Is x^y<1?

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Is x^y<1?

by Max@Math Revolution » Thu Feb 01, 2018 12:28 am
[GMAT math practice question]

$$Is\ x^y<1?$$

$$\left(1\right)\ x>1$$
$$\left(2\right)\ y<1$$

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by elias.latour.apex » Fri Feb 02, 2018 9:01 am
It is best to start off with questions such as these by asking ourselves: What do we need? Generally speaking, we would need to know values for both x and y. However, if either x or y were 0 that would be sufficient on its own. Similarly, if x were 1, that would also be sufficient. So perhaps a narrow range of values for both or one specific value for one or the other would work.

Statement 1: This is not sufficient because y could be pretty much anything.
Statement 2: This is not sufficient because x could be pretty much anything.

Together: Still not sufficient because x could be 2 and y could be 0, in which case it would be 1 and the answer would be no. On the other hand, x could be 2 and y could be -1, in which case it would be 0.5 and the answer would be yes.

So (E)
Elias Latour
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by Max@Math Revolution » Sun Feb 04, 2018 5:03 pm
=>

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.

Conditions 1) & 2):
If x = 4 and y = -1, then xy = 1/4 < 1, and the answer is 'yes'.
If x = 4 and y = ½, then xy = 2 > 1, and the answer is 'no'.

Since we don't have a unique answer, both conditions are not sufficient when taken together by CMT (Common Mistake Type) 2.

Therefore, the answer is 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.
Answer: E