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

Question

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 !

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 !

Bunuel · Answer

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 · Answer

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.

guerrero25 · Answer

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

GeorgeA023 · Answer

I went with the following

77*16=1232

78*17=1326

1326-1232=94

94 was the score.

Hope it makes sense

Skag55 · Answer

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.

Bunuel · Answer

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

OptimusPrepJanielle · Answer

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. -- Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course

bumpbot · Answer

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