Question

Find the greatest number from the options that will divide $1025,1299$ and $1575$ leaving remainders $5,7$ and $11$ respectively.

• A. $70$
• B. $78$
• C. $68$
• D. $98$

Answer 1

The correct option is C $68$

Required number must divide the number if we subtract the remainder from the given numbers
$\therefore$ Required number must divide $(1025-5),(1299-7)$ and $(1575-11)$ exactly.
$\therefore$ Required number $=HCF$ of $1020,1292$ and $1564$
Hence Required number $=68$