Data Sufficiency

The ratio of water and ammonia in solution A is 1 : 4; the ratio of the same two substances in solution B is 3 : 1. If solutions A and B are mixed, what will be the ratio of water and ammonia in the resultant solution?

(1) Solutions A and B are mixed in ratio 2 : 3.
(2) 20 liters of solution A is used

OA: A

Hi Experts,

Can you pls explain this problem?

Thanks
Nandish

NandishSS wrote:The ratio of water and ammonia in solution A is 1 : 4; the ratio of the same two substances in solution B is 3 : 1. If solutions A and B are mixed, what will be the ratio of water and ammonia in the resultant solution?

(1) Solutions A and B are mixed in ratio 2 : 3.
(2) 20 liters of solution A is used

OA: A

Hi Experts,

Can you pls explain this problem?

Thanks
Nandish

Solution A
water: 1x
ammonia: 4x
total: 5x.

So A is 1/x/5x = 20% water

Solution B
water: 3y
ammonia: y
total: 4y.

So B is 3y/4y = 75% water

(Notice that if we had equal amounts of A and B, the percentage of water in our overall solution would be exactly halfway between 20 and 75.)

Statement 1: If the ratio of A to B is 2:3, we know there's a little more B than A in the solution, so we're pulled a little more toward the 75 than we are toward the 20. If we were to plot the water percentages on a number line, the distances from A and B to the overall average, can be represented as 3t and 2t respectively.

20----------------- Average--------75
Dist:------ 3t-----Average--2t----

Total distance between 20 and 75 = 3t + 2t = 5t.
5t = 55
t = 11

20 + 3t = 20 + 3*11 = 53. So the combined solution is 53% water and 47% ammonia. Sufficient. (Notice that we don't have to solve here. We have to see that it's possible to solve.)


Statement 2: tells us nothing about the quantity of Solution B. Not Sufficient.

The Answer is A

NandishSS wrote:The ratio of water and ammonia in solution A is 1 : 4; the ratio of the same two substances in solution B is 3 : 1. If solutions A and B are mixed, what will be the ratio of water and ammonia in the resultant solution?

(1) Solutions A and B are mixed in ratio 2 : 3.
(2) 20 liters of solution A is used

Question stem, rephrased:
What fraction of the resultant solution is water?

Statement 1:
Case 1: A=20 liters and B=30 liters, for a total of 50 liters
Since A is 1/5 water, the amount of water in 20 liters of A = (1/5)(20) = 4.
Since B is 3/4 water, the amount of water in 30 liters of B = (3/4)(30) = 22.5.
Thus, (total water)/(total volume) = (4 + 22.5)/50 = 26.5/50 = 53/100.

Case 2: A=40 liters and B=60 liters, for a total of 100 liters
Since A is 1/5 water, the amount of water in 40 liters of A = (1/5)(40) = 8.
Since B is 3/4 water, the amount of water in 60 liters of B = (3/4)(60) = 45.
Thus, (total water)/(total volume) = (8 + 45)/100 = 53/100.

Since (total water)/(total volume) is THE SAME VALUE in each case -- 53/100 --
Statement 1 is SUFFICIENT.

Statement 2:
No information about the amount of B in the resultant solution.
INSUFFICIENT.

The correct answer is A.