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B boys and G girls

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by Needgmat » Tue Sep 13, 2016 7:08 am
If there are B boys and G girls in a club, can the girls be divided equally among 6 teams with no girls left over?

1) If there were 4 fewer girls, then the number of girls would be twice the number of boys.

2) If the number of boys were 2 less than twice the actual number of boys, then the boys could be divided equally equally among 6 teams with no boys left over.



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Source: — Data Sufficiency |

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by [email protected] » Tue Sep 13, 2016 9:34 am
Hi Needgmat,

This question can be solved by TESTing VALUES.

We're told that there are a certain number of boys and girls in a club. We're asked if the number of girls is a multiple of 6. This is a YES/NO question.

1) If there were 4 fewer girls, then the number of girls would be twice the number of boys.

IF there were....
6 girls and 1 boy, then the answer to the question is YES.
8 girls and 2 boys, then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) If the number of boys were 2 less than twice the actual number of boys, then the boys could be divided equally equally among 6 teams with no boys left over.

This tells us NOTHING about the number of girls, but I'm going to work through a few examples for future reference...

This Fact tells us that (2B-2) is a multiple of 6, so there COULD be...

4 boys
7 boys
10 boys
13 boys
Etc.
Notice the pattern here (the number of boys increases by 3)...
Fact 2 is INSUFFICIENT

Combined, we know what the number of boys COULD be, so we can use that to figure out the number of girls in each possibility...

IF there were....
4 boys, then we'd have 12 girls and the answer to the question is YES.
7 boys, then we'd have 18 girls and the answer to the question is YES.
10 boys, then we'd have 24 girls and the answer to the question is YES.
This pattern will continue and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

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by Matt@VeritasPrep » Fri Sep 16, 2016 2:00 pm
Let's rephrase the prompt as "Is G divisible by 6?"

S1:

G - 4 = 2B

This tells us (G - 4) = some even number, so G is even. But it could be almost any even positive integer: 4, 6, 8, 10, 12, ...

Some of those divide by 6, some don't; NOT SUFFICIENT.

S2:

2B - 2 is divisible by 6

Doesn't tell us about the girls, so NOT SUFFICIENT.

S1 + S2:

We know that G - 4 = 2B and that (2B - 2) divides by 6. Let's subtract 2 from each side of the first equation to get to (2B - 2):

G - 4 - 2 = 2B - 2, or

G - 6 = 2B - 2, or

G - 6 = a multiple of 6, or

G = 6 + (a multiple of 6)

So G = a multiple of 6, sufficient!
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