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In a certain school, the ratio of boys to girls is

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by M7MBA » Sat May 05, 2018 11:56 pm
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In a certain school, the ratio of boys to girls is 5 to 13. If there are 72 more girls than boys, how many boys are there?

A. 27
B. 36
C. 45
D. 72
E. 117

The OA is the option C.

How can I determine the correct answer? What is the best way? Thanks.
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by Brent@GMATPrepNow » Sun May 06, 2018 4:47 am
M7MBA wrote:In a certain school, the ratio of boys to girls is 5 to 13. If there are 72 more girls than boys, how many boys are there?

A. 27
B. 36
C. 45
D. 72
E. 117
One approach:

GIVEN: the ratio of boys to girls is 5 to 13
There are several possible cases that meet this condition:
- there are 5 boys and 13 girls
- there are 10 boys and 26 girls
- there are 15 boys and 39 girls
.
.
.
NOTE: We're also told that there are 72 more girls than boys.
So, as we continue listing possible cases, we'll keep track of the DIFFERENCE in the number of boys and girls
.
.
.
- there are 20 boys and 52 girls (there are 32 more girls than boys)
- there are 25 boys and 65 girls (there are 40 more girls than boys)
- there are 30 boys and 78 girls (there are 48 more girls than boys)
- there are 35 boys and 91 girls (there are 56 more girls than boys)
- there are 40 boys and 104 girls (there are 64 more girls than boys)
- there are 45 boys and 117 girls (there are 72 more girls than boys)

So, there must be 45 boys and 117 girls

Answer: C
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by Brent@GMATPrepNow » Sun May 06, 2018 4:54 am
M7MBA wrote:In a certain school, the ratio of boys to girls is 5 to 13. If there are 72 more girls than boys, how many boys are there?

A. 27
B. 36
C. 45
D. 72
E. 117
Another approach:
Let B = # of boys
Let G = # of girls

The ratio of boys to girls is 5 to 13.
We can write: B/G = 5/13
Cross multiply to get: 13B = 5G

There are 72 more girls than boys
We can write G = B + 72
Alternatively, we can write: G - 72 = B

We now have two equations:
13B = 5G
G - 72 = B

Take bottom equation and multiply both sides by 5 to get: 5G - 360 = 5B
Now replace 5G with 13B [since the top equation tells us that 13B = 5G]
We get: 13B - 360 = 5B
Add 36 to both sides: 13B = 5B + 360
Subtract 5B from both sides: 8B = 360
Solve: B = 45

Answer: C

Cheers,
Brent
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by Scott@TargetTestPrep » Wed May 09, 2018 4:03 pm
M7MBA wrote:In a certain school, the ratio of boys to girls is 5 to 13. If there are 72 more girls than boys, how many boys are there?

A. 27
B. 36
C. 45
D. 72
E. 117
We can express the ratio B : G as 5 : 13, or 5x : 13x. We can create the equation:

13x - 72 = 5x

8x = 72

x = 9

So there are 5 x 9 = 45 boys.

Answer: C

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by [email protected] » Wed May 09, 2018 7:06 pm
Hi M7MBA,

We're told that in a certain school, the ratio of boys to girls is 5 to 13 and that there are 72 more girls than boys. We're asked for the total number of boys in the school. The ratio data in this prompt can be used in a number of different ways to get the correct answer.

You can't have a 'fraction' of a boy or girl, so the number of boys MUST be a multiple of 5 and the number of girls MUST be an equivalent multiple of 13 (re: 5 and 13, 10 and 26, etc.). By extension, the DIFFERENCE in the number of boys and girls MUST be a multiple of 8. We're told that the difference is 72, which is 72/8 = 9 times the difference of the numbers 5 and 13....

Thus, there must be (9)(5) = 45 boys and (9)(13) = 117 girls. This gives us a difference of 117 - 45 = 72, which is an exact match for what we were told.

Final Answer: C

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