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27 Oct 2015, 19:10
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62% (02:40) correct
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The positive integer n is greater than 10. What is the remainder when the positive integer n is divided by 12?
(1) n is 20 more than a multiple of 36.
(2) n is 4 less than a multiple of 3 and n is 4 less than a multiple of 8.
Please help!, I know the official answer i just want a clear explanation, because Kaplan explanation left me
(1) n is 20 more than a multiple of 36.
(2) n is 4 less than a multiple of 3 and n is 4 less than a multiple of 8.
Please help!, I know the official answer i just want a clear explanation, because Kaplan explanation left me
28 Oct 2015, 01:54
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The positive integer n is greater than 10. What is the remainder when the positive integer n is divided by 12?
(1) n is 20 more than a multiple of 36.
(2) n is 4 less than a multiple of 3 and n is 4 less than a multiple of 8.
st 1 --> 0 is multiple of 36 , next multiple is 36 and so on is 72
now 0 + 20 = 20 when divided by 12 = remainder = 8
36 +20 = 56 when divided by 12 = remainder = 8
72 +20 =92 when divided by 12 = remainder = 8
Also note that 12 = 2^2 * 3
36 = 2^2* 3^3
so all the multiple of 36 is divisible by 12
also note that question ask n is 20 more than multiple of 36 ----- as we know that all multiple of 36 are divisible by 12 and effectively it becomes now 20 divided by 12 , so the remainder is 8 .
It hold true for all the cases .
st 2 --> in way it is saying that the number is multiple of both 8 and 3 and 4 less .Therefore the first number 24 - 4 = 20
when you divide 20/12 = remainder is 8
hence both the statement is sufficient
D .
Press Kudos if it helps.
(1) n is 20 more than a multiple of 36.
(2) n is 4 less than a multiple of 3 and n is 4 less than a multiple of 8.
st 1 --> 0 is multiple of 36 , next multiple is 36 and so on is 72
now 0 + 20 = 20 when divided by 12 = remainder = 8
36 +20 = 56 when divided by 12 = remainder = 8
72 +20 =92 when divided by 12 = remainder = 8
Also note that 12 = 2^2 * 3
36 = 2^2* 3^3
so all the multiple of 36 is divisible by 12
also note that question ask n is 20 more than multiple of 36 ----- as we know that all multiple of 36 are divisible by 12 and effectively it becomes now 20 divided by 12 , so the remainder is 8 .
It hold true for all the cases .
st 2 --> in way it is saying that the number is multiple of both 8 and 3 and 4 less .Therefore the first number 24 - 4 = 20
when you divide 20/12 = remainder is 8
hence both the statement is sufficient
D .
Press Kudos if it helps.
11 Apr 2017, 12:38
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a33jcfve
Target question: What is the remainder when the positive integer n is divided by 12?
Statement 1: n is 20 more than a multiple of 36.
In other words, n = 36k + 20 for some integer k
Let's do some rewriting.
n = 36k + 20
= (12)(3)k + 12 + 8
= 12(3k + 1) + 8
= 12(some integer) + 8
Here, we can see that n equals 8 more than some multiple of 12
This means that, if we divide n by 12, the remainder will be 8
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: n is 4 less than a multiple of 3 and n is 4 less than a multiple of 8
Let's examine both pieces separately:
n is 4 less than a multiple of 3
In other words, n = 3k - 4 for some integer k
If we add 4 to both sides, we get n + 4 = 3k
This means that n+4 is a multiple of 3
n is 4 less than a multiple of 8
In other words, n = 8j - 4 for some integer j
If we add 4 to both sides, we get n + 4 = 8j
This means that n+4 is a multiple of 8
If n+4 is a multiple of 3 AND 8, then we can conclude that n+4 is a multiple of 24
ALSO, if n+4 is a multiple of 24, then we can conclude that n+4 is a multiple of 12
Finally, if if n+4 is a multiple of 12, we can write: n+4 = 12q for some integer q
We can also write: n+4 = 12q - 12 + 12 [you'll see why shortly]
n+4 = 12(q - 1) + 12
n = 12(q - 1) + 8 [I subtracted 4 from both sides]
n = 12(some integer) + 8
Once again, we can see that n equals 8 more than some multiple of 12
This means that, if we divide n by 12, the remainder will be 8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer:
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