scored 80 on the test. In that case, the average score of 21 students will be 80.
Is the average of the 21 scores greater than 75 ? → Yes !
Case 2: Let's assume that 10 students scored 0 on the test and 11 students scored 80 on the test. In that case, the average will be around 40.
Is the average of the 21 scores greater than 75? → No !
As we are getting contradicting answers, the statement alone is not sufficient and we can eliminate A and D.
Statement 2
(2)The minimum of the 21 test scores was 70
Case 1: Let's assume that all the students scored 70 on the test. In that case, the average score of 21 students will be 70.
Is the average of the 21 scores greater than 75? → No!
Case 2: Let's assume that only one student scored 70 on the test and the rest 20 students scored 100 on the test. In that case, the average will be greater than 75.
Is the average of the 21 scores greater than 75? → Yes!
As we are getting contradicting answers, the statement alone is not sufficient and we can eliminate B.
Combined
From statement 2, we know that the minimum score on the test is 70. Hence to find the lowest possible average, let's assume that the 10 students scored a 70 on the test, and 11 students scored an 80 on the test.
Attachment:
Sc2.jpg [ 20.2 KiB | Viewed 28906 times ]
If that were the case, the average = \(\frac{(80*11)+(70*10)}{21} = \frac{1580}{21} = 75.XX\)
Hence, the minimum possible average is greater than 75.
The statements combined are sufficient.
Option C
08 Jul 2023, 15:09
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houston1980
n = 21
We need to answer the question:
Is average > 75 ?
Statement One Alone:
=> The median of the 21 test scores was 80.
Since 21 is an odd number, the median is the middle value (the 11th value) in the list of test scores in ascending order.
If 10 students scored 0 and 11 students scored 80, then the average is clearly less than 75.
Whereas, if each of the 21 students scored 80, then the average is 80, which is greater than 75.
Statement one is not sufficient. Eliminate answer choices A and D.
Statement Two Alone:
=> The minimum of the 21 test scores was 70.
If each of the 21 students scored 70, then the average is 70, which is less than 75.
Whereas, if 1 student scored 70 and 20 students scored 100, then the average is clearly greater than 75.
Statement two is not sufficient. Eliminate answer choice B.
Statements One And Two Together:
If 10 students scored 70 and 11 students scored 80, then the average takes its smallest possible value, which is greater than 75. So, the average must be greater than 75, and thus the answer is a definite Yes.
The two statements together are sufficient.
Answer: C
