What is the remainder when P is divided by 9 when the number P is expr

I think then I took the question wrongly where I took it as 1000*x since in my view it was showing like that, but per your solution I can see that it is 1000^x, which will make option A suitable

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Hi,

Remainder questions can be tricky, if not approached the right way. Any test taker will use one of the following two approaches while solving remainder questions:

1. Use equations - Dividend = (divisor)*(quotient) + remainder - An algebraic reasoning based approach
2. Use numbers - An arithmetic mathematical approach

Knowing when to use the above two approaches becomes super important as each one of them have their benefits.

For questions where you need to find the remainder of an addition or subtraction of values, using equations and the remainder rule is a better way to proceed.

There are two remainder rules:

Remainder(A * B * C.......) = Remainder(A) * Remainder(B) * Remainder(C)........

for e.g. Remainder of (43 * 37 * 68)/9 -----> Remainder of (43/9 * 37/9 * 68/9) -----> remainder of (7 * 1 * 5)/9 = remainder of (35/9) = 8

The question here asks for the remainder when P is divided by 9 when the number P is expressed as y+1000^x where x and y are positive integers.

So we need the remainder of (y + 1000^x)/9. Since x is a positive integer 1000^x/9 will always give us a remainder of 1. We only need the remainder when y is divided by 9, or simply the value of y.

Statement 1: 2y^2 = 32

y^2 = 16 ----> y = +/-4, since y is a positive integer, y = 4. Sufficient.

Statement 1 : 3x^2 = 27

This just gives us x = 3, it does not give us a value of y. Insufficient.

The answer is A.