changhiskhan wrote:
The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to girls in Class B is 4 to 5. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A?
A. 8
B. 9
C. 10
D. 11
E. 12
The information
the ratio of boys to girls in the combined class would be 17 to 22 is superfluous.
Too much info just to try to confuse you. If one counts the unknowns, we have 4: number of boys in class A, girls in A, boys in B and girls in B.
Without the info of the combined rate, we already have in fact four equations:
1) the ratio in class A
2) the ratio in class B
3) one more boy in class A in comparison with class B
4) two more girls in class A in comparison with class B
So, we don't need a fifth equation.
If we denote by B and G the number of boys and girls respectively in class A, we can write the following set of equations:
\(B/G=3/4\)
\((B-1)/(G-2)=4/5\)
Two equations, two unknowns, solve and get G=12.
Or, go with divisibility criteria, G must be a multiple of 4, so choose between A and E.
For A, B=6, G=8 but B-1=5, G-2=6, so \(5/6\neq4/5\).
For E, B=9, G=12 and B-1=8, G-2=10, so 8/10=4/5, OK. Also the additional condition holds, as (9+8)/(12+10)=17/22.
_________________
PhD in Applied Mathematics
Love GMAT Quant questions and running.