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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: 56257
Three students were given three tests, the results of the first two te  [#permalink]

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10 Jul 2015, 02:39
1
2
00:00

Difficulty:

35% (medium)

Question Stats:

76% (02:33) correct 24% (02:58) wrong based on 138 sessions

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Three students were given three tests, the results of the first two tests are shown above. Student 1 and Student 3 received equal scores on Test 3. As a result, Student 1’s average (arithmetic mean) score over the three tests was 50 percent higher than Student 3’s average. What was the score Students 1 and 3 received on Test 3?

A. 33
B. 34
C. 35
D. 36
E. 39

Kudos for a correct solution.

Attachment:

tests.gif [ 4.61 KiB | Viewed 1990 times ]

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Math Expert
Joined: 02 Aug 2009
Posts: 7764
Re: Three students were given three tests, the results of the first two te  [#permalink]

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10 Jul 2015, 03:32
3
Bunuel wrote:

Three students were given three tests, the results of the first two tests are shown above. Student 1 and Student 3 received equal scores on Test 3. As a result, Student 1’s average (arithmetic mean) score over the three tests was 50 percent higher than Student 3’s average. What was the score Students 1 and 3 received on Test 3?

A. 33
B. 34
C. 35
D. 36
E. 39

Kudos for a correct solution.

Attachment:
tests.gif

30+50+x=(14+28+x)*3/2..
x=34
ans B
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Re: Three students were given three tests, the results of the first two te  [#permalink]

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10 Jul 2015, 04:07
1
Bunuel wrote:

Three students were given three tests, the results of the first two tests are shown above. Student 1 and Student 3 received equal scores on Test 3. As a result, Student 1’s average (arithmetic mean) score over the three tests was 50 percent higher than Student 3’s average. What was the score Students 1 and 3 received on Test 3?

A. 33
B. 34
C. 35
D. 36
E. 39

Kudos for a correct solution.

Attachment:
tests.gif

Per the question, (30+50+x) / 3 = 1.5* (14+28+x)/3 ---> x=34. Thus B is the correct answer.
Math Expert
Joined: 02 Sep 2009
Posts: 56257
Re: Three students were given three tests, the results of the first two te  [#permalink]

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13 Jul 2015, 02:33
Bunuel wrote:

Three students were given three tests, the results of the first two tests are shown above. Student 1 and Student 3 received equal scores on Test 3. As a result, Student 1’s average (arithmetic mean) score over the three tests was 50 percent higher than Student 3’s average. What was the score Students 1 and 3 received on Test 3?

A. 33
B. 34
C. 35
D. 36
E. 39

Kudos for a correct solution.

Attachment:
tests.gif

800score Official Solution:

Let x be the score that both Student 1 and Student 3 received on Test 3.
Since Student 1's average is 50% higher than Student 3's average, Student 1's average is 1.5 times that of Student 3.
The average for Student 1 is (30 + 50 + x)/3, and the average for Student 3 is (14 + 28 + x)/3.

So we can solve for x as follows:
(30 + 50 + x)/3 = ((14 + 28 + x)/3) × 1.5
(80 + x)/3 = ((42 + x)/3) × 1.5
(80 + x)/3 = (63 + 1.5x)/3
80 + x = 63 + 1.5x
17 = 0.5x
x = 34.

The correct answer is choice (B).
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Re: Three students were given three tests, the results of the first two te  [#permalink]

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31 May 2017, 10:22
I got the answer by process elimination

The average of student 1 with 34 is 38
The average of student 3 with 34 is 25 1/3

25 1/3 x 1 1/2
38

The answer has to be B.
Process elimination can be a life saver sometime.
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Re: Three students were given three tests, the results of the first two te  [#permalink]

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05 Jun 2017, 16:14
Bunuel wrote:
Three students were given three tests, the results of the first two tests are shown above. Student 1 and Student 3 received equal scores on Test 3. As a result, Student 1’s average (arithmetic mean) score over the three tests was 50 percent higher than Student 3’s average. What was the score Students 1 and 3 received on Test 3?

A. 33
B. 34
C. 35
D. 36
E. 39

We can let x = the score for student 1 and student 3 on test number 3. Thus, the average score for student 1 is:

(30 + 50 + x)/3 = (80 + x)/3

The average for student 3 is:

(14 + 28 + x)/3 = (42 + x)/3

Student 1’s average (arithmetic mean) score over the three tests was 50 percent higher than Student 3’s average. Using that fact, we can create the following equation to determine x:

(80 + x)/3 = 1.5[(42 + x)/3]

(80 + x) = 1.5(42 + x)

80 + x = 63 + 1.5x

17 = 0.5x

34 = x

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

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21 Dec 2018, 16:05
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Re: Three students were given three tests, the results of the first two te   [#permalink] 21 Dec 2018, 16:05
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