If x and y are positive integers greater than two then what is the

Question

If x and y are positive integers greater than two then what is the remainder when x^356 is divided by y ?

(1) x = 6
(2) y = x - 1

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gmatophobia · Answer

Question

Remainder  \frac{x^{356}}{ y}

Statement 1

The only thing that we can infer is the number will end in 6. However do not know the value of y, hence the statement is not sufficient.

We can eliminate A and D.

Statement 2

y = x - 1

We know x and y are greater than 2, so the least value of y = 3 and the least value of x = 4.

In this case, x when divided by y will leave a remainder = 1.

So Remainder  (\frac{x}{y})  = 1.

So, remainder ( \frac{x^{356} }{ y}  ) =  1^{356}  = 1

Sufficient.

Option B

Rabab36 · Answer

gmatophobia  can you pls explain statement 2

y=x-1

x=4,y=3
x=5,y=4
x=6,y=5
x=7,y=6

remainder will be same for x=4,5,6 
not for x=7,8

therefore option c

and i think you have taken x^365

actually as per q is x^356

gmatophobia · Answer

Rabab36 We know that y (denominator) is one less than x (numerator). Hence except for when the denominator = 1, if we divide the numerator by denominator the remainder will always be equal to 1. In this case the denominator cannot be equal to 1 as the question states that both the numerator and denominator are integers greater than 2. Hence the remainder will always be one. To the address the second point - x = 7 & y = 6, the remainder will when \frac{7}{6} will be 1. Hence 1^{356} = 1; hence 1 is the remainder. Thanks for noticing. Me and my typo

This wouldn't change the solution because 1^n is 1 (n can be any number). Hope this helps.

If x and y are positive integers greater than two then what is the

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