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# If the average (arithmetic mean) score for a certain student in Ms Swe

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Math Expert
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Posts: 50009
If the average (arithmetic mean) score for a certain student in Ms Swe  [#permalink]

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12 May 2017, 05:15
00:00

Difficulty:

25% (medium)

Question Stats:

91% (01:17) correct 9% (01:14) wrong based on 39 sessions

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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?

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

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Re: If the average (arithmetic mean) score for a certain student in Ms Swe  [#permalink]

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12 May 2017, 05:33
Bunuel wrote:
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

Since student scored average of 74 in the first 6 tests & we need to increase his average from 74 to 78 from the 7th test
So student should score 74+ 7*4 = 102
OR
So student should score 78 +6*4 = 102.

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If the average (arithmetic mean) score for a certain student in Ms Swe  [#permalink]

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Updated on: 13 May 2017, 07:06
Bunuel wrote:
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

Old-fashioned but quick, see diagram below ... A*n=S

1. Find the total current point score total (sum) by multiplying his current average (74, given) by the 6 tests he has taken: 74 * 6 = 444

2. To find what score he needs to boost his overall average, first find needed overall points (second sum):

a. find what would be the overall new number of tests: 6 + 1 = 7

b. take the hoped-for average (78, given), multiply by overall number of tests: 78 * 7 = 546

3. Then, to find the value for the score he needs, simply subtract old total from needed total: 546-444 =

Attachment:

TEST SCORE AVE FROM 74 TO 78.jpg [ 33.52 KiB | Viewed 594 times ]
Edited to replace lost text. Why does this interface sometimes eat parts of my posts?
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Originally posted by generis on 12 May 2017, 16:31.
Last edited by generis on 13 May 2017, 07:06, edited 1 time in total.
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Re: If the average (arithmetic mean) score for a certain student in Ms Swe  [#permalink]

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13 May 2017, 01:53
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 Swe  [#permalink]

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13 May 2017, 03:31
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.

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Re: If the average (arithmetic mean) score for a certain student in Ms Swe  [#permalink]

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13 May 2017, 05:28
Bunuel wrote:
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

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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Re: If the average (arithmetic mean) score for a certain student in Ms Swe &nbs [#permalink] 13 May 2017, 05:28
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