121. How many numbers between 1 and 200 are exactly
divisible by exactly two of 3, 9 and 27?
(a) 14
(b) 15
(d) 17
(c) 16
mi
Answers
Answer:
15 numers between 1 to 200 can be divisble by 3,9 and 27
Answer:
hope it help u.....
Step-by-step explanation:
Case 1: Divisible by 3 and 27, but not by 9
9 is a factor of 27. Therefore, if a number is divisible by 27, it is also divisible by 9.
Hence, no such numbers which are only divisible by 3 and 27, but not by 9.
Case 2: Divisible by 9 and 27, but not by 3
3 is a factor of 9. Therefore, if a number is divisible by 9, it is also divisible by 3.
Hence, no such numbers which are only divisible by 9 and 27, but not by 3.
Case 3: Divisible by 3 and 9, but not by 27
Numbers divisible by 9 are 9, 18, 27, ..., 198.
Count of such numbers
=
198
9
=
22
⋯
(
1
)
All these 22 numbers are divisible by 3 also
But
(
1
)
also covers numbers divisible by 27 which needs to be reduced.
27, 54, ..., 189 are the numbers divisible by 27.
Count of such numbers
=
189
27
=
7
⋯
(
2
)
Therefore, count of numbers which are divisible by 3 and 9, but not by 27
= 22 - 7 = 15
Since this is the only case possible, count of numbers between 1 and 200 which are exactly divisible by exactly two of 3,9 and 27
= 15