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

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Math Expert
Joined: 02 Sep 2009
Posts: 46217
On a particular exam, the boys in a history class averaged 86 points a [#permalink]

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30 Jun 2015, 05:05
00:00

Difficulty:

25% (medium)

Question Stats:

70% (00:57) correct 30% (01:11) wrong based on 204 sessions

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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.

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Re: On a particular exam, the boys in a history class averaged 86 points a [#permalink]

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30 Jun 2015, 06:07
1
3
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

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.
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Re: On a particular exam, the boys in a history class averaged 86 points a [#permalink]

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30 Jun 2015, 07:13
1
Bunuel wrote:
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.

G B
80 86
82
4 2
2 : 1

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

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Joined: 20 Jul 2011
Posts: 80
GMAT 1: 660 Q49 V31
Re: On a particular exam, the boys in a history class averaged 86 points a [#permalink]

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30 Jun 2015, 10:03
2
Bunuel wrote:
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.

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
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On a particular exam, the boys in a history class averaged 86 points a [#permalink]

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Updated on: 30 Jun 2015, 11:20
1
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

Thanks,

Originally posted by lipsi18 on 30 Jun 2015, 10:30.
Last edited by lipsi18 on 30 Jun 2015, 11:20, edited 1 time in total.
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Re: On a particular exam, the boys in a history class averaged 86 points a [#permalink]

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30 Jun 2015, 10:37
80 - 82 - 86

86-82/82-80 = 4/2 = 2/1. D.
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Re: On a particular exam, the boys in a history class averaged 86 points a [#permalink]

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30 Jun 2015, 11:01
1
1
86 ----------- 80
-------82-----------
2-------------- 4 .... hence 2:4 = 1:2

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

C
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Manager
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Posts: 177
Re: On a particular exam, the boys in a history class averaged 86 points a [#permalink]

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01 Jul 2015, 07:51
1
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
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Joined: 02 Sep 2009
Posts: 46217
Re: On a particular exam, the boys in a history class averaged 86 points a [#permalink]

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06 Jul 2015, 02:59
1
Bunuel wrote:
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.

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.

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Concentration: Finance, General Management
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Re: On a particular exam, the boys in a history class averaged 86 points a [#permalink]

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06 Oct 2016, 05:40
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!
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Re: On a particular exam, the boys in a history class averaged 86 points a [#permalink]

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10 Dec 2016, 10:26
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

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Re: On a particular exam, the boys in a history class averaged 86 points a [#permalink]

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01 Aug 2017, 03:22
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?
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Re: On a particular exam, the boys in a history class averaged 86 points a [#permalink]

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07 Aug 2017, 09:26
ashokk138 wrote:
Bunuel wrote:
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.

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

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?
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Posts: 122
Re: On a particular exam, the boys in a history class averaged 86 points a [#permalink]

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07 Aug 2017, 12:22
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)
Re: On a particular exam, the boys in a history class averaged 86 points a   [#permalink] 07 Aug 2017, 12:22
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