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A number is divided by 2, 3, 4, 5 or 6, reminder in each case is one. But the number is exactly divisible by 7. The number lies between 250 and 350, the sum of digits of the number will be
- a)4
- b)7
- c)6
- d)10
- e)Can not be determined
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A number is divided by 2, 3, 4, 5 or 6, reminder in each case is one. ...
To solve this problem, we need to find a number that satisfies the following conditions:
- When divided by 2, 3, 4, 5, or 6, the remainder is 1.
- The number is divisible by 7.
- The number lies between 250 and 350.
Let's start by finding the least common multiple (LCM) of 2, 3, 4, 5, and 6, which is the smallest number divisible by all of these numbers.
LCM(2, 3, 4, 5, 6) = 60
We need to find a number of the form 7k, where k is an integer, that leaves a remainder of 1 when divided by 60. The numbers in this sequence can be expressed as 60n + 1, where n is an integer.
Now, let's find the first few numbers of the form 60n + 1 that are divisible by 7 and lie between 250 and 350:
- For n = 4: 60(4) + 1 = 241 (not divisible by 7)
- For n = 5: 60(5) + 1 = 301 (divisible by 7)
So, the number we're looking for is 301.
Now, let's find the sum of its digits: 3 + 0 + 1 = 4
Therefore, the sum of the digits of the number is 4.
Most Upvoted Answer
A number is divided by 2, 3, 4, 5 or 6, reminder in each case is one. ...
Find the LCM of given numbers then we get 60
now it is asked that the number should be between 250 and 350
and in the multiples of 60, 300 is the least number which comes under 250 and 350
then add 300 with 1 we get 301 which is also divisible by 7
so the sum of the digits of 301
3+0+1=4
now it is asked that the number should be between 250 and 350
and in the multiples of 60, 300 is the least number which comes under 250 and 350
then add 300 with 1 we get 301 which is also divisible by 7
so the sum of the digits of 301
3+0+1=4
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Community Answer
A number is divided by 2, 3, 4, 5 or 6, reminder in each case is one. ...
LCM of 2, 3, 4, 5 and 6 is 60
60 * 5 + 1 = 7x
7x = 301
Number – 301 ; The sum of digits of the number = 4
60 * 5 + 1 = 7x
7x = 301
Number – 301 ; The sum of digits of the number = 4
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