Let N = 1421 × 1423 × 1425. What is the remainder when N is divided by 12?
A. 0
B. 9
C. 3
D. 6
Answer: Option C
Solution(By Examveda Team)
Remainder,$$\eqalign{ & \frac{{1421 \times 1423 \times 1425}}{{12}} = R \cr & R \Rightarrow \frac{{5 \times 7 \times 9}}{{12}} \cr} $$
[Here, we have taken individual remainder such as 1421 divided by 12 gives remainder 5, 1423 and 1425 gives the remainder as 7 and 9 on dividing by 12.]
Now, the sum is reduced to,
$$\frac{{5 \times 7 \times 9}}{{12}} = \frac{{35 \times 9}}{{12}}$$
$$\frac{{35 \times 9}}{{12}}$$ = Remainder ⇒ -1 × -3 = 3 [Here, we have taken negative remainder.] So, required remainder will be 3.
Note: When, $$\frac{9}{{12}}$$ it gives positive remainder as 9 and it also give a negative remainder -3. As per our convenience,we can take any time positive or negative remainder.
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Comments ( 6 )
Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
Why we can taking individual remainders
Why second option is not correct✅
Guys suggest me a book for aptitude test preparation
We can just multiplying of the last digit 1×3×5 then divided by 12 to get remainder 3
See, we can take Positive or negative remainder in the shake of simplicity.
Why are we taking negative remainder?