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12 Mar 2024, 09:57
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
82% (01:47) correct
18%
(02:07)
wrong
based on 97
sessions
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Not Attempted Yet
When m+n is divided by 9, the remainder is 1. If m is divisible by 9, which of the following could equal the sum of the digits of n?
A. 34
B. 35
C. 36
D. 37
E. 38
A. 34
B. 35
C. 36
D. 37
E. 38
12 Mar 2024, 12:15
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The first bit of info we are given is that \(\frac{m+n}{9} = y \frac{1}{9}\) where y is an integer value.
The second bit of information we are given is that \(\frac{m}{9} = x\) where x is an integer value
Now as we know that that when \(m\) and \(n\) are added we get a value that is 1 greater than a multiple of 9, and that \(m\) is a multiple of 9 then \(n\) has to be the value that is creating the remainder and thus must be a value which is 1 greater than a multiple of 9.
The divisibility rule of 9 is that if the sum of the digits of a number is divisible by 9 then the number is divisible by 9. This means that the sum of \(n\) also has to be 1 greater than a multiple of 9. Looking at the answer choices:
A) 7 above a multiple of 9
B) 8 above a multiple of 9
C) Is a multiple of 9
D) 1 above a multiple of 9
ANSWER D
The second bit of information we are given is that \(\frac{m}{9} = x\) where x is an integer value
Now as we know that that when \(m\) and \(n\) are added we get a value that is 1 greater than a multiple of 9, and that \(m\) is a multiple of 9 then \(n\) has to be the value that is creating the remainder and thus must be a value which is 1 greater than a multiple of 9.
The divisibility rule of 9 is that if the sum of the digits of a number is divisible by 9 then the number is divisible by 9. This means that the sum of \(n\) also has to be 1 greater than a multiple of 9. Looking at the answer choices:
A) 7 above a multiple of 9
B) 8 above a multiple of 9
C) Is a multiple of 9
D) 1 above a multiple of 9
ANSWER D
12 Jan 2025, 04:46
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↧↧↧ Detailed Video Solution to the Problem ↧↧↧
m+n is divided by 9, the remainder is 1
=> Remainder of m + n by 9 = 1
=> Remainder of m by 9 + Remainder of n by 9 = 1
If m is divisible by 9
=> Remainder of m by 9 = 0
=> 0 + Remainder of n by 9 = 1
=> Remainder of n by 9 = 1
=> Remainder of sum of digits of n by 9 = 1
Which of the following could equal the sum of the digits of n?
A. 34
Remainder of 34 by 9 = Remainder of 3+4 by 9 = 7
But we are looking for 1 as the remainder
=> FALSE
B. 35
Remainder of 35 by 9 = Remainder of 3+5 by 9 = 8
But we are looking for 1 as the remainder
=> FALSE
C. 36
Remainder of 36 by 9 = Remainder of 3+6 by 9 = 0
But we are looking for 1 as the remainder
=> FALSE
D. 37
Remainder of 37 by 9 = Remainder of 3+7 by 9 = 1
=> TRUE
E. 38 (we don't need to check further but solving to complete the solution)
Remainder of 38 by 9 = Remainder of 3+8 by 9 = 2
But we are looking for 1 as the remainder
=> FALSE
So, Answer will be D
Hope it helps!
Watch the following video to MASTER Remainders
m+n is divided by 9, the remainder is 1
=> Remainder of m + n by 9 = 1
=> Remainder of m by 9 + Remainder of n by 9 = 1
If m is divisible by 9
=> Remainder of m by 9 = 0
=> 0 + Remainder of n by 9 = 1
=> Remainder of n by 9 = 1
=> Remainder of sum of digits of n by 9 = 1
Which of the following could equal the sum of the digits of n?
A. 34
Remainder of 34 by 9 = Remainder of 3+4 by 9 = 7
But we are looking for 1 as the remainder
=> FALSE
B. 35
Remainder of 35 by 9 = Remainder of 3+5 by 9 = 8
But we are looking for 1 as the remainder
=> FALSE
C. 36
Remainder of 36 by 9 = Remainder of 3+6 by 9 = 0
But we are looking for 1 as the remainder
=> FALSE
D. 37
Remainder of 37 by 9 = Remainder of 3+7 by 9 = 1
=> TRUE
E. 38 (we don't need to check further but solving to complete the solution)
Remainder of 38 by 9 = Remainder of 3+8 by 9 = 2
But we are looking for 1 as the remainder
=> FALSE
So, Answer will be D
Hope it helps!
Watch the following video to MASTER Remainders
