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# Three students were given three tests, the results of the first two te

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Math Expert
Joined: 02 Sep 2009
Posts: 55670
Three students were given three tests, the results of the first two te  [#permalink]

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26 Dec 2014, 08:46
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Difficulty:

15% (low)

Question Stats:

84% (02:21) correct 16% (01:57) wrong based on 102 sessions

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Tough and Tricky questions: Word Problems.

Three students were given three tests, the results of the first two tests are shown above. Their scores on Test 3 were 34, 44, and x respectively. What is the value of x if the average total score of the three students is 109?

A. 31
B. 32
C. 33
D. 34
E. 44

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Attachment:

2014-12-26_1946.png [ 7.09 KiB | Viewed 2700 times ]

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Re: Three students were given three tests, the results of the first two te  [#permalink]

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26 Dec 2014, 09:18
The Average of all three students in the three exams is 109, so the total number of points scored by all three students is 3 * 109 = 327.

Summing all 8 Test results we have given in the table and the question stem gives us 294.

(30 + 50 + 34) + (40 + 54 + 44) + (14 + 28 + x) = 294 + x = 327

=> x = 33

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Re: Three students were given three tests, the results of the first two te  [#permalink]

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26 Dec 2014, 17:55
Bunuel wrote:

Tough and Tricky questions: Word Problems.

Three students were given three tests, the results of the first two tests are shown above. Their scores on Test 3 were 34, 44, and x respectively. What is the value of x if the average total score of the three students is 109?

A. 31
B. 32
C. 33
D. 34
E. 44

Kudos for a correct solution.

Attachment:
2014-12-26_1946.png

Average = 109
Total score = 109 * 3 = 327

Total Score = 30 + 40 + 14 + 50 + 54 + 28 + 34 + 44 + x = 327
=> 294 + x = 327
=> x = 33

Ans C
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Re: Three students were given three tests, the results of the first two te  [#permalink]

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31 Dec 2014, 21:41
1

Refer diagram below:

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2014-12-26_1946.png [ 15.59 KiB | Viewed 2238 times ]

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Re: Three students were given three tests, the results of the first two te  [#permalink]

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08 Jan 2015, 09:08
Bunuel wrote:

Tough and Tricky questions: Word Problems.

Three students were given three tests, the results of the first two tests are shown above. Their scores on Test 3 were 34, 44, and x respectively. What is the value of x if the average total score of the three students is 109?

A. 31
B. 32
C. 33
D. 34
E. 44

Kudos for a correct solution.

Attachment:
2014-12-26_1946.png

OFFICIAL SOLUTION:

С) The total scores of the students are:
30 + 50 + 34 = 114
40 + 54 + 44 = 138
14 + 28 + x = 42 + x

The average total score is (114 + 138 + 42 + x)/3 = 109.
294 + x = 327
x = 33

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Re: Three students were given three tests, the results of the first two te  [#permalink]

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03 Jun 2017, 08:31
$$\frac{( 30 + 50 + 34 ) + ( 40 + 54 + 44 ) + ( 14 + 28 + x )}{3} = 109$$

Or, $$294 + x = 327$$

Or, $$x = 33$$

Thus, answer must be (C) 33
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Re: Three students were given three tests, the results of the first two te  [#permalink]

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14 Sep 2018, 09:04
Bunuel wrote:

Tough and Tricky questions: Word Problems.

Three students were given three tests, the results of the first two tests are shown above. Their scores on Test 3 were 34, 44, and x respectively. What is the value of x if the average total score of the three students is 109?

A. 31
B. 32
C. 33
D. 34
E. 44

We can use the average equation: average = sum / quantity

The sum of the scores of student 1 is 30 + 50 + 34 = 114, the sum of the scores of student 2 is 40 + 54 + 44 = 138, and the sum of scores of student 3 is 14 + 28 + x = 42 + x; thus:

(114 + 138 + 42 + x)/3 = 109

294 + x = 327

x = 33

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Re: Three students were given three tests, the results of the first two te  [#permalink]

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15 Sep 2018, 14:03
Bunuel wrote:

Tough and Tricky questions: Word Problems.

Three students were given three tests, the results of the first two tests are shown above. Their scores on Test 3 were 34, 44, and x respectively. What is the value of x if the average total score of the three students is 109?

A. 31
B. 32
C. 33
D. 34
E. 44

Kudos for a correct solution.

Attachment:
2014-12-26_1946.png

add the total score for test1 and test two respectively, which are, 84,132.
we know the total score of last test=78+x.

total marks in all three tests=294+x.

also we know that the avg is 109. so the total marks in all three test for all students is 109*3=327.

327-294=33.Option C
Re: Three students were given three tests, the results of the first two te   [#permalink] 15 Sep 2018, 14:03
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