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What is remainder of the division (1325*1327*1329)/12?

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What is remainder of the division (1325*1327*1329)/12?  [#permalink]

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New post 15 Jun 2011, 21:45
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What is remainder of the division (1325*1327*1329)/12?

A. 3

B. 5

C. 9

D. 0

E. 6

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What is remainder of the division (1325*1327*1329)/12?  [#permalink]

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New post 18 Jul 2017, 15:14
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soaringAlone wrote:
What is remainder of the division (1325*1327*1329)/12?

A. 3

B. 5

C. 9

D. 0

E. 6

Quote:
General rule

The remainder of the product of three large numbers divided by x is the remainder of the product of their remainders divided by x.***

For this problem, the rule translates to:

Divide 1325, 1327, and 1329, respectively, by 12.
All three will yield remainders.
Multiply those remainders together, and divide again by 12.
You will have your answer.


To simplify further

1. Do the arithmetic for \(\frac{1325}{12}\). You'll get quotient 110 with remainder 5, or R5.

1327 is 1325 + 2. You can either do the arithmetic for 1327 divided by 12, or you can realize that you just need to add 2 to R5.

So the next number, \(\frac{1327}{12}\) leaves R7.

Finally, the last number is 1,329. (Same pattern for 1329, which is 1327 + 2. Add 2 to R7.) Or:
\(\frac{1329}{12}\) leaves R9. Summarized:

\(\frac{1325}{12}\) leaves remainder 5
\(\frac{1327}{12}\) leaves remainder 7
\(\frac{1329}{12}\) leaves remainder 9


2. Take all three remainders and multiply them. 5*7*9 = 315


3. Divide the product of those remainders by 12: \(\frac{315}{12}\) = 26 with remainder 3

Answer A

***From InstantMBA in an excellent post whose link is below. That post explains, and gives the more general rule for, TrueLie 's similar post above.
https://gmatclub.com/forum/if-n-775-778-781-what-is-the-remainder-when-n-is-divided-by-217323.html#p1677321

Hope it helps.
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Re: What is remainder of the division (1325*1327*1329)/12?  [#permalink]

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New post 15 Jun 2011, 21:58
soaringAlone wrote:
What is remainder of the division (1325*1327*1329)/12?

A. 3

B. 5

C. 9

D. 0

E. 6


1325*1327*1329 / 3*4
Now the given product will be divided by 3 since 1329 is divisible by 3.....divisibility test of 3

Now, the last digit of the product will be 5*7*9 = 5 ...therefore the remainder will be either 1 or 3...1 is not in options hence the answer is 3 i.e. A

Also, after dividing by 4 the remainder will be less than 4 there are only 2 options that r less than 4 i.e. 0 and 3 ..
0 is not possible since 4 does not divide any of the number completely ...hence the remainder should be 3. Thus option A
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Re: What is remainder of the division (1325*1327*1329)/12?  [#permalink]

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New post 15 Jun 2011, 23:34
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remainder will be number/ 100 here as the divisor is two digit number = 12.

hence checking for the last two digits = 5*7*9 = 15

Thus remainder = 3.
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Re: What is remainder of the division (1325*1327*1329)/12?  [#permalink]

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New post 08 Jul 2011, 19:54
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Note that: 12x110 = 1320 -> (1325*1327*1329)/12 = (1320 + 5)((1320 + 7 )(1320 +9)/12 -> remainder = remainder of 5x7x9/12 -> 3
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Re: What is remainder of the division (1325*1327*1329)/12?  [#permalink]

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New post 18 Jul 2017, 20:13
We can use the concept of negative remainders to solve this problem.

The question stem asks us for the remainder of expression (1325*1327*1329)/12.

The number closest to these three numbers which is exactly divisible by 12 is 1332.
So, in essence, the expression yields a remainder of -7 * -5 * -3, which can be written as 35 * -3

Again, when we divide the number 35 by 12, we will get a negative remainder of -1
So, the remainder of the expression is -1*-3 = 3(Option A)
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Re: What is remainder of the division (1325*1327*1329)/12?  [#permalink]

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Re: What is remainder of the division (1325*1327*1329)/12?   [#permalink] 26 Feb 2019, 07:36
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