What is the least number which when divided b...
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

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 MULLA WASIMAHAMAD SALIM 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?
Approach 1 - Direct Observation
The number must be divisible by 13.
Option a, b. d are divisible. C is not.
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

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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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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