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

Question

What is 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?

(1) 2 y^2  = 32

(2) 3 x^2 =27

Last edit: Edited spacing

Apt0810 · Answer

Answer should be C because if we consider A then y=4 so the equation becomes 4+1000x and for x=1 remainder is 5, while for x=2 remainder is 6..so how can the answer be A?

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EncounterGMAT · Answer

SOLUTION

Given: Number P expressed as y+ 1000^x , x and y are integers.

We need to determine the reminder of P when divided by 9.
So, P =  1000^x  ]/9 = \frac{y}{9}  +  \frac{1000^x}{9}  and add the individual remainders to determine the final answer.
Irrespective of the value of p, if we divide 1000^x by 9, we will always get the remainder 1 –> hence, our final answer doesn’t depend on the value of p.

(1) 2 y^2  = 32
y^2 = 16
y= 4
From what we calculated above ->  \frac{4}{9}  +  \frac{1000^x}{9} -> we now know the remainder of both individual fractions. 
( You don't actually need to calculate the reminder!)

SUFFICIENT!

(2) 3 x^2 =27
x^2 = 9
x = 3

\frac{y}{9}  +  \frac{1000^3}{9} .......we already knew that no matter what the value of x will be, the remainder would always be 1 but we know nothing about y -> so not possible to find the remainder of  \frac{y}{9} .

INSUFFICIENT!

Thus, the answer is   option A  .

P.S: In DS questions, if the question stem is not analyzed in detail, before jumping onto statements, then you would end up getting incorrect answers (trap answer in this question is option C)

Apt0810 · Answer

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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CrackverbalGMAT · Answer

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.

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

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GMAT Data Sufficiency (DS) Questions

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

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