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11 Jun 2020, 03:48
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
66% (02:32) correct
34%
(02:40)
wrong
based on 223
sessions
History
Date
Time
Result
Not Attempted Yet
How many numbers between 101 and 1001 are divisible by 6 but not by 15?
A. 90
B. 120
C. 140
D. 150
E. 180
A. 90
B. 120
C. 140
D. 150
E. 180
yashikaaggarwal
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Joined: 19 Jan 2020
Last visit: 29 Mar 2026
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11 Jun 2020, 04:05
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No. Between 101 to 1001 divisible by 6 = 102,108,114,120........up to 996
An = A+(n-1)d
996 = 102 + (n-1)*6
894 = (n-1)*6
894/6 = (n-1)
149 = n-1
150 = n ------------(1)
So, there are 150 no. Divisible by 6 between 101&1001
=> The no. Which are not divisible by 15 but 6 = total no. Divisible by 6 - The no. Which are divisible by both 15&6
=> The numbers between 101 and 1001 are divisible by 15 & 6 = LCM Of 15&6 = 30
Multiple of 30 between 101&1001 = 120,150,180,..........990
An=A+(n-1)*d
990 = 120+(n-1)*30
870 = (n-1)*30
870/30 = n-1
29 = n-1
30 = n .......(2)
So, there are 30 no. Divisible by 6&15 between 101&1001
The no. Which are divisible by 6 but not 15 = total no. Divisible by 6 - The no. Which are divisible by both 15&6.
=> 150-30
=> 120
IMO B
Posted from my mobile device
An = A+(n-1)d
996 = 102 + (n-1)*6
894 = (n-1)*6
894/6 = (n-1)
149 = n-1
150 = n ------------(1)
So, there are 150 no. Divisible by 6 between 101&1001
=> The no. Which are not divisible by 15 but 6 = total no. Divisible by 6 - The no. Which are divisible by both 15&6
=> The numbers between 101 and 1001 are divisible by 15 & 6 = LCM Of 15&6 = 30
Multiple of 30 between 101&1001 = 120,150,180,..........990
An=A+(n-1)*d
990 = 120+(n-1)*30
870 = (n-1)*30
870/30 = n-1
29 = n-1
30 = n .......(2)
So, there are 30 no. Divisible by 6&15 between 101&1001
The no. Which are divisible by 6 but not 15 = total no. Divisible by 6 - The no. Which are divisible by both 15&6.
=> 150-30
=> 120
IMO B
Posted from my mobile device
General Discussion
11 Jun 2020, 04:10
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LCM of 6,15 = 30
Number of digits divisible by 6 between 101 & 1001 is (166-16) = 150
Number of digits divisible by 30 between 101 & 1001 is (166-16) = 30
Final answer 150 - 30 =120
Posted from my mobile device
Number of digits divisible by 6 between 101 & 1001 is (166-16) = 150
Number of digits divisible by 30 between 101 & 1001 is (166-16) = 30
Final answer 150 - 30 =120
Posted from my mobile device
