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The remainder when the positive integer m is divided by 7 is
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Updated on: 30 May 2018, 16:07
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The remainder when the positive integer m is divided by 7 is x. The remainder when m is divided by 14 is x + 7. Which one of the following could m equal?
Re: The remainder when the positive integer m is divided by 7 is
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05 Jun 2018, 13:22
Expert Reply
Lets re-write \(m= 7k+x\). In this way when you divide \(m\) by 7 you get a remainder of \(x\).
Also given that \(\frac{m}{14}= \frac{7k+x}{14}\) has a remainder \(x+7\).
So rearranging \(7k+x\) as \(7(k-1)+ x+7\). Since \(\frac{7k+x}{14}=\frac{7(k-1)+ x+7}{14}\) has a remainder \(x+7\). \(7(k-1)\) must be divisible by 14 or \(k-1\) must be divisible by 2.
k can be any odd number 3,5,... and x has to be less than 7.
So looking at the options one by one...
(A) 45 = 7*6 + 3 No
(B) 53 = 7*7+ 4 yes
(C) 72 = 7*8 No
(D) 85 = 7*12 +1 No
(E) 100= 7*14 +2 No
Hence B. _________________
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Re: The remainder when the positive integer m is divided by 7 is
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22 Feb 2021, 02:31
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shahul wrote:
The remainder when the positive integer m is divided by 7 is x. The remainder when m is divided by 14 is x + 7. Which one of the following could m equal?
(A) 45
(B) 53
(C) 72
(D) 85
(E) 100
We can note here that when \(m\) is divided by 7 and 14, it gives us different values of remainder! This means that the remainder cannot be same.
A. 45 when divided by 7 and 14 gives us remainder 3 B. 53 when divided by 7 and 14 gives us remainder 4 and 11 C. 72 when divided by 7 and 14 gives us remainder 2 D. 85 when divided by 7 and 14 gives us remainder 1 E. 100 when divided by 7 and 14 gives us remainder 2
Re: The remainder when the positive integer m is divided by 7 is
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31 Aug 2022, 07:59
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Theory: Dividend = Divisor*Quotient + Remainder
Given that the remainder when the positive integer m is divided by 7 is x and the remainder when m is divided by 14 is x + 7. And we need to find which of the following could be the value of m
Let's solve the problem using Substitution
We will take each option choice and find out the remainder with 7 and 14 and see which one has remainder by 14, 7 greater than the remainder by 7.
(A) 45 45 when divided by 7 gives 3 remainder 45 when divided by 14 gives 3 remainder Clearly, Remainder by 14 is NOT 7 greater than Remainder by 7 => NOT POSSIBLE
(B) 53 53 when divided by 7 gives 4 remainder 53 when divided by 14 gives 11 remainder Clearly, Remainder by 14 IS 7 greater than Remainder by 7 => POSSIBLE In Test, we don't need to solve further, but I am solving to complete the solution.
(C) 72 72 when divided by 7 gives 2 remainder 72 when divided by 14 gives 2 remainder Clearly, Remainder by 14 is NOT 7 greater than Remainder by 7 => NOT POSSIBLE
(D) 85 85 when divided by 7 gives 1 remainder 85 when divided by 14 gives 1 remainder Clearly, Remainder by 14 is NOT 7 greater than Remainder by 7 => NOT POSSIBLE
(E) 100 100 when divided by 7 gives 2 remainder 45 when divided by 14 gives 2 remainder Clearly, Remainder by 14 is NOT 7 greater than Remainder by 7 => NOT POSSIBLE
So, Answer will be B Hope it helps!
Watch the following video to learn the Basics of Remainders