Max@Math Revolution wrote:[GMAT math practice question]

If x and y are positive integers, what is the remainder when x+y is divided by 2?

1) xy is divisible by 4
2) y is divisible by 2

We need to determine the remainder of x + y divided by 2, or, in other words, we need to determine whether x + y is even or odd.

Statement One Alone:

xy is divisible by 4

We see that xy is a multiple of 4. If xy is 8, we could have x = 2 and y = 4, so x + y is even, or we could have x = 1 and y = 8, in which case x + y would be odd. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

y is divisible by 2

Since we have no information regarding x, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using our two statements together, we still cannot answer the question. We could have x = 2 and y = 4, so x + y is even, or we could have x = 1 and y = 8, in which case x + y would be odd.

Answer: E

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables (x and y) and 0 equations, C is most likely to be 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):
If x = 4 and y = 1, x + y = 5 has remainder 1 when it is divided by 4.
If x = 2 and y = 2, x + y = 4 has remainder 0 when it is divided by 4.

Since we don't have a unique solution, both conditions together 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.

$$\frac{\left(x+y\right)}{2}=\ T\arg et\ question$$
If two positive integers x and y is divisible by 2 the only position remainder is 0 and 1
1st statement x and y is divisible by 4 case study to test value
if x= 2 and y= 4 : xy = 2*4 = 8
8 is divisible by 4 implementing the value into $$\frac{x+y}{2}\ =\ \frac{2+4}{2}\ =\ \frac{6}{2\ }=\ 3.0$$
if x= 3 and y = 4 xy = 3*4 = 12
12 is divisible by 4 implementing the value into
$$\frac{\left(x+y\right)}{2}=\ \frac{\left(3+4\right)}{2}=\frac{7}{2}=3r1$$
This certifies that $$\frac{\left(x+y\right)}{2}is\ not\ definite\ and\ cannot\ be\ answered\ with\ certainty$$
therefore the first statement is not SUFFICIENT
2nd statement , therefore Y is divisible by 2
No information is given about integer x so the answer to the question is not definite
Therefore, the 2nd statement is NOT SUFFICIENT
Statement (1) and (2) together are NOT SUFFICIENT.
Hence, option E is the answer