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Justin took a test of French at school and scored 72 marks

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Justin took a test of French at school and scored 72 marks

by BTGmoderatorDC » Thu Sep 19, 2019 4:37 pm

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Justin took a test of French at school and scored 72 marks out of 100. If there were 20 students who appeared for the test, within how many standard deviations from the mean did Justin's score lie?

(1) Darren and Matthew scored 70 and 75 respectively and their scores were within one standard deviation from the mean.

(2) The mean score of 20 students was 65 and Andrew who scored 59 was within one standard deviation of the mean.

OA A

Source: e-GMAT
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Mon Sep 23, 2019 9:30 pm

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BTGmoderatorDC wrote:Justin took a test of French at school and scored 72 marks out of 100. If there were 20 students who appeared for the test, within how many standard deviations from the mean did Justin's score lie?

(1) Darren and Matthew scored 70 and 75 respectively and their scores were within one standard deviation from the mean.

(2) The mean score of 20 students was 65 and Andrew who scored 59 was within one standard deviation of the mean.

OA A

Source: e-GMAT
This question involves the concept of standard deviation. Note that the computation of SD is not within the scope of the GMAT; however, its application is within the scope.

Let's take each statement one by one.

(1) Darren and Matthew scored 70 and 75 respectively and their scores were within one standard deviation from the mean.

We see that Justin's score 72, is greater than 70 as well as smaller than 75. Given that both scores 72 and 75 are within one standard deviation from the mean, 72 must also be within one standard deviation from the mean. Sufficient.

(2) The mean score of 20 students was 65 and Andrew who scored 59 was within one standard deviation of the mean.

So, we have mean = 65 and a score 59 (< 65) is within one standard deviation of the mean; thus, Mean - 1SD ≤ 59 => 65 - 1SD ≤ 59 => SD ≤ 6.

Thus, on the upper limit ≥ Mean + 1SD = 65 + 1*6 = 71.

Since 72 is greater than 71, we cannot determine how many standard deviations from the mean Justin's score lie. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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by deloitte247 » Wed Sep 25, 2019 11:09 am

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Justin score = 72
Question=> How many standard deviations from the mean did Justin's score lie?

Statement 1=> Darren and Matthew scored 70 and 75 respectively and their scores were within one standard deviation from the mean.
Let the mean = x
First standard deviation is within 70 and 75.
Justin score = 72
Three possible cases for x
Case 1=> 70 < x < 75
Case 2=> x < 70 < 75
Case 3=> x > 70 < 75
In all cases, Justin's scores falls within the range of one standard deviation which is 70 - 75. Hence, statement 1 is SUFFICIENT.

Statement 2=> The mean score of 20 students was 65 and Andrew who scored 59 was within one standard deviation of the mean.
Andrew's score = 59
Since 65 - 6 = 59 which is within one standard deviation. The information provided does not provide us with the range of standard deviation for Justin's score, hence, statement 2 is NOT SUFFICIENT.

Therefore, only statement 1 is SUFFICIENT, hence, option A is the correct answer.
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