Data Sufficiency

[GMAT math practice question]

What are the values of x and y?

1) x and y are numbers such that 3x - 2y = 6(x - 1).
2) x and y are integers with -3 < x ≤ 3,

From 1, 3x + 2y =6
x and y can take multiple values. Hence not sufficient.

From 2, x = -2, -1, 0, 1, 2, 3
y can take multple values. Hence not sufficient

From 1 and 2,
x = 0 , y =3
x=2, y= 0

Hence not sufficient.

Hence, answer E.

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Since we have 2 variables (x and y) and 0 equations, C is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

3x - 2y = 6(x - 1)
=> 3x - 2y = 6x - 6
=> -2y = 3x - 6
=> -2y = 3(x - 2)
=> 2y = -3(x - 2)
=> 2y = 3(2 - x)
=> y = (3/2)(2 - x)

Since x and y are integers from condition 2) and x - 2 is an even number, x must be an even number. Also, y is a multiple of 3.

Since we have -3 < x ≤ 3 from condition 2, we have -2 ≤ x ≤ 3. The possible values of x are -2, 0 and 2. Substituting these values into y = (3/2)(2 - x) gives the possible pairs of (x, y), which are (-2, 6), (0, 3) and (2, 6).

Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.
Answer: E

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.