Ratios

1.
Let number of professors be 3x and number of administrators be 4x. (This gives the ratio of 3:4 which is as per the question).

Now, profs increase by 5 => profs=3x+5.
Admins increase by 5=> admins=4x+5.

New ratio = (3x+5)/(4x+5). This does not give a firm ratio because of the presence of the additive terms in both numerator and denominator. So, ratio cannot be determined.

Answer E!


2.
Let nurses be 5x and doctors be 7x.
It is given that number of nurses = 35=> 5x=35. This gives x=7.
So, number of doctors =7x=7*7=49.
When 6 doctors leave the room, number of doctors remaining = 49-6=43.

Hence, answer is B!

phoenix9801 wrote:The ratio of professors to administrators is 3 to 4. If the number of professors increased by 5 and the number of administrators also increased by 5, what is the ratio of these two new quantities?

A) 23/24
B) 18/19
C) 8/9
D) 3/4
E) It cannot be determined from the information given

Case 1: 3 professors, 4 administrators
When each value is increased by 5, the new ratio = (3+5)/(4+5) = 8/9.

Case 2: 6 professors, 8 administrators
When each value is increased by 5, the new ratio = (6+5)/(8+5) = 11/13.

Since different new ratios are possible, the value of the new ratio cannot be determined.

The correct answer is E.

phoenix9801 wrote: Initially, the nurses and doctors in a room were in the ratio of 5:7. Six doctors leave the room. If there are 35 nurses in the room, how many doctors are left in the room?

A) 49
B) 43
C) 30
D) 25
E) 19

In the RATIO, the nurses are represented by 5.
The ACTUAL number of nurses = 35.
Thus, the MULTIPLIER here = 35/5 = 7.
Multiplying both values in the ratio by 7, we get:
N : D = 5:7 = 35:49.
Thus, after 6 doctors leave, the number of doctors left = 49-6 = 43.

The correct answer is B.