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There are 17 students in a certain class. On the day the te [#permalink]
17 Mar 2013, 06:00

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Question Stats:

94% (02:06) correct
6% (01:17) wrong based on 87 sessions

There are 17 students in a certain class. On the day the test was given, Taqeesha was absent. The other 16 students took the test, and their average was 77. The next day, Taqeesha took the test, and with her grade included, the new average is 78. What is Taqeesha’s grade on the test?

A. 78 B. 80 C. 87 D. 91 E. 94

I took this question from Magoosh . I saw somebody coming up with a very quick solution -

"When Taqeesha took the test, the average increased from 77 to 78. That means, Taqeesha scored 78 plus 1 mark for each one of the other students. i.e., 78 + 16 = 94."

approach is unclear

I could easily solve this using the conventional way i.e with average formula . I would like to understand the above approach . Also, Kindly help me with some similar questions that I can practice to make sure I nail this concept well .

Re: There are 17 students in a certain class. On the day the te [#permalink]
17 Mar 2013, 06:08

2

This post received KUDOS

Expert's post

guerrero25 wrote:

There are 17 students in a certain class. On the day the test was given, Taqeesha was absent. The other 16 students took the test, and their average was 77. The next day, Taqeesha took the test, and with her grade included, the new average is 78. What is Taqeesha’s grade on the test?

A. 78 B. 80 C. 87 D. 91 E. 94

I took this question from Magoosh . I saw somebody coming up with a very quick solution -

"When Taqeesha took the test, the average increased from 77 to 78. That means, Taqeesha scored 78 plus 1 mark for each one of the other students. i.e., 78 + 16 = 94."

approach is unclear

I could easily solve this using the conventional way i.e with average formula . I would like to understand the above approach . Also, Kindly help me with some similar questions that I can practice to make sure I nail this concept well .

As always , thank you !

Say all 16 students got 77 (so the average is naturally 77).

Now, what should be the 17th student score in order the average to be 78? If all 17 had 78 then the average would be 78, but 16 have 77, so Taqeesha should get 78+16*1=94.

Re: There are 17 students in a certain class. On the day the te [#permalink]
17 Mar 2013, 06:11

1

This post received KUDOS

Expert's post

Bunuel wrote:

guerrero25 wrote:

There are 17 students in a certain class. On the day the test was given, Taqeesha was absent. The other 16 students took the test, and their average was 77. The next day, Taqeesha took the test, and with her grade included, the new average is 78. What is Taqeesha’s grade on the test?

A. 78 B. 80 C. 87 D. 91 E. 94

I took this question from Magoosh . I saw somebody coming up with a very quick solution -

"When Taqeesha took the test, the average increased from 77 to 78. That means, Taqeesha scored 78 plus 1 mark for each one of the other students. i.e., 78 + 16 = 94."

approach is unclear

I could easily solve this using the conventional way i.e with average formula . I would like to understand the above approach . Also, Kindly help me with some similar questions that I can practice to make sure I nail this concept well .

As always , thank you !

Say all 16 students got 77 (so the average is naturally 77).

Now, what should be the 17th student score in order the average to be 78? If all 17 had 78 then the average would be 78, but 16 have 77, so Taqeesha should get 78+16*1=94.

Hope it's clear.

Another example: two students got 5 points each, how much should the third student get in order the average to be 10?

Re: There are 17 students in a certain class. On the day the te [#permalink]
16 Oct 2013, 02:56

Bunuel wrote:

guerrero25 wrote:

There are 17 students in a certain class. On the day the test was given, Taqeesha was absent. The other 16 students took the test, and their average was 77. The next day, Taqeesha took the test, and with her grade included, the new average is 78. What is Taqeesha’s grade on the test?

A. 78 B. 80 C. 87 D. 91 E. 94

I took this question from Magoosh . I saw somebody coming up with a very quick solution -

"When Taqeesha took the test, the average increased from 77 to 78. That means, Taqeesha scored 78 plus 1 mark for each one of the other students. i.e., 78 + 16 = 94."

approach is unclear

I could easily solve this using the conventional way i.e with average formula . I would like to understand the above approach . Also, Kindly help me with some similar questions that I can practice to make sure I nail this concept well .

As always , thank you !

Say all 16 students got 77 (so the average is naturally 77).

Now, what should be the 17th student score in order the average to be 78? If all 17 had 78 then the average would be 78, but 16 have 77, so Taqeesha should get 78+16*1=94.

Hope it's clear.

Bunuel, What are we adding here? It seems to me that we are adding score+number of students = score? Can you please explain? Btw I did it the long way as described above.

Re: There are 17 students in a certain class. On the day the te [#permalink]
16 Oct 2013, 03:19

Expert's post

Skag55 wrote:

Bunuel wrote:

guerrero25 wrote:

There are 17 students in a certain class. On the day the test was given, Taqeesha was absent. The other 16 students took the test, and their average was 77. The next day, Taqeesha took the test, and with her grade included, the new average is 78. What is Taqeesha’s grade on the test?

A. 78 B. 80 C. 87 D. 91 E. 94

I took this question from Magoosh . I saw somebody coming up with a very quick solution -

"When Taqeesha took the test, the average increased from 77 to 78. That means, Taqeesha scored 78 plus 1 mark for each one of the other students. i.e., 78 + 16 = 94."

approach is unclear

I could easily solve this using the conventional way i.e with average formula . I would like to understand the above approach . Also, Kindly help me with some similar questions that I can practice to make sure I nail this concept well .

As always , thank you !

Say all 16 students got 77 (so the average is naturally 77).

Now, what should be the 17th student score in order the average to be 78? If all 17 had 78 then the average would be 78, but 16 have 77, so Taqeesha should get 78+16*1=94.

Hope it's clear.

Bunuel, What are we adding here? It seems to me that we are adding score+number of students = score? Can you please explain? Btw I did it the long way as described above.

We are adding average score (78) and surplus score (16*1), so that the average to be 78. _________________

Re: There are 17 students in a certain class. On the day the te [#permalink]
24 Feb 2015, 06:40

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Re: There are 17 students in a certain class. On the day the te [#permalink]
28 Feb 2015, 07:56

Expert's post

guerrero25 wrote:

There are 17 students in a certain class. On the day the test was given, Taqeesha was absent. The other 16 students took the test, and their average was 77. The next day, Taqeesha took the test, and with her grade included, the new average is 78. What is Taqeesha’s grade on the test?

A. 78 B. 80 C. 87 D. 91 E. 94

I took this question from Magoosh . I saw somebody coming up with a very quick solution -

"When Taqeesha took the test, the average increased from 77 to 78. That means, Taqeesha scored 78 plus 1 mark for each one of the other students. i.e., 78 + 16 = 94."

approach is unclear

I could easily solve this using the conventional way i.e with average formula . I would like to understand the above approach . Also, Kindly help me with some similar questions that I can practice to make sure I nail this concept well .

As always , thank you !

Using the conventional method of average would be easier if the numbers are small but can be time consuming if the values are too high. Let us say that 16 students scored 77 marks on Day 1. So average is obviously 77.

Next day when Taqeesha appears for the test, the average rises to 78. So let's assume that all of them score 78. So, we need to increase 1 mark in all previous 16 students and add 78 marks of Taqeesha. So, 78 + 1 * 16 = 94. Hence option E.

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