The incomplete table above shows a distribution of scores fo

we can write it like

83= (92*4 + 91*6 + x*3 + 83*7 + 71*5)/ 25

Solving this will give x=75 Ans.

Hi
Easiest way of solving this questions finding the deviation from the mean.
Average given is 83.
92 is 9 more than 83 and we have 4 students. So total points will be (9*4)36.
91 is 8 more than 83 and we have 6 students. So total points will be (8*6)48.
83 is more than the average. So no need of counting this.
71 is 12 less than 83 and we have 5 students. So total points will(12*5) 60.
So total points more is 84 and less is 60. So the value will be less than 83(84-60points) 24 points. Since there are 3 students. 24/3 is 8 . So the value will 8 less than the average which is 83-8= 75.
So 75 is the answer.

Answer is A.

Sum of all = Average * 25 = 83*25=2075. -- (1)

From the table we can say, sum of all numbers = 92*4 + 91 *6 +83*7 + 71*5 + 3*X [X is the Value of Unknown score) -- (2)

Equating (1) and -- (2), we will get X= 75.

92*4 + 91*6 + 3x+83*7+71*5 / 25 = 83

1850 + 3x = 2075
3x = 225 => x =75

Option A.

Is there any short cut method ?

can ignore 83.

92-83 = 9 so +36
91-83 = 8 so +48

83-71 =12 so -60

total effect = 24
need to be distriubted in 3.
s0 83-8 =75

I tried to avoid working through big chunks of numbers, and wanted to find the last digit of the numbers only...
25*83 - smth smth in the end 5. good.
now
92*4 - smth smth end is 8.
91*6 - smth smth end is 6.
83*7 - smth smth end is 1.
71*5 - smth smth end is 5.
so, last digit of the sum of these numbers is 8+6+1+5 = zero.
smth smth 5 - smth smth 0 = smth smth 5.
since we need an integer number, and since the smth smth 5 number would be divided by 3, it is logically to assume that the last digit would be 5 as well...

only A works...

\(\frac{(92*4)+(91*6)+(x*3)+(83*7)+(71*5)}{25} = 83\)

Or, \(368 + 546 +3x + 581 + 355 = 2075\)

Or, \(3x = 225\)

Or, \(x = 75\), answer will be (A) 75

Hi
I have a different approach to this question, Please confirm that this approach is right. See attachment.

(1850+3x)/25=83
x=75

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app

We are given that the average (arithmetic mean) score for the class is 83. Since we are given the average, we can find the difference between the average and each score and multiply their respective frequencies, and the sum of these products should be 0. That is, if we let n = the missing score, we can create the following equation:

(92 - 83) x 4 + (91 - 83) x 6 + (n - 83) x 3 + (83 - 83) x 7 + (71 - 83) x 5 = 0

36 + 48 + 3n - 249 + 0 - 60 = 0

3n - 225 = 0

3n = 225

n = 75

Alternate Solution:

We can calculate a weighted mean for the 25 scores, using the formula average = sum/number:

83 = [4(92) + 6(91) + 3x + 7(83) + 5(71)]/25

2075 = 368 + 546 + 3x + 581 +355

2075 = 1850 + 3x

225 = 3x

75 = x

Answer: A

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