How many three-digit positive integers are divisible by 11 and 35?

Question

A. 0
B. 1
C. 2
D. 3
E. 4

Yashvardhan08 · Answer

lcm of 11 and 35 = 385
only 385 and 770 is divisible.
answer=c

ramlala · Answer

3 digit numbers: from 100 to 999

3 digit numbers divided by 11 & 35
= 5*7*11= 385 
=385*2=  770 
=385*3= more than 3 digits.

Ans = 2

IMO C

EgmatQuantExpert · Answer

Solution

To find  
We need to determine
 • The number of 3-digit positive integers which are divisible by both 11 and 35

Approach and Working out  
If a number is divisible by both 11 and 35, then we can say the number is a common multiple of both 11 and 35
 • As LCM denotes the least among the common multiples, we can say that the number must be a multiple of the LCM of 11 and 35

LCM(11, 35) = 385
Now, the multiples of 385 are 385 (= 385 x 1), 770 (385 x 2), 1155 (= 385 x 3) and so on.
However, 1155 or values beyond that will not be possible as the number must be a 3-digit number
 • Hence, only two values are possible: 385 and 770

Thus, option C is the correct answer.

Correct Answer: Option C

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How many three-digit positive integers are divisible by 11 and 35?

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How many three-digit positive integers are divisible by 11 and 35?

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