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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42 GPA: 3.82
M60-19  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 71% (01:10) correct 29% (01:10) wrong based on 7 sessions

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Is $$x^y < 1$$?

1) $$x > 1$$

2) $$y < 1$$

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42 GPA: 3.82
M60-19  [#permalink]

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Official Solution:

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 $$x^y = 1/4 < 1$$, and the answer is 'yes'.

If $$x = 4$$ and $$y = ½$$, then $$x^y = 2 > 1$$, 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.

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.

Answer: E
_________________

Originally posted by MathRevolution on 11 Jun 2018, 06:42.
Last edited by MathRevolution on 05 Aug 2018, 22:53, edited 1 time in total.
Intern  B
Joined: 25 Jun 2016
Posts: 11
Re M60-19  [#permalink]

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I think this is a poor-quality question and I don't agree with the explanation. Here the question is x raised to the power y and not x multiplied by y.
Intern  Joined: 10 Apr 2019
Posts: 2
Re M60-19  [#permalink]

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I think this is a poor-quality question and I agree with explanation. The stem gives us x^y<1.
And the solution proceeds with x*y. Is this a typo mistake in the stem or is it something i don't get? Just in case, i give a feedback for the stem to see if its wrong. Sorry for the inconvenience Re M60-19   [#permalink] 11 Apr 2019, 04:22
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# M60-19

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