Here is a nice qs on reminder and AM (Courtesy: TIME) A natural number when divided by 6, 8, 9 and 12 leaves reminders 3, 5, 6 and 9 respectively. What is the arithmetic mean of all such numbers less than 1000? a. 429 b. 465 c. 501 d. 537
A natural number when divided by 6, 8, 9 and 12 leaves reminders 3, 5, 6 and 9 respectively. What is the arithmetic mean of all such numbers less than 1000? a. 429 b. 465 c. 501 d. 537
Solution:
The smallest number satisfying the given property is of the form 72k - 3.
So, all the numbers less than 1000 satisfying the given condition are:
A natural number when divided by 6, 8, 9 and 12 leaves reminders 3, 5, 6 and 9 respectively. What is the arithmetic mean of all such numbers less than 1000?
a. 429
b. 465
c. 501
d. 537
Soln.
As diff between divisor n remainder is same i.e. 3 fr all cases.
D first no. whch will satisfy ds condn is L.C.M. of (6,8,9,12)-3=72-3=69....
nd the last no. wthin 1000 is (72 x 13)-3= 936 - 3=933
AM is (933+69)/2=1002/2=501......
SO OPTION (c) is the correct one.....
Giv ur best to the world...
Nd d best will cm back to you....
A natural number when divided by 6, 8, 9 and 12 leaves reminders 3, 5, 6 and 9 respectively. What is the arithmetic mean of all such numbers less than 1000?
a. 429
b. 465
c. 501
d. 537
Solution:
The smallest number satisfying the given property is of the form 72k - 3.
So, all the numbers less than 1000 satisfying the given condition are:
69, 141, 213, ............., 861, 933
Their Arithmetic Mean is: (69 + 933)/2 = 501
Thank You
Ravi Raja
n/a
A natural number when divided by 6, 8, 9 and 12 leaves reminders 3, 5, 6 and 9 respectively. What is the arithmetic mean of all such numbers less than 1000?
a. 429
b. 465
c. 501
d. 537
Soln.
As diff between divisor n remainder is same i.e. 3 fr all cases.
D first no. whch will satisfy ds condn is L.C.M. of (6,8,9,12)-3=72-3=69....
nd the last no. wthin 1000 is (72 x 13)-3= 936 - 3=933
AM is (933+69)/2=1002/2=501......
SO OPTION (c) is the correct one.....
Giv ur best to the world...
Nd d best will cm back to you....
Regards,
Dipanjan.......
n/a
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