The incomplete table above shows a distribution of scores fo

Question

incomplete.png The incomplete table above shows a distribution of scores for a class of 25 students. If the average (arithmetic mean) score for the class is 83, what score is missing from the table? A. 75 B. 77 C. 81 D. 84 E. 86

ProleFeed13 · Accepted Answer

Yeah, this is the long way. For the short way, simply calculate the deviations from the mean for each score to figure out what the other score is.

92 is 9 away from the mean, so 4x9=36 pts above
91 is 8 away from the mean, so 6x8=48 pts above
83 is equal, no worries
71 is 12 away from the mean, so 5x12=60 pts below.

We have 84 pts above and 60 below, so the unknown score's deviation must be 84-60=24 pts below distributed among 3 students, so 8 pts per student. 83-8 = 75pts.

Donnie84 · Answer

Possible shortcut:

First, find the unit digit of the total sum.
Total sum = Avg * number of students
 = 83 * 25 -> unit digit is 5.

Next, find the unit digit of each pair from the table and add them up.

92 * 4 -> xx8
91 * 6 -> xx6
83 * 7 -> xx1
71 * 5 -> xx5

8+6+1+5 -> 0

So, the remaining pair must end with 5. The number of student is 3 so the score must have 5 as the units digit. Only 75 from the given options satisfies.

Answer (A).

madhurs254 · Answer

we can write it like

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

Solving this will give x=75 Ans.

CrackverbalGMAT · Answer

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.

abhimahna · 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.

msk0657 · Answer

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 ?

abrakadabra21 · Answer

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

mvictor · Answer

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...

Abhishek009 · Answer

\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

Aim800score · Answer

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

rahulswimmer · Answer

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

Sent from my ONEPLUS A3003 using  GMAT Club Forum mobile app

ScottTargetTestPrep · Answer

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 =  /25

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

2075 = 1850 + 3x

225 = 3x

75 = x

Answer: A

bumpbot · Answer

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