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# Dan had an average of 72 on his first four math tests. After taking

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Joined: 02 Sep 2009
Posts: 58409
Dan had an average of 72 on his first four math tests. After taking  [#permalink]

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01 Mar 2018, 00:21
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15% (low)

Question Stats:

96% (00:51) correct 4% (00:52) wrong based on 32 sessions

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Dan had an average of 72 on his first four math tests. After taking the next test, his average dropped to 70. Which of the following is his most recent test grade?

(A) 60

(B) 62

(C) 64

(D) 66

(E) 68

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Dan had an average of 72 on his first four math tests. After taking  [#permalink]

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01 Mar 2018, 00:35
Bunuel wrote:
Dan had an average of 72 on his first four math tests. After taking the next test, his average dropped to 70. Which of the following is his most recent test grade?

(A) 60

(B) 62

(C) 64

(D) 66

(E) 68

Let the score in the fifth test be x

$$\frac{72*4 + x}{5} = 70$$ --> x = $$350 - 72*4 = 350 - 288 = 62$$

Therefore, Dan would have scored a 62(Option B) in his fifth test to score an average of 70.

Shortcut: In the first four tests, he scores $$2*4 = 8$$ more than the average.

In the last test, he would have scored {average - extra score} = $$70 - 8 = 62$$ in order to average 70 overall!
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Dan had an average of 72 on his first four math tests. After taking  [#permalink]

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01 Mar 2018, 20:14
Bunuel wrote:
Dan had an average of 72 on his first four math tests. After taking the next test, his average dropped to 70. Which of the following is his most recent test grade?

(A) 60

(B) 62

(C) 64

(D) 66

(E) 68

$$A * n = S$$

First set of scores, A = 72, n = 4:
(72 * 4) = 288 = Sum1

Second set of scores, A = 70, n = 5:
(70 * 5) = 350 = Sum2

The difference between sums is the missing score.
(350 - 288) = 62

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Re: Dan had an average of 72 on his first four math tests. After taking  [#permalink]

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03 Mar 2018, 00:51
Bunuel wrote:
Dan had an average of 72 on his first four math tests. After taking the next test, his average dropped to 70. Which of the following is his most recent test grade?

(A) 60

(B) 62

(C) 64

(D) 66

(E) 68

IMO B total score is 72*4=288 and new test lets say x
=288+x/5=70
=x=350-288=62
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Re: Dan had an average of 72 on his first four math tests. After taking  [#permalink]

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03 Mar 2018, 02:41
Bunuel wrote:
Dan had an average of 72 on his first four math tests. After taking the next test, his average dropped to 70. Which of the following is his most recent test grade?

(A) 60

(B) 62

(C) 64

(D) 66

(E) 68

The average of 4 tests = 72

the average to be dropped for the 4 tests = 72-70 = 2

i.e. The sum of the 4 is greater than average 70 by = 2*4 = 8 units

so we need the new number to be 8 shorter than the new average i.e. 70

i.e. new number = 70-8 = 62

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Re: Dan had an average of 72 on his first four math tests. After taking   [#permalink] 03 Mar 2018, 02:41
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