Question

The smallest number which when divided by 20, 25, 35 and 40 and leaves remainders as of 14, 19, 29 and 34 respectively is

• A. 1,394
• B. 1,404
• C. 1,664
• D. 1,406

Answer 1

The correct option is A 1,394

5, 20, 25, 35, 40
$|\underset{–}{24,5,7,8}$
$|\underset{–}{22,5,7,4}$
$|\underset{–}{1,5,7,2}$
$\therefore L.C.M.=5\times 2\times 2\times 5\times 7\times 2=1400$
$20-14=25-19=35-29$
$=40-34=6$
$\therefore$ required number
$=LCM-6$
$=1400-6$
$=1394$.