BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Is y^x = x^y?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

Is y^x = x^y?

by Max@Math Revolution » Tue Nov 12, 2019 11:17 pm
[GMAT math practice question]

Is y^x = x^y?

1) x = y
2) x = (1 + (1/n))^n, y = (1 + (1/n))^{n+1} for a positive integer n.
Top
Source: — Data Sufficiency |
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

by Max@Math Revolution » Fri Nov 15, 2019 12:16 am
=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Condition 1) is sufficient, obviously.

Condition 2)
Since yx = ((1 + (1/n))^{n+1})^(1 + (1/n))^n = ((1 + (1/n)))^(n + 1)*(1 + (1/n))^n, the exponent of y^x with the base (1 + (1/n)) is (n+1)*(1+(1/n))^n = n(1+1/n)* (1+(1/n))^n = n(1+(1/n))^{n+1}
Since xy = ((1 + (1/n))n)^(1 + (1/n))^{n+1} = ((1 + (1/n)))^n(1 + (1/n))^n, the exponent of x^y with the base (1 + (1/n)) is n(1 + (1/n))n is equal to the exponent of y^x.
So, we have y^x = x^y.

Therefore, D is the answer.
Answer: D

This question is a CMT4 (B) question: condition 1) is easy to work with, and condition 2) is difficult to work with. For CMT4 (B) questions, D is most likely to be the answer.
Top
Post new topic Post Reply
• Page 1 of 1