Question

The smallest number which when divided by $20,25,35and40$ and leaves remainders of $14,19,29and34$ respectively is:

• A. $1394$
• B. $1404$
• C. $1664$
• D. $1406$

Answer 1

Answer: (A)

$1394$

Let us first find the factors of the given numbers $20,25,35$ and $40$ to find the LCM of these numbers:

$20=2\times 2\times 525=5\times 535=5\times 740=2\times 2\times 2\times 5$

Therefore, LCM$(20,25,35,40)=5\times 5\times 2\times 2\times 2\times 7=1400$

Now we find the difference of the given numbers using remainders as follows:

$20-14=6,$ $25-19=6,$ $35-29=6$ and $40-34=6$

So, we are getting $6$ less than the divisor in each case, and thus the required number is $1400-6=1394$

Hence, the number would be $1394$.