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Find smallest number that leaves remainder 3, 4, 5 when divided by 5, 6, 7 respectively and leaves remainder 1 when divided by 11.
- a)208
- b)426
- c)600
- d)628
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Find smallest number that leaves remainder 3, 4, 5 when divided by 5, ...
We have just seen above in TYPE-2 how to tackle the first part of the questionThus the number for the first part would be the [(LCM of 5, 6, 7) – (Common difference of divisors and their remainders)] i.e. 210 – 2 = 208
Here now, we have one more condition to satisfy i.e. remainder 1 when divided by 11
Here we should remember that if LCM of the divisors is added to a number; the corresponding remainders do not change i.e if we keep adding 210 to 208… the first 3 conditions for remainders will continue to be fulfilled.
Therefore now, let 208 + 210k be the number that will satisfy the 4th condition i.e. remainder 1 when (208 + 210k)/11
Now let’s see how
The expression (208 + 210k)/11 = 208/11 + 210k/11
Now the remainder when 208 is divided by 11 = 10
And remainder when 210k is divided by 11 = 1*k = k
The expression (208 + 210k)/11 = 208/11 + 210k/11
Now the remainder when 208 is divided by 11 = 10
And remainder when 210k is divided by 11 = 1*k = k
Therefore the sum of both the remainders i.e. 10 + k should leave remainder 1 on division of the number by 11
Obviously k = 2
Hence the number = 208 + 210*2 = 628 (option ‘D’)
Obviously k = 2
Hence the number = 208 + 210*2 = 628 (option ‘D’)
Most Upvoted Answer
Find smallest number that leaves remainder 3, 4, 5 when divided by 5, ...
Explanation:
Finding the smallest number:
To find the smallest number that satisfies the given conditions, we need to consider the LCM (Least Common Multiple) of the numbers 5, 6, 7, and 11. This is because the number should leave remainders of 3, 4, 5 when divided by 5, 6, 7 respectively, and leave a remainder of 1 when divided by 11.
Calculating the LCM:
- LCM of 5, 6, and 7 is 210
- LCM of 210 and 11 is 2310
Finding the smallest number:
To find the smallest number that satisfies the given conditions, we need to find a number that is 1 less than a multiple of 2310 and leaves remainders of 3, 4, and 5 when divided by 5, 6, and 7 respectively.
Let's check the options given:
- 208: Not divisible by 7
- 426: Not divisible by 7
- 600: Not divisible by 7
- 628: Divisible by 7 and leaves remainders of 3, 4, 5 when divided by 5, 6, 7 respectively. Also, it leaves a remainder of 1 when divided by 11.
Therefore, the smallest number that satisfies all the given conditions is 628, which is option 'D'.
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Find smallest number that leaves remainder 3, 4, 5 when divided by 5, ...
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Find smallest number that leaves remainder 3, 4, 5 when divided by 5, 6, 7 respectively and leaves remainder 1 when divided by 11.a)208b)426c)600d)628Correct answer is option 'D'. Can you explain this answer?
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Find smallest number that leaves remainder 3, 4, 5 when divided by 5, 6, 7 respectively and leaves remainder 1 when divided by 11.a)208b)426c)600d)628Correct answer is option 'D'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find smallest number that leaves remainder 3, 4, 5 when divided by 5, 6, 7 respectively and leaves remainder 1 when divided by 11.a)208b)426c)600d)628Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find smallest number that leaves remainder 3, 4, 5 when divided by 5, 6, 7 respectively and leaves remainder 1 when divided by 11.a)208b)426c)600d)628Correct answer is option 'D'. Can you explain this answer?.
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