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What is the remainder when x is divided by 9?
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Updated on: 19 May 2017, 07:02
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78% (01:07) correct 22% (02:15) wrong based on 51 sessions
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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?
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Originally posted by papagorgio on 18 May 2017, 18:57.
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?
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18 May 2017, 20:33
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?
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18 May 2017, 22:06
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?
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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? &nbs
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19 May 2017, 07:02






