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If x and y are nonzero integers, is x^y < y^x? (1) x =

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Senior Manager
Senior Manager
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 408

Kudos [?]: 25 [0], given: 283

Re: If x and y are nonzero integers, is x^y < y^x? (1) x = [#permalink]

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New post 23 Sep 2016, 11:01
I agree with C being correct

(1) x = y^2 --> from this we know x>0, but y can be either positive or negative, thus INSUFFICIENT

(2) y > 2 --> we don't know anything about x, thus INSUFFICIENT

(1) + (2) --> SUFFICIENT; we know that y must be positive from (2), therefore we can figure out the main equation without hesitation

Kudos [?]: 25 [0], given: 283

Senior Manager
Senior Manager
avatar
B
Joined: 05 Jan 2017
Posts: 435

Kudos [?]: 62 [0], given: 15

Location: India
Premium Member
Re: If x and y are nonzero integers, is x^y < y^x? (1) x = [#permalink]

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New post 23 Feb 2017, 05:54
Prompt analysis
Let the number of tapes with carmen and rafael be x and y respectively.

x+12 = 2y

Superset
Value of x and y will be a whole number.

Translation
St 1: y =x +5. Solving 2 equations we get x = 2, y =7. ANSWER
St 2: x<12. Cannot determine the exact value of x. INSUFFICIENT

Option A

Kudos [?]: 62 [0], given: 15

Manager
Manager
avatar
B
Joined: 23 Dec 2013
Posts: 235

Kudos [?]: 14 [0], given: 21

Location: United States (CA)
GMAT 1: 760 Q49 V44
GPA: 3.76
Re: If x and y are nonzero integers, is x^y < y^x? (1) x = [#permalink]

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New post 03 Jun 2017, 21:16
conocieur wrote:
I would pick A

x = y^2

so y^2^y = y^y^2 which i think is

y^2y = y^2y

so they are equal and you can answer the question



The goal of this problem is to determine if x^y < y^x.

Statement 1) x = y^2

x | y
0 | 0
1 | 1
9 | 3

1^1 = 1^1 BUT 9^3 < 3^9. Not sufficient.

Statement 2) y > 2.

No information provided for x. Insufficient.

Statements 1+2) Now we can do some algebra.

x^y = y^2y

y^x = y^(y^2)

For all y, y^2 > 2y. Sufficient.

Kudos [?]: 14 [0], given: 21

Re: If x and y are nonzero integers, is x^y < y^x? (1) x =   [#permalink] 03 Jun 2017, 21:16

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