question_answer

What is the smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively?

A) 1394                       

B) 1404

C) 1664     

D) 1406

Correct Answer: A

Solution :

  \[\therefore \,\,\,\text{L}\text{.C}\text{.M}\text{.=5 }\!\!\times\!\!\text{ 2 }\!\!\times\!\!\text{ 2 }\!\!\times\!\!\text{ 5 }\!\!\times\!\!\text{ 7 }\!\!\times\!\!\text{ 2=1400}\] \[\text{20-14=25-19=35-29=40-34=6}\] \[\therefore \]The required number = L.C.M. - 6                                                 =1400-6=1394