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

Question

A. 3

B. 5

C. 9

D. 0

E. 6

generis · Accepted Answer

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.

TrueLie · Answer

Note that: 12x110 = 1320 -> (1325*1327*1329)/12 = (1320 + 5)((1320 + 7 )(1320 +9)/12 -> remainder = remainder of 5x7x9/12 -> 3

vyassaptarashi · Answer

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

amit2k9 · Answer

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.

pushpitkc · Answer

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)

muhammaddk92 · Answer

Each number divided by 12.

Then look at units digit of each numerator and denominator so for example 1325 / 12 = 5/2. Remainder is 1.

Same for rest two numbers. Each has a remainder of 1. Add 1+1+1 =3

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What is remainder of the division (132513271329)/12?

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What is remainder of the division (132513271329)/12?