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What is the remainder when x is divided by 9?

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What is the remainder when x is divided by 9? [#permalink]

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New post 18 May 2017, 18:57
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What is the remainder when x is divided by 9?

(1) The remainder is 4 when x is divided by 27.

(2) The remainder is 1 when x is divided by 4.

What's the most efficient way to solve these types of questions?
[Reveal] Spoiler: OA

Last edited by papagorgio on 19 May 2017, 07:02, edited 1 time in total.
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Re: What is the remainder when x is divided by 9? [#permalink]

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Statement 1. x is an integer of the form = 27a + 4 (where a is a non negative integer)

When 27a + 4 is divided by 9, remainder will be 4 only.
Thats because 27a will always be divisible by 9 (so giving remainder 0 here) while 4 when divided by 9 will give a remainder of 4 only (a smaller natural number when divided by a larger natural number leads to the smaller number, dividend, as remainder itself).

OR you could look at numbers of the form (27a + 4) - 31, 58, 85, 112... each of these numbers when divided by 9 gives a remainder of 4 only.
Statement is Sufficient.


Statement 2. x is an integer of the form 4b + 1 (where b is a non negative integer)

Some examples of such integers - 5, 9, 13, 17, 21... you can see that the possible remainders here (when divided by 9) can be various - 5, 0, 4, .... etc. There is no unique value.

So statement is NOT Sufficient.

Hence answer should be A.

(OA is given to be C. Either its wrong or i am missing something)
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Re: What is the remainder when x is divided by 9? [#permalink]

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New post 18 May 2017, 22:06
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Hi,

The most efficient way to solve like these remainder question is write down few initial values, you can figure out the answer.

Question: Remainder, when x is divided by 9?

That is, x = 9* q + R?

What is the value of R?

Statement I is sufficient:

x = 27*k + 4.

Since 27 is divisible by 9, remainder has to be 4.

Otherwise just write down few values here,

4, 31, 58, 85….

All these above values when divided by 9 leaves the remainder 4.

So, statement I is sufficient.

Statement II is insufficient:

x= 4*m+1

So, the values could be,

1, 5, 9, 13, 17, …

So, you can see that in above values remainder keep changing when divided by 9.

So, not sufficient.

So, answer is A.

Hope this helps.

I too think the answer has to be A.
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Re: What is the remainder when x is divided by 9? [#permalink]

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New post 19 May 2017, 07:02
amanvermagmat wrote:
Statement 1. x is an integer of the form = 27a + 4 (where a is a non negative integer)

When 27a + 4 is divided by 9, remainder will be 4 only.
Thats because 27a will always be divisible by 9 (so giving remainder 0 here) while 4 when divided by 9 will give a remainder of 4 only (a smaller natural number when divided by a larger natural number leads to the smaller number, dividend, as remainder itself).

OR you could look at numbers of the form (27a + 4) - 31, 58, 85, 112... each of these numbers when divided by 9 gives a remainder of 4 only.
Statement is Sufficient.


Statement 2. x is an integer of the form 4b + 1 (where b is a non negative integer)

Some examples of such integers - 5, 9, 13, 17, 21... you can see that the possible remainders here (when divided by 9) can be various - 5, 0, 4, .... etc. There is no unique value.

So statement is NOT Sufficient.

Hence answer should be A.

(OA is given to be C. Either its wrong or i am missing something)



You're correct. I've amended the OA to reflect your answer!

Thanks. +1
Re: What is the remainder when x is divided by 9?   [#permalink] 19 May 2017, 07:02
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