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The number m yields a remainder p when divided by 14 and a r : Multiple-choice Questions — Select One Answer Choice

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Re: The number m yields a remainder p when divided by 14 and a r [#permalink]
1
I solved it this way. Since it says m=14x+p and p=q+7, so p must be greater than 7 and less than 14 (7<p<14)
Use the calculator to quickly list the multiples of 14 in the range of the options(45-100) which are: 42, 56, 70, 84, 98.
Now subtract the multiple of 14 inmediately lower than the options to see which fulfills the requisite 7<p<14:
45-42=3 no, 53-42=11 yes, 72-70=2 no, 85-84=1 no, 100-98=2 no. Here you can see that the correct answer is 53.
But we can check: 53/7=7+R4, and 4+7=11=p
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Re: The number m yields a remainder p when divided by 14 and a r [#permalink]
Given that The number m yields a remainder p when divided by 14 and a remainder q when divided by 7. And we need to find If \(p = q + 7\), what can be the value of m

Theory: Dividend = Divisor*Quotient + Remainder

Now, m when divided by 14 gives p remainder and p = q + 7

m -> Dividend
14 -> Divisor
a -> Quotient (Assume)
q + 7 -> Remainders
=> m = 14a + q + 7 = 7*2a + 7 + q = 7*(2a + 1) + q = odd multiple of 7 + q (where q is less than 7)

let's take each option choice and check which one satisfies this

(A) 45 = 42 + 3 = Even multiple of 7 + 3 => NOT POSSIBLE

(B) 53 = 49 + 4 = Odd multiple of 7 + 4 => POSSIBLE
In Test we don't need to check further but I am solving to complete the solution

(C) 72 = 70 + 2 = Even multiple of 7 + 2 => NOT POSSIBLE

(D) 85 = 84 + 1 = Even multiple of 7 + 1 => NOT POSSIBLE

(E) 100 = 98 + 2 = Even multiple of 7 + 2 => NOT POSSIBLE

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Remainders

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Re: The number m yields a remainder p when divided by 14 and a r [#permalink]
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Re: The number m yields a remainder p when divided by 14 and a r [#permalink]
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