12. | If n is a positive integer, which one of the following numbers must have a remainder of 3 when divided by any of the numbers 4, 5, and 6?
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| A. | 12n + 3 |
| B. | 24n + 3 |
| C. | 90n + 2 |
| D. | 120n + 3
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Answer – (D)
Solution:
Let m be a number that has a remainder of 3 when divided by any of the numbers 4, 5, and 6.
Then m–3 must be exactly divisible by all three numbers.
Hence,m–3 must be a multiple of the Least Common Multiple of the numbers 4, 5, and 6.
The LCM is 3*4*5=60.
Hence, we can suppose m–3=60p, where p is a positive integer. Replacing p with n, we get m–3=60n.
So, m=60n+3.
Choice (D) is in the same format 120n + 3 =60(2n)+3
Title : Numbers Q12
Description : 12. If n is a positive integer, which one of the following numbers must have a remainder of 3 when divided by any of the numbers 4, 5, and...
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