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When the number of people in an office is divided by 12, the remainder

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Bunuel
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When the number of people in an office is divided by 12, the remainder [#permalink] New post   01 May 2018, 06:03
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When the number of people in an office is divided by 12, the remainder is 0. If 3/2 times the number of people in the office is divided by 12, and the remainder resulting from this operation is greater than 0, the remainder must be

A. 1
B. 2
C. 3
D. 5
E. 6
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E
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Re: When the number of people in an office is divided by 12, the remainder [#permalink] New post   01 May 2018, 06:48
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Bunuel wrote:
When the number of people in an office is divided by 12, the remainder is 0. If 3/2 times the number of people in the office is divided by 12, and the remainder resulting from this operation is greater than 0, the remainder must be

A. 1
B. 2
C. 3
D. 5
E. 6


Number of people in an office is divided by 12, the remainder is 0
This means the number of people is 12K (k is a positive integer)

Now when 3/2 times 12K divided by 12, rem is >0
or 3/2*12K = 18K = (12+6)K

so when ever the value of K is even, the number when divided by 12 will leave a remainder of 12
but when the value of K is odd, the number 18K will leave remainder of 6

hence E
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Re: When the number of people in an office is divided by 12, the remainder [#permalink] New post   01 May 2018, 07:07
When the number of people in an office is divided by 12, the remainder is 0. If 3/2 times the number of people in the office is divided by 12, and the remainder resulting from this operation is greater than 0, the remainder must be

1. when the number of people in office is divided by 12, the remainder is 0. So, the number of people must be a multiple of 12. We can consider 12n.

2. If 3/2 times i.e 1.5 times the number of people in office is divided by 12, the remainder is > 0.

If N is even i.e 2, 4.. etc , the remainder will always be 0.
If N is odd i.e 1,3...etc, the remainder will always 6. For Eg N=3 , 18N = 54 , when divided by 12 , remainder is 6.

Ans: E
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Re: When the number of people in an office is divided by 12, the remainder [#permalink] New post   01 May 2018, 07:23
Bunuel wrote:
When the number of people in an office is divided by 12, the remainder is 0. If 3/2 times the number of people in the office is divided by 12, and the remainder resulting from this operation is greater than 0, the remainder must be


A. 1
B. 2
C. 3
D. 5
E. 6

Solution:
Let People=P. Given P=12x (note, there is no remainder because 12 divides P completely.)
Question if \(\frac{3}{2}\)(P) is divided by 12 what will be the remainder?
\(\frac{3}{2}\)(P)/12= {\(\frac{3}{2}\)(12x)}/12 = \(\frac{18x}{12}\) = \(\frac{12x}{12}\)+ \(\frac{2x}{12}\) = x+\(\frac{1}{6}\)*x. The remainder is \(\frac{1}{6}\)*x, looking at the answer choices only 6 is a multiple 6.

Answer: (E).
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Re: When the number of people in an office is divided by 12, the remainder [#permalink] New post   02 May 2018, 10:24
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Bunuel wrote:
When the number of people in an office is divided by 12, the remainder is 0. If 3/2 times the number of people in the office is divided by 12, and the remainder resulting from this operation is greater than 0, the remainder must be

A. 1
B. 2
C. 3
D. 5
E. 6


Because division by 12 yields a remainder of 0, we see that the number of people in the office is a multiple of 12. We can multiply a few multiples of 12 by 3/2, and we have:

12 x 3/2 = 18 ---> 18/12 = 1 R 6

24 x 3/2 = 36 ---> 36/12 = 3 R 0

36 x 3/2 = 54 ---> 54/12 = 4 R 6

48 x 3/2 = 72 ---> 72/12 = 6 R 0

We see that when we divide those results by 12, we get a remainder of either 0 or 6. So, the only possible remainder that is greater than 0 is 6.

Answer: E
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Re: When the number of people in an office is divided by 12, the remainder [#permalink] New post   19 Oct 2022, 11:06
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Given that When the number of people in an office is divided by 12, the remainder is 0. And we need to find the remainder when 3/2 times the number of people in the office is divided by 12

Since the number of people is divisible by 12 (because remainder when divided by 12 is 0)
=> Number of people can be taken as 12k (Where k is an integer)

\(\frac{3}{2}\) of number of people = \(\frac{3}{2}\) * 12k = 18k

Now, 18k when divided by 12 gives a remainder greater than 0
If we take k = 1, we will get 18

18 when divided by 12 gives 6 remainder.

So, Answer will be E
Hope it helps!



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Re: When the number of people in an office is divided by 12, the remainder [#permalink]
19 Oct 2022, 11:06
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