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Is x^y<1?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4876
GPA: 3.82

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01 Feb 2018, 00:33
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Difficulty:

45% (medium)

Question Stats:

68% (01:00) correct 32% (01:05) wrong based on 50 sessions

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[GMAT math practice question]

Is $$x^y<1$$?

$$1) x>1$$
$$2) y<1$$
[Reveal] Spoiler: OA

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Senior Manager
Joined: 07 Jul 2012
Posts: 276
Location: India
Concentration: Finance

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01 Feb 2018, 02:16
(1) x=2 and y=0 [No]
x=2 and y=-1 [Yes]
Two possibilities. So [Insuff]

(2) x=2 and y=0 [No]
x=2 and y=-1[Yes] [Insuff]

Combine (1) & (2)
No common info.

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GPA: 3.82

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04 Feb 2018, 17:08
=>

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.

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.
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Re: Is x^y<1?   [#permalink] 04 Feb 2018, 17:08
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