Is x > y? (1) x = y + 2 (2) x/2 = y - 1

SOLUTION

Is x > y?

(1) x = y+2.

The above says that \(x\) is 2 greater than \(y\), thus it's clear that \(x > y\). Sufficient.

(2) x/2 = y-1

Rewrite as \(x=2y-2\). If \(y=0\), then \(x=-2\) and the answer is NO. However, if \(y=3\) then \(x=4\) and the answer is YES. Not sufficient.

Answer: A.
_________________

Hi,

Difficulty level: 600

Using (1),
x = y + 2, so for any value of y, x > y. Sufficient.

Using (2),
x/2 = y - 1
for x = 0, y = 1 or x < y
for x = 2, y = 2 or x = y
for x = 4, y = 3 or x > y, Thus the relationship depends on value of x & y. Insufficient.

Thus, Answer is (A)

Regards,

Is x > y?

(1) x = y+2
Regardless of whether y is a positive or negative, if x=y+2, then y is greater than x. SUFFICIENT.
(2) x/2 = y-1
This kind of logic pops up frequently from the GMAT probelms I have done.
x=2(y-1)
x=2y-2
Whenever you see mult/div AND sub/add on the other side of x, you won't be able to tell whether whether one integer is greater than the other. It could be either of the case.

Answer: A

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is x > y?

(1) x = y+2
(2) x/2 = y-1

We get x-y>0? when we modify the questions.
For condition 1, x-y=2>0 This is a 'yes', and sufficient.
For condition 2, x=2y-2, x-y=y-2. We cannot determine the sign of x-y, so this is insufficient.
The answer (A).

For (C), x=y+2, x=2y-2 --> y=2, x=4. This is insufficient as it is too trivial.

Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.

Hi All,

We're asked if X is greater than Y. This is a YES/NO question. We can solve it by TESTing VALUES.

1) X = Y +2

With this Fact, we can see that X is "2 greater" than Y, so the answer to the question is ALWAYS YES. You can see this pattern with a few TESTs:
IF....
Y = 0, X = 2
Y = 5, X = 7
Y = -3, X = -1
Etc.
Fact 1 is SUFFICIENT

2) X/2 = Y - 1

IF....
Y = 1, X = 0 and the answer to the question is NO
Y = 3, X = 4 and the answer to the question is YES
Fact 2 is INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Bunuel VeritasPrepKarishma

Could you please provide graphical approach to solve Statement 2? I am able to draw the line on the graph. The line meets the x axis and y axis at points (-2,0) and (0,1) respectively. From this point, how do we determine if there would be a case when y < x. Number plugging approach doesn't come very easily to me, so trying out other ways to solve.

Thanks for your help!!

Hi

They can provide better explanation but I will try. So you have drawn a line of x/2 = y - 1. The other line you should also draw is x = y (or y = x). Why you may ask? Because the question asks you whether x is > y or not? Once you have the line y = x on the graph (it will be a line with positive slope of 1 passing through origin inclined at 45 degrees with x axis), you can see that:- the area on graph below this line y=x will be the area where x > y and the area on the graph above this line y=x will be the area where x < y.

So on one hand, you have this line y=x and on the other hand you have the line x/2 = y-1. You will see that some part of line x/2 = y-1 will fall below the y=x line and some part of line x/2 = y-1 will be above the y=x line. So what does this tell us? This tells us that with the data x/2 = y-1, we CANNOT be sure whether x > y or not.

Yes, you have the line which depicts x/2 = y-1. You see that this represents a line with slope 1/2. So y increases by 1/2 for every 1 unit increase in x.
It passes through (-2, 0) and (0, 1). So if x increases by 2, y increases by 1 so (2, 2) lies on this line. If x increases by another 2, y increases just by 1 so (4, 3) lies on this line too.
In case of some points x > y and in other cases x < y. So this statement alone is not sufficient.

To determine whether x is greater than y, we can evaluate the statements (1) and (2) separately.

Statement (1) x = y + 2:
This statement states that x is equal to y plus 2. By subtracting 2 from both sides of the equation, we have x - 2 = y. This equation implies that x is greater than y by exactly 2 units. Therefore, based on statement (1), we can conclude that x is greater than y.

Statement (2) x/2 = y - 1:
This statement states that half of x is equal to y minus 1. By multiplying both sides of the equation by 2, we have x = 2(y - 1). This equation implies that x is equal to 2 times y minus 2. It does not provide a direct comparison between x and y, and we cannot determine whether x is greater than y based solely on statement (2).