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

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Difficulty:   35% (medium)

Question Stats: 68% (01:35) correct 32% (02:14) wrong based on 117 sessions

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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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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.

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

***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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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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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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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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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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