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What is the least number which when divided by the numbers 3, 5, 6, 8, 10 and 12 leaves in each case a remainder 2 but which when divided by 13 leaves no remainder?
  • a)
    312
  • b)
    962
  • c)
    1586
  • d)
    1562
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?

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Related What is the least number which when divided by the numbers 3, 5, 6, 8, 10 and 12 leaves in each case a remainder 2 but which when divided by 13 leaves no remainder?a)312b)962c)1586d)1562e)None of theseCorrect answer is option 'C'. Can you explain this answer?
Approach 1 - Direct Observation
The number must be divisible by 13.
Option a, b. d are divisible. C is not.
So Cis not the answer
Now the number leaves remainder 2 when divided by 3, 5, 6, 8, 10, and 12.
So 'Number -r should be divisible by 3, 5, 4 8, 10, and 12
Take Option A i.e. 312-2 = 310.
But 310 is not divisible by 3
Take Option D i.e. 1586-2 = 1584
We see that 1584 is not divisibleby 10
So mark C as answer 

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Saurab Rauniyar
Nov 18, 2019
C, simply because if you try to subtract 2 from all the options available then we will observe that only option C is not divisible by all of the number mentioned above. So, the answer has to be divisible by 7.

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Ilyaskhan Sokari
Aug 11, 2019
Related What is the least number which when divided by the numbers 3, 5, 6, 8, 10 and 12 leaves in each case a remainder 2 but which when divided by 13 leaves no remainder?a)312b)962c)1586d)1562e)None of theseCorrect answer is option 'C'. Can you explain this answer?
C

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What is the least number which when divided by the numbers 3, 5, 6, 8, 10 and 12 leaves in each case a remainder 2 but which when divided by 13 leaves no remainder?a)312b)962c)1586d)1562e)None of theseCorrect answer is option 'C'. Can you explain this answer? for GMAT 2022 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the least number which when divided by the numbers 3, 5, 6, 8, 10 and 12 leaves in each case a remainder 2 but which when divided by 13 leaves no remainder?a)312b)962c)1586d)1562e)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2022 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the least number which when divided by the numbers 3, 5, 6, 8, 10 and 12 leaves in each case a remainder 2 but which when divided by 13 leaves no remainder?a)312b)962c)1586d)1562e)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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Approach 1 - Direct ObservationThe number must be divisible by 13.Option a, b. d are divisible. C is not.So Cis not the answerNow the number leaves remainder 2 when divided by 3, 5, 6, 8, 10, and 12.So Number -r should be divisible by 3, 5, 4 8, 10, and 12Take Option A i.e. 312-2 = 310.But 310 is not divisible by 3Take Option D i.e. 1586-2 = 1584We see that 1584 is not divisibleby 10So mark C as answer