We can make a table like the one in the attached figure to help solve this problem.
-----------Brown---Blue
White------A--------B
Grey--------C------- D
Total--------X--------Y------55
Referring to the table.
We are given that B > 3 and X + Y = 55
Is Y > X ?
1. D:B = 4:3
Or, for a constant 'P, the values are
D = 4P and B = 3P , where P is an integer.
So the value of Y is in terms of 7P.
Thus possible values of Y can be- 7, 14,21,28,35,42,49
We cannot determine the value of X from this. And X can be lower or greater than Y depending on the value of Y here.
Not Sufficient
2. A:C = 2:1
For a constant 'Q', the values are
A = 2Q and C = Q, where Q is an integer.
So the value of X is in terms of 3Q.
Thus possible values of X can be- 3,6,9,12,15,18.......54
We cannot determine the value of Y from this. And Y can be lower or greater than X depending on the value of X here.
Not Sufficient
1 + 2
X is in terms of 3Q and Y is in terms of 7P. Also, X + Y = 55
So if we substitute values in 7P and subtract it from 55, the difference should be in terms of 3Q.
For example, if P = 4
Y = 28 and X = 27 <- valid
We will find that the only valid values are when P = 4 and P = 7. The other values are invalid because the difference is not divisible by 3.
When P = 7
Y = 49 and X = 6
Now in both cases, we find that Y > X
Hence Sufficient.
Answer C
