Data Sufficiency

Does Country X have more citizens than Country Y?

(1) 60% of Country X's citizens are also citizens of Country Y.
(2) 30% of Country Y's citizens are not citizens of Country X.

sud21 wrote:Does Country X have more citizens than Country Y?

(1) 60% of Country X's citizens are also citizens of Country Y.
(2) 30% of Country Y's citizens are not citizens of Country X.

Is X>Y?
Let B = the number of people who are citizens of BOTH countries.

Statement 1:
In other words, 60% of X's citizens are citizens of BOTH countries:
0.6X = B.
No way to determine whether X>Y.
INSUFFICIENT.

Statement 2:
Since 30% of Y's citizens are NOT also citizens of X, 70% of Y's citizens ARE citizens of both countries:
0.7Y = B.
No way to determine whether X>Y.

Statements combined:
Since 0.6X = B and 0.7Y = B, we get:
0.6X = 0.7Y
6X = 7Y
X = (7/6)Y.
Thus, X>Y.
SUFFICIENT.

The correct answer is C.

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Remember equal number of variables and independent equations ensures a solution.

Does Country X have more citizens than Country Y?

(1) 60% of Country X's citizens are also citizens of Country Y.
(2) 30% of Country Y's citizens are not citizens of Country X.

In the original condition there are 2 variables (number of citizens in X,Y) and thus we need 2 equations to match the number of variables and equations. Since there is 1 each in 1) and 2), C has high probability of being the answer. Using both 1) & 2) together, number of citizens in country X:x,number of citizens in country Y:y and 0.6x=0.7y. 6x=7y --> x>y. The answer is yes, and therefore the conditions are sufficient. Therefore the answer is C.

Normally for cases where we need 2 more equations, such as original conditions with 2 variable, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using ) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

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sud21 wrote:Does Country X have more citizens than Country Y?

(1) 60% of Country X's citizens are also citizens of Country Y.
(2) 30% of Country Y's citizens are not citizens of Country X.

(1) This means that number of citizens who belong to both countries represent 60 percent of the population of Country X. But we don't know this number represent what percent of the population of Country Y. For example, if this number represents 70 percent of the population of Country Y, then Country X have more citizens than Country Y; hence YES. Or if this number represent 50 percent of the population of Country Y, then Country X have less citizens than Country Y; hence NO. Insufficient so go for BCE.

(2) This means that number of citizens who belong to both countries represent 70 percent of the population of Country Y. But we don't know this number represent what percent of the population of Country X. For example, if this number represents 50 percent of the population of Country X, then Country X have more citizens than Country Y; hence YES. Or if this number represent 80 percent of the population of Country X, then Country X have less citizens than Country Y; hence NO. Insufficient so go for CE.

Taking together, we realize that 60% of Country X's citizens are equal to 70% of Country Y's citizens, and hence, [spoiler]YES, Country X have more citizens than Country Y.

SUFFICIENT

It's (C)[/spoiler]

Let's say that Country X has x unique citizens, Country Y has y unique citizens, and the two countries have z shared citizens.

S1 gives us z = .6(x + z), or .4z = .6x, or z = 1.5x. This tells us nothing about y, so it's insufficient.

S2 gives us y = .3(y + z), or .3z = .7y, or z = (7/3)y. This tells us nothing about x, so it's insufficient.

Together we have z = (7/3)y = (3/2)x. This DOES allow us to compare x and y definitively, so it IS sufficient.