After the division of a number successively by 3, 4 and 7, the remainder obtained is 2, 1 and 4 respectively. What will be remainder if 84 divide the same number?
A. 80
B. 75
C. 42
D. 53
Answer: Option D
Solution(By Examveda Team)
As the Number gives a remainder of 4 when it is divided by 7, then the number must be in form of (7x + 4) The same gives remainder 1 when it is divided 4, so the number must be in the form of {4 × (7x + 4) + 1} Also, the number when divided by 3 gives remainder 2, thus number must be in form of [3 × {4 × (7x + 4) + 1} + 2] Now, On simplifying, [3 × {4 × (7x + 4) + 1} + 2] = 84x + 53 We get the final number 53 more than a multiple of 84 Hence, if the number is divided by 84, The remainder will be 53Join The Discussion
Comments ( 4 )
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
how can slow 84X+53
Z=7×1+4=11
Y=4×Z+1=4×11+1=45
X=3×Y+2=3×45+2=137
Now, divide 137 by 84, we get remainder 53
Hence, 53 is the answer
Why can't we take and start with 3 or 4 , because if we take that then the answer is not coming and if we take 7 then answer is coming. Can you plz tell why we started with 7 divisor and not 3 and 4 ??
[3*{4*(7x+4)+1}+2]=84x+53
Hence, how u got 53 ?