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 3Answer 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#p1677321Hope it helps.
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