topspin20 wrote:
Thanks for the question Mitch-that certainly did make things a little more difficult. First I used the given information to solve for the number of men (120), which gives a 'multiplier' of 40 to the ratio of x:y:z. So it follows that [spoiler]4(40)-1(40)=120[/spoiler]. Answer C
Nice work! Below is an alternate approach.
In a certain room, the ratio of women to men to children is 4 to 3 to 1. The room currently contains x women, y men and z children. If 40 women were to enter the room and 20 men were to leave the room, the ratio of women to men to children would then be 10 to 5 to 2. What is the value of x-z?
30
90
120
150
180
The ratio of women to men to children is 4 to 3 to 1.
In other words, W:M:C = 4:3:1.
Since all of the values in the problem are multiples of 10, list multiples of 10 in this ratio:
W:M:C
40:30:10
80:60:20
120:90:30
160:120:40
200:150:50
If 40 women were to enter the room and 20 men were to leave the room, the ratio of women to men to children would then be 10 to 5 to 2.
Here, since W:M = 10:5 = 2:1, there must be twice as many women as men.
Adding 40 women and subtracting 20 men from the list of ratios above, we get:
W:M:C
80:10:10
120:40:20
160:70:30
200
40
220:130:50
Only the option in red satisfies the constraint that W:M = 2:1.
Thus, the original ratio = 160:120:40, implying that x=160, z=40, and x-z = 160-40 = 120.
The correct answer is
C.
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