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A positive number is divided by 100 to get a remainder thrice as the quotient. If the number is divisible by 11, then how many such numbers are possible that are less than 100000?
Correct answer is '3'. Can you explain this answer?
Verified Answer
A positive number is divided by 100 to get a remainder thrice as the q...
Let the number be N and the quotient when divided by 100 be k. Then remainder is 3k. 3k < 100
N = 100k + 3k = 103k,
Also, N is divisible by 11.
Also, N is divisible by 11.
=> k = 11p, where p is an integer.
=> N = 103*11p = 1133p...
As N < 100000, it implies that p can range from 1 to [100000/1133] i.e between 1 and 88
=> So, p can can range from 1 to 88
=> So, p can can range from 1 to 88
Also 3k < 100 => 3 * 11p < 100 => p < 4 Hence, p can take values 1,2,3
Most Upvoted Answer
A positive number is divided by 100 to get a remainder thrice as the q...
Solution:
Let's suppose the positive number is 'x'.
Given,
x = 100q + 3q
x = 103q
As x is divisible by 11,
103q is divisible by 11
11 divides 103q if and only if 11 divides q.
q can take values from 1 to 9071 (as 103 * 9071 = 935413)
Therefore, the possible values of q are 1, 2, 3, ... , 9071.
We need to find the number of such values of q which give x less than 100000.
As x = 103q, the maximum value of x can be 103 * 9071 = 935413.
Therefore, the maximum value of q for which x is less than 100000 is 970.
We need to find the number of values of q from 1 to 970 which give x less than 100000.
Let's calculate the value of x for q = 1, 2, 3, ... , 970.
We get x = 103, 206, 309, ... , 99989.
The number of values of q for which x is less than 100000 is 3.
Therefore, the required number of such numbers is 3.
Let's suppose the positive number is 'x'.
Given,
x = 100q + 3q
x = 103q
As x is divisible by 11,
103q is divisible by 11
11 divides 103q if and only if 11 divides q.
q can take values from 1 to 9071 (as 103 * 9071 = 935413)
Therefore, the possible values of q are 1, 2, 3, ... , 9071.
We need to find the number of such values of q which give x less than 100000.
As x = 103q, the maximum value of x can be 103 * 9071 = 935413.
Therefore, the maximum value of q for which x is less than 100000 is 970.
We need to find the number of values of q from 1 to 970 which give x less than 100000.
Let's calculate the value of x for q = 1, 2, 3, ... , 970.
We get x = 103, 206, 309, ... , 99989.
The number of values of q for which x is less than 100000 is 3.
Therefore, the required number of such numbers is 3.
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A positive number is divided by 100 to get a remainder thrice as the quotient. If the number isdivisible by 11, then how many such numbers are possible that are less than 100000?Correct answer is '3'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A positive number is divided by 100 to get a remainder thrice as the quotient. If the number isdivisible by 11, then how many such numbers are possible that are less than 100000?Correct answer is '3'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A positive number is divided by 100 to get a remainder thrice as the quotient. If the number isdivisible by 11, then how many such numbers are possible that are less than 100000?Correct answer is '3'. Can you explain this answer?.
A positive number is divided by 100 to get a remainder thrice as the quotient. If the number isdivisible by 11, then how many such numbers are possible that are less than 100000?Correct answer is '3'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A positive number is divided by 100 to get a remainder thrice as the quotient. If the number isdivisible by 11, then how many such numbers are possible that are less than 100000?Correct answer is '3'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A positive number is divided by 100 to get a remainder thrice as the quotient. If the number isdivisible by 11, then how many such numbers are possible that are less than 100000?Correct answer is '3'. Can you explain this answer?.
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