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If a, b, x and y are positive integers, what is the value of a - b?

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Bunuel
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If a, b, x and y are positive integers, what is the value of a - b? [#permalink] New post  06 Nov 2014, 09:05
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Tough and Tricky questions: Algebra.



If a, b, x and y are positive integers, what is the value of a - b?

(1) x^a = x^b + x^b + x^b
(2) y^a = y^b + y^b + y^b + y^b

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kinghyts
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Re: If a, b, x and y are positive integers, what is the value of a - b? [#permalink] New post  06 Nov 2014, 20:18
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Statement 1:

x^a = x^b + x^b + x^b
x^a=3*x^b
Since all are integer we can say x = 3, 3^a=3^b+1
and therefore a= b+1, a-b=1
Sufficient

Statement 2:

y^a = y^b + y^b + y^b + y^b
y^a = 4^1* y^b
or, y^a = 2^2* y^b

If y=4, a=b+1
If y=2, a =b+2
Hence insufficient

Therefore answer is A
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anupamadw
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Re: If a, b, x and y are positive integers, what is the value of a - b? [#permalink] New post  06 Nov 2014, 23:49
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Bunuel wrote:

Tough and Tricky questions: Algebra.



If a, b, x and y are positive integers, what is the value of a - b?

(1) x^a = x^b + x^b + x^b
(2) y^a = y^b + y^b + y^b + y^b

Kudos for a correct solution.




Stmn1)
x^a = 3x^b
x^a-b = 3

x=3 , a-b=1
as all are positive integers ,we cant consider x=9 and a-b=1/2
Suff

Stmn2)
y^a = 4y^b
y^a-b= 4
y=4 a-b=1
y=2 a-b=2
Insuff

IMO A
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sillyboy
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Re: If a, b, x and y are positive integers, what is the value of a - b? [#permalink] New post  19 Jan 2017, 21:00
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A.

S1: x^a = 3x^b
(x^a)/(x^b) = 3
x^(a-b) = 3

since a,b,x,y are +ve integers, only possible value of x here is 3 and a-b=1. Therefore, SUFFICIENT.


S2: y^a = 4y^b
(y^a)/(y^b)=4
y^(a-b)=4

Therefore, if y=4 then a-b=1 OR if y=2, a-b=2. Hence, NOT SUFFICIENT.
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Re: If a, b, x and y are positive integers, what is the value of a - b? [#permalink] New post  04 Sep 2021, 10:40
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Re: If a, b, x and y are positive integers, what is the value of a - b? [#permalink]
04 Sep 2021, 10:40
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