What is the remainder when X is divided by 3, where 3 is not

Question

What is the remainder when X is divided by 3, where 3 is not a factor of X ?

i. Sum of the digits of X is 7
ii. X is a square number

Source: Indian CAT

i. Remainder of sum of digits/3 = remainder of x/3
ii. Any square number that is not divisible by 3 is in the form 3k + 1.

Temurkhon · Answer

Stimulus says that 0<r<3 that means r=1 or 2

1) we can use picking, but we know that when 3 is a factor we can sum product's digits and divide it 3 and remainder in constant for any number. Here we have 1. Eliminate B,C,E
2) take the row of perfect square which is 1,4,9,16,25,36,49 and eliminate multiple of 3. We get the 1.

Answer in two options are the same, that the sign of D

crazu4 · Answer

just came across this question and don't understand why D is the answer. as you said, 36 is a perfect square number and when divides by 3, the remainder is 0, not 1. When we try with 25, the remainder is 1, so the second statemant should be insufficient. Can someone please clarify where i went wrong?

EMPOWERgmatRichC · Answer

Hi crazu4,

When dealing with DS questions, you have to make note of any "restrictions" that exist in the original prompt. Here, we're told that 3 is NOT a factor of X (in other words, X is NOT a multiple of 3).

In Fact 2, we're told that X is a perfect square, BUT we're not allowed to use any perfect squares that are multiples of 3....

36 is a multiple of 3, so it is not allowed.

GMAT assassins aren't born, they're made,
Rich

anshsharma2k · Answer

From the question we know that X is not a multiple of 3. So when X is divided by 3, the only possible remainders are 1 and 2.
Now, Statement 1: Sum of digits is 7. If we subtract 1 from this number we get sum of digits = 6 which will make it a factor of 3. Hence we can say that when we divide this number by 3, the remainder will always be 1. Hence Sufficient.

Statement 2 is tough! we can take a sample of square numbers to verify but If i have to generalize for every number, then if x is a square which is not a multiple of 3 then its square root (say y) should also not be a multiple of 3. This gives only 2 options for y i.e 3z+1 or 3z+2. (z is some positive integer)
If we square these 3z+1 we get 9z^2 + 6z + 1 which we can clearly see will leave a remainder 1 when divided by 3.
And for 3z +2, we get 9z^2 + 12z + 4 = 9z^2 + 12z + 3 + 1 (Again remainder is 1). Hence this statement is also sufficient.

Anandanwar · Answer

Hello,

Here we dont even know whether X is positive or not.
for X = 25: remainder is 1
for X = -25: remainder is 2.
That is why in opinion D should not be answer.
Could you tell where I am going wrong?

Regards,
Ankit

samarpan.g28 · Answer

For statement i, is X positive? The possible remainders can be 1 and 2.

What is the remainder when X is divided by 3, where 3 is not

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GMAT Data Sufficiency (DS) Questions

What is the remainder when X is divided by 3, where 3 is not

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