On a particular exam, the boys in a history class averaged 86 points a

Question

On a particular exam, the boys in a history class averaged 86 points and the girls in the class averaged 80 points. If the overall class average was 82 points, what was the ratio of boys to girls in the class?

A. 1:4
B. 1:3
C. 1:2
D. 2:1
E. 3:1

Kudos for a correct solution.

A. 1:4
B. 1:3
C. 1:2
D. 2:1
E. 3:1

Kudos for a correct  solution .

balamoon · Accepted Answer

On a particular exam, the boys in a history class averaged 86 points and the girls in the class averaged 80 points. If the overall class average was 82 points, what was the ratio of boys to girls in the class?

A. 1:4
B. 1:3
C. 1:2
D. 2:1
E. 3:1

Kudos for a correct solution.

A. 1:4
B. 1:3
C. 1:2
D. 2:1
E. 3:1

Solution -

Given that Boys average is 86 and Girls average is 80 points. Total average is 82 points.

(86B+80G)/(B+G) = 82 --> 4B=2G --> B/G = 1/2. ANS C.

ashokk138 · Answer

Solution: We can use the X method to solve similar questions

B...................G
86................80
 
..........82........

2..................4

Hence, Boys: Girls => 2: 4 => 1:2

Option C

AmoyV · Answer

G B
80 86
 82
4 2
2 : 1

G:B=2:1
B:G=1:2

Answer: C

lipsi18 · Answer

Let # boys in the class=x & # of girls in class =y
so we have (sum of boys)=86X
(sum of girls)=80y

total average =82=>
86x+80y=82(x+y) =? we get 4x=2y
so x/y =1/2

Hence answer is C
Thanks,

TimeTraveller · Answer

80 - 82 - 86

86-82/82-80 = 4/2 = 2/1. D.

adityadon · Answer

86 ----------- 80
-------82-----------
2-------------- 4 .... hence 2:4 = 1:2

Did cross subtraction here , 
86-82 = 4 , 82-80 = 2

Required answer = 1:2 
C

noTh1ng · Answer

I think its 2:1 as question asks for the ratio of Boys to girls.

Let x be number of boys, y number of girls.

86x + 80y / (x+y) = 82

86x + 80y = 82x + 82y
4x = 2y
2x = y
2:1

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

The boys in the class scored 4 points higher on average than the entire class. The boys have a + 4 differential. Similarly, the girls scored 2 points lower on average than the class. They have a - 2 differential. You need to balance out the differentials:

b*(+4) + g*(-2) = 0

If b = 1 and g = 2, the equation will be true. Thus, the ratio of boys to girls is 1:2.

Answer: C.

SQUINGEL · Answer

I got that 86-82 & 82-80 are the two sets of numbers we are using to arrive at the answer however im getting 2:1 and not 1:2..... help!

stonecold · Answer

Here is my solution for this one-->
Sum(Boys scores)= 86*B 
Sum(Girls scores)= 80*G 
Total ->  86*B+80*G = 82*B+82*G 
Hence  4B=2G => \frac{B}{G}=\frac{1}{2}

Hence C

dcummins · Answer

I can't seem to apply a consistent approach to weighted average problems.

Could someone please point me to the right direction for a good explanation of the approach?

Blackbox · Answer

I have come across this - "X - method" in several posts on this forum. Is there a theory/article describing this? Seems like a sure shot approach to weighted averages. Can someone point me to the resource, please?

cbh · Answer

lets x be the number of boys and y number of girls
(86x + 80y) / (x + y) = 82
86x + 80 y = 82x + 82y
86x - 82x = 82y - 80y
4x = 2y
2x = y

1:2 (boys:girls)

bumpbot · Answer

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On a particular exam, the boys in a history class averaged 86 points a

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