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16 Sep 2014, 01:19
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Mike has to take five tests, each with 80 questions. After completing four tests, Mike's average (arithmetic score) is 80% correct answers. What is the minimum number of questions Mike must answer correctly on the fifth test to raise his average (arithmetic score) to 82%?
A. 70
B. 72
C. 75
D. 78
E. 80
A. 70
B. 72
C. 75
D. 78
E. 80
16 Sep 2014, 01:19
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Official Solution:
Mike has to take five tests, each with 80 questions. After completing four tests, Mike's average (arithmetic score) is 80% correct answers. What is the minimum number of questions Mike must answer correctly on the fifth test to raise his average (arithmetic score) to 82%?
A. 70
B. 72
C. 75
D. 78
E. 80
To answer the question, we need to know how many questions were answered correctly in the first four tests. which would be:
\((80*4)*80\% = 256\).
Now, we must determine how many of the 400 questions from the 5 tests must be answered correctly to achieve an average of 82%:
\(400*82\%=328\)
By finding the difference between 328 and 256, we can answer the question:
\(328-256=72\)
Answer: B
Mike has to take five tests, each with 80 questions. After completing four tests, Mike's average (arithmetic score) is 80% correct answers. What is the minimum number of questions Mike must answer correctly on the fifth test to raise his average (arithmetic score) to 82%?
A. 70
B. 72
C. 75
D. 78
E. 80
To answer the question, we need to know how many questions were answered correctly in the first four tests. which would be:
\((80*4)*80\% = 256\).
Now, we must determine how many of the 400 questions from the 5 tests must be answered correctly to achieve an average of 82%:
\(400*82\%=328\)
By finding the difference between 328 and 256, we can answer the question:
\(328-256=72\)
Answer: B
03 Jul 2017, 07:35
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I guess this can be approached using the Alligation method as well. In case anyone interested, this is how I did it. Snapshot attached
From the Alligation we get
\(\frac{4}{1} = \frac{(x - 82)}{2}\)
\(8 = (x-82)\)
\(90 = x\)
Meaning mike has to get 90% questions right in his 5th attempt
=\((90/100) * 80 = 72\)
Final Answer : B
From the Alligation we get
\(\frac{4}{1} = \frac{(x - 82)}{2}\)
\(8 = (x-82)\)
\(90 = x\)
Meaning mike has to get 90% questions right in his 5th attempt
=\((90/100) * 80 = 72\)
Final Answer : B
Attachments
M23-19_Alligation.PNG [ 1.33 KiB | Viewed 7111 times ]
