Find the number of three-digit numbers which when divided by 11 leave a remainder of 9 and when divided by 7 leave a remainder of 2.

A. 11
B. 12
C. 14
D. 10

Question

Find the number of three-digit numbers which when divided by 11 leave a remainder of 9 and when divided by 7 leave a remainder of 2.

A. 11
	B. 12
	C. 14
	D. 10

ganeshie8 · Answer

numbers which when divided by 11 leave a remainder of 9 and when divided by 7 leave a remainder of 2 will be in the form :
77x + 86

number of 3 digit numbers will be from x=1, and x= 11
so 11 is your answer

ganeshie8 · Answer

let me know if you dont understand how we put that expression : 77x + 86

shubhamsrg · Answer

\yes please tell me how you got that expression

ganeshie8 · Answer

11x + 9 : 20, 31, 42, 53, 64, 75, 86, ......
7x  + 2 :  9, 16, 23, ... ... 86,.... 

86 is the first number that satisfies both contraints.
so, the cycle starts after 86 and it repeats every (lcm of 11 and 7)

shubhamsrg · Answer

nice..that was quite smart of you ^_^//thank you..

ganeshie8 · Answer

yw (: thanks