# Quantitative Reasoning – Practice – Mary raises the average!

PSA_PRACTICE_QNR21.

Ans: Let us solve this using the conventional method first:

Let, including Mary total students be ‘m+1’.

Now, average is 81; the sum of the scores of all the students would be= 81*(m+1).

Without Mary’s score, average is 80; the sum of the scores of all the students excluding Mary would be= 80*m

Thus, Mary’s score must be = 81*(m+1) – 80*m = 100

=> m= 100-81=19. Total students must be m+1= 20. Option B.

However, the above can also be calculated mentally without involving equation by visualizing 2 things:

a) Average of 80 means every student can be thought of having received the score 80.

b) Had Mary scored only 80, the average would have been 80. But since she scored 100 which is 20 points more than 80, this extra 20 caused the average to increase by 1 unit (i.e from 80 to 81). This 1 unit increase must have affected on everyone’s score of 80 [+1 +1 +1 +1 …..20 times]. Since, total increase is 20 points, total students must have been 20.