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What is the ratio of the number of boys to girls on the school bus?

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Source: — Data Sufficiency |
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Re: What is the ratio of the number of boys to girls on the school bus?

by dg1900 » Wed Aug 26, 2020 10:00 am

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Let B be number of boys
Let G be number of girls
We first look at the first condition
1) The number of boys is 5 less than twice the number of girls
This gives us the equation:
2G-5=B (Eq1)
Which is not sufficient to give the ratio of number of boys to girls so we can conclude that the first condition is not sufficient.

We now look at the second condition
2) The difference between the number of boys and the number of girls is 35
This gives us |B-G|=35 (Eq2)
This conditon alone is again insufficient to answer the question.

Now we take both the conditions together.
The Eq1 tells us that the the number of boys is greater than the number of girls.
We can use this information to remove the modulus from Eq2.
So we have:
B-G=35 i.e B=G+35 Eq3
Substituting Eq3 in Eq1 we get:
2G-5=G+35
G=40
Using this value of G we get B=75.

Therefore the ratio of number of boys to number of girls is 75:35.
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