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There are 17 students in a certain class. On the day the te

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There are 17 students in a certain class. On the day the te [#permalink] New post 17 Mar 2013, 06:00
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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 !
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Re: There are 17 students in a certain class. On the day the te [#permalink] New post 17 Mar 2013, 06:08
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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.
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Re: There are 17 students in a certain class. On the day the te [#permalink] New post 17 Mar 2013, 06:11
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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?

10+2*5=20.

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: There are 17 students in a certain class. On the day the te [#permalink] New post 17 Mar 2013, 07:01
Makes sense . Thanks Bunuel !


I found this thread that has more example . Posting it here just to help somebody like me in search of Average tricks .

average-accelerated-guide-to-solve-averages-quickly-77148.html


Regards
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Re: There are 17 students in a certain class. On the day the te [#permalink] New post 18 Apr 2013, 13:42
I went with the following

77*16=1232

78*17=1326

1326-1232=94

94 was the score.

Hope it makes sense
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Re: There are 17 students in a certain class. On the day the te [#permalink] New post 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.
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Re: There are 17 students in a certain class. On the day the te [#permalink] New post 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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: There are 17 students in a certain class. On the day the te [#permalink] New post 24 Feb 2015, 06:40
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Re: There are 17 students in a certain class. On the day the te [#permalink] New post 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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Re: There are 17 students in a certain class. On the day the te   [#permalink] 28 Feb 2015, 07:56
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