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

Question

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

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

Bunuel · Accepted Answer

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

(1) x^a = y^b + y^b + y^b -->  x^a=3y^b . If x=y=0, then each of a and b can be any positive integer. Not sufficient.

(2) x^a = y^b + y^b + y^b + y^b -->  x^a=4y^b . If x=y=0, then each of a and b can be any positive integer. Not sufficient.

(1)+(2) Subtract the equations:  y^b=0  -->  x^a=0 . Since given that a and b are positive integers, then  x=y=0  --> both a and b can take any integer values. Not sufficient.

Answer: E.

Hope it's clear.

duttsit · Answer

A.

a, b > 0

i) x ^ a = Y^b + Y^b + Y^b or
x ^ a = 3 y ^ b or
x ^ (a - b) = 3 = 3 ^ 1
a - b = 1

sufficient

ii)
x ^ a = 4 y ^b or
x ^ (a - b) = 4

insufficient because:
4 = 2 ^ 2 OR 4 = 4^1

ranga41 · Answer

Are you considering x = y? If so why? or else i dont understand how you get x ^ (a - b) = 3 from x ^ a = 3 y ^ b .......

ranga41 · Answer

There is something crazy about this problem, to my capability both equation alone is not sufficient, because there will be one equation and 4 variables...

If we combine both equations we get 3 = 4 , which is again ultra crazy......I go with E...

duttsit · Answer

You right. I mistook y for x. In fact, i remember I saw this problem before where it was stated as:
x ^ a = x ^b + x^b + x^b
y^a = y^a + y ^ b + y^b + y^b

coming back to this question. it will be E.

macca · Answer

It's an E.

what is the value of a-b, assume a, b are positive integers.. 

1) x^a=Y^b + Y^b + Y^b 
2) x^a=Y^b + Y^b + Y^b + Y^b 

There's not much to do here it seems. 

1,
x^a =3y^b ->
x^a/3y^b=x^a*y^(-b)=3

Insuff

2,

same reasoning. 
is this question fully stated?

ranga41 · Answer

Duttsit changed his explanation in the posting above yours...can you clarify...if the question is the way he puts it?

silentell · Answer

hold on a second are we saying that x is y here? i think both statements are insuff if they aren't

FN · Answer

OA is E...

X and Y both are 0, but we dont know the value of a nd b....

honchos · Answer

Bunuel OA has dispute I believe A is correct, Can you Please take over this question. Thanks!

law258 · Answer

E is correct. Here's why:

(1) x^a = y^b + y^b + y^b --> Rewrite to be x^a = 3(y^b)

INSUFFICIENT - we can't arrive at a value from this for a-b

(2) x^a = y^b + y^b + y^b + y^b --> Rewrite as x^a = 4(y^b)

INSUFFICIENT - same as (1)

Together - (1) + (2) --> 3(y^b) = 4(y^b) --> INSUFFICIENT

rishab0507 · Answer

Statement 1: Doesnot tell us any relation between a and b by giving any values for X and Y. Insufficient

Statement 2: Again same as statement A, no value and relation given.
Combining also yields same result.

E answer

bumpbot · Answer

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

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

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