Data Sufficiency

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

(1) The number of boys is 5 less than twice the number of girls.

(2) The difference between the number of boys and the number of girls is 35.

Answer: C

Source: Princeton Review

Let no. of boys = b, and no. of girls = g
Find b:g on the school bus.
Statement 1: The number of boys is 5 less than twice the number of girls.
b = 2g - 5
Since the total no. of girls is unknown, the value of g is unknown, and the target question cannot be answered. Statement 1 is NOT SUFFICIENT.

Statement 2: The difference between the number of boys and the number of girls is 35.
b - g = 35
b = 35 + g or g = -(35-b)
The value of b and g still remain unknown. Statement 2 is NOT SUFFICIENT.

Combining both statements together
From statement 1: b = 2g - 5
From statement 2: b - g = 35
Substituting statement 1 in 2.
2g - 5 - g = 35
g - 5 = 35
g = 40

From statement 2 => b - g = 35, where g=40
b - 40 = 35
b = 35 + 40 = 75
b:g = b/g = 75/40 = 15/8 = 15:8
Therefore, combining both statement together is SUFFICIENT.
Answer = C