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If x is a positive integer, what is the remainder when x is divided by

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If x is a positive integer, what is the remainder when x is divided by  [#permalink]

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New post 04 Dec 2019, 02:52
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Re: If x is a positive integer, what is the remainder when x is divided by  [#permalink]

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New post 04 Dec 2019, 03:29
#1 x^2 has a remainder of 4 when divided by 5
x=2,7 x^2 ; remainder is 4 and x /5 is 2
x=8 , remainder is 3 insufficient
#2
x^3 has a remainder of 2 when divided by 5
x=3,13,23
so x divided by 5 ; remainder is 3
IMO B sufficient


Bunuel wrote:
If x is a positive integer, what is the remainder when x is divided by 5?

(1) x^2 has a remainder of 4 when divided by 5
(2) x^3 has a remainder of 2 when divided by 5


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Re: If x is a positive integer, what is the remainder when x is divided by  [#permalink]

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New post 04 Dec 2019, 04:58
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Since this is a division by 5, we only need to know the units digit to determine the remainder.

(1) x^2 has a remainder of 4 when divided by 5

For a remainder of 4, the units digit of x^2 must be 4 or 9

So x can be any integer with units digit 2, 3, 7 or 8 and so the remainder when x is divided by 5 can be 2 or 3

1 is insufficient

(2) x^3 has a remainder of 2 when divided by 5

x^3 must have units digit 2 or 7

So, x can be any integer with units digit 8 or 3

The remainder in both cases is 3

2 is sufficient

Answer is (B)
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If x is a positive integer, what is the remainder when x is divided by  [#permalink]

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New post 04 Dec 2019, 06:08
If x is a positive integer, what is the remainder when x is divided by 5?

we need a unique remainder value

(1) x^2 has a remainder of 4 when divided by 5 :we know x^2 has remainder 4 so min x^2 can be 4,9,64,49.....
from this x can be 2 or 3 etc : remainder 2/5 = 2 and 3/5 = 3 so Insufficient

(2) x^3 has a remainder of 2 when divided by 5 : we know x^3 has remainder 2 when divided by 5 so units digit of the cube ends in either 2 or 7 : multiple of 5 ends in 0 and 5 so remainder of 2 can be obtained if
number is A0+ 2 or A5+2
having inferred that the cubes will end in 7 or 2, we see x can be 3,8,13,18....
diving each of them by 5 given remainder of 3 a unique answer : sufficient
(B)
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If x is a positive integer, what is the remainder when x is divided by   [#permalink] 04 Dec 2019, 06:08
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If x is a positive integer, what is the remainder when x is divided by

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