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One can save a lot of time by looking at the answer questions first. Since we need our average score to go up all scores that are below or equal to 78 are out. That leaves us with A and B. B is clearly too low because we need the 7th test to add an average of 4 points to each of the 6 tests and 78 to the 7th test.
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If the average (arithmetic mean) score for a certain student in Ms Sweeney's class is 74 on his first 6 tests then how many points must that student score on this next test to bring his overall average to 78?

Average of first 6 tests = 74 .
Sum of first 6 test = Average x Number of test = 74 x 6 = 444

Average of 7 tests = 78
Sum of 7 tests = 78 x 7 = 546

Therefore required score in 7th test = 546 - 444 = 102.
Answer A...

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Bunuel
If the average (arithmetic mean) score for a certain student in Ms Sweeney's class is 74 on his first 6 tests then how many points must that student score on this next test to bring his overall average to 78?

A. 102
B. 84
C. 78
D. 76
E. 74

Average for the first 6 tests = 74
i.e. Total Score of first 6 tests = 74*6 = 444

After taking the next test, total tests taken = 6+1= 7
Average required = 78
i.e. Total Required = 78*7 = 546

Extra score needed in 7th test = total of 7 tests - total of 6 tests = 546 - 444 = 102

Answer: OPtion A

P.S. The questions of Average should be solved by calculating Total of all which makes understanding of the numbers and sums much simpler
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Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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