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22 May 2017, 01:17
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C
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Difficulty:
45%
(medium)
Question Stats:
69% (02:07) correct
31%
(01:51)
wrong
based on 181
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When a positive integer x is divided by 12, what is the remainder?
1) x is divisible by 9
2) When x is divided by 4, the remainder is 1
1) x is divisible by 9
2) When x is divided by 4, the remainder is 1
22 May 2017, 04:59
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Statement 1. x is divisible by 9
x could be 9, 18, 27, 36, 45, 54, 63, 72, ....
When we divide these numbers by 12, there is no fixed remainder. But there is a pattern..
On dividing these various values of x in this order 9, 18, 27, 36, 45, 54, 63, 72, ....
by 12, the remainders are: 9, 6, 3, 0, 9, 6, 3, 0,...
We can get a pattern with 4 different values of remainders possible, but no unique value.
So Insufficient
Statement 2. When x is divided by 4, the remainder is 1
x is of the form: (4k+1) where k is a non negative integer.
x could be: 5, 9, 13, 17, 21, 25, 29, 33,...
On dividing these values by 12, we get various remainders as:
5, 9, 1, 5, 9, 1, 5, 9, 1, ....
There is a pattern with three different remainders but no unique value.
So Insufficient
On combining, the only common remainder from statement 1 and statement 2 is '9'
So we got a unique value of remainder as '9'. Sufficient
Hence answer is C
(so basically this also means that if a number is divisible by 9, and also gives remainder '1' when divided by 4: then that number will always give a remainder of '9' when divided by 12)
x could be 9, 18, 27, 36, 45, 54, 63, 72, ....
When we divide these numbers by 12, there is no fixed remainder. But there is a pattern..
On dividing these various values of x in this order 9, 18, 27, 36, 45, 54, 63, 72, ....
by 12, the remainders are: 9, 6, 3, 0, 9, 6, 3, 0,...
We can get a pattern with 4 different values of remainders possible, but no unique value.
So Insufficient
Statement 2. When x is divided by 4, the remainder is 1
x is of the form: (4k+1) where k is a non negative integer.
x could be: 5, 9, 13, 17, 21, 25, 29, 33,...
On dividing these values by 12, we get various remainders as:
5, 9, 1, 5, 9, 1, 5, 9, 1, ....
There is a pattern with three different remainders but no unique value.
So Insufficient
On combining, the only common remainder from statement 1 and statement 2 is '9'
So we got a unique value of remainder as '9'. Sufficient
Hence answer is C
(so basically this also means that if a number is divisible by 9, and also gives remainder '1' when divided by 4: then that number will always give a remainder of '9' when divided by 12)
24 May 2017, 00:33
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==> In the original condition, there is 1 variable and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For remainder questions, you find the first overlapping number after direct substitution, then you add the least common multiple of the dividing numbers.
For con 1), from x=9=12(0)+9, the remainder is 9.
For con 2), from x=4p+1=1,5,9…., the remainder of x=1=12(0)+1 is 1, and from x=5=12(0)+5, the remainder is 5, hence it is not unique and not sufficient.
By solving con 1) and con 2), the first overlapping number is 9 and the least common multiple of the dividing numbers is LCM(From 4,9+36, you get x=9, 9+36=45, 45+36=81,.., and the remainder when divided by 12 always becomes 9, hence it is unique and sufficient. Therefore, the answer is C.
Answer: C
For con 1), from x=9=12(0)+9, the remainder is 9.
For con 2), from x=4p+1=1,5,9…., the remainder of x=1=12(0)+1 is 1, and from x=5=12(0)+5, the remainder is 5, hence it is not unique and not sufficient.
By solving con 1) and con 2), the first overlapping number is 9 and the least common multiple of the dividing numbers is LCM(From 4,9+36, you get x=9, 9+36=45, 45+36=81,.., and the remainder when divided by 12 always becomes 9, hence it is unique and sufficient. Therefore, the answer is C.
Answer: C
