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03 May 2023, 01:30
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D
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Difficulty:
35%
(medium)
Question Stats:
68% (01:31) correct
32%
(01:32)
wrong
based on 88
sessions
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If m is a two-digit number, what is the remainder when m is divided by 3?
(1) m+1 is divisible by 3.
(2) m is positive, and the sum of its two digits is 8.
(1) m+1 is divisible by 3.
(2) m is positive, and the sum of its two digits is 8.
03 May 2023, 07:31
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(1) m+1 is divisible by 3.
When m is positive, m = 3k+2 since m+1 = multiple of 3. Hence remainder will be 2 always.
When m is negative, we will get the same remainder. Example let m= -16, since -16+1= -15(multiple of 3). -16= -6x3+2. Therefore remainder is 2.
(2) m is positive, and the sum of its two digits is 8.
Possible values include 17,26,35,... All the values will have remainder = 2.
Hence answer is D.
When m is positive, m = 3k+2 since m+1 = multiple of 3. Hence remainder will be 2 always.
When m is negative, we will get the same remainder. Example let m= -16, since -16+1= -15(multiple of 3). -16= -6x3+2. Therefore remainder is 2.
(2) m is positive, and the sum of its two digits is 8.
Possible values include 17,26,35,... All the values will have remainder = 2.
Hence answer is D.
03 May 2023, 09:28
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Statement (1): m + 1 is divisible by 3.
If m + 1 is divisible by 3, it means that m is two less than a multiple of 3. In other words, m can be written as m = 3n - 1, where n is an integer.
To determine the remainder when m is divided by 3, we need to consider the possible values of n.
If n = 1, then m = 3(1) - 1 = 2, which gives a remainder of 2 when divided by 3.
If n = 2, then m = 3(2) - 1 = 5, which gives a remainder of 2 when divided by 3.
If n = 3, then m = 3(3) - 1 = 8, which gives a remainder of 2 when divided by 3.
From these calculations, we can see that regardless of the value of n, the remainder when m is divided by 3 is always 2. Therefore, statement (1) alone is sufficient to answer the question.
Statement (2): m is positive, and the sum of its two digits is 8.
Since m is a two-digit number, we can express it as m = 10a + b, where a and b are the digits of the number.
According to statement (2), a + b = 8.
To find the remainder when m is divided by 3, we need to consider the possible values of a and b.
If a = 1 and b = 7, then m = 10(1) + 7 = 17, which gives a remainder of 2 when divided by 3.
If a = 2 and b = 6, then m = 10(2) + 6 = 26, which gives a remainder of 2 when divided by 3.
If a = 3 and b = 5, then m = 10(3) + 5 = 35, which gives a remainder of 2 when divided by 3.
Again, regardless of the values of a and b, the remainder when m is divided by 3 is always 2. Therefore, statement (2) alone is sufficient to answer the question.
In conclusion, both statements (1) and (2) individually provide enough information to determine the remainder when m is divided by 3.
If m + 1 is divisible by 3, it means that m is two less than a multiple of 3. In other words, m can be written as m = 3n - 1, where n is an integer.
To determine the remainder when m is divided by 3, we need to consider the possible values of n.
If n = 1, then m = 3(1) - 1 = 2, which gives a remainder of 2 when divided by 3.
If n = 2, then m = 3(2) - 1 = 5, which gives a remainder of 2 when divided by 3.
If n = 3, then m = 3(3) - 1 = 8, which gives a remainder of 2 when divided by 3.
From these calculations, we can see that regardless of the value of n, the remainder when m is divided by 3 is always 2. Therefore, statement (1) alone is sufficient to answer the question.
Statement (2): m is positive, and the sum of its two digits is 8.
Since m is a two-digit number, we can express it as m = 10a + b, where a and b are the digits of the number.
According to statement (2), a + b = 8.
To find the remainder when m is divided by 3, we need to consider the possible values of a and b.
If a = 1 and b = 7, then m = 10(1) + 7 = 17, which gives a remainder of 2 when divided by 3.
If a = 2 and b = 6, then m = 10(2) + 6 = 26, which gives a remainder of 2 when divided by 3.
If a = 3 and b = 5, then m = 10(3) + 5 = 35, which gives a remainder of 2 when divided by 3.
Again, regardless of the values of a and b, the remainder when m is divided by 3 is always 2. Therefore, statement (2) alone is sufficient to answer the question.
In conclusion, both statements (1) and (2) individually provide enough information to determine the remainder when m is divided by 3.
