If m is a two-digit number, what is the remainder when m is divided by

Question

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.

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szcz · Answer

(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.

imtiaz91 · Answer

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.

udaypratapsingh99 · Answer

Given: m is a two-digit number.

To find out: The remainder when m is divided by 3.

Let's take each statement one by one.

(1) m+1 is divisible by 3.

Since m+1 is divisible by 3, m is not divisible by 3, leaving a remainder of 3 - 1 = 2. Sufficient.

You may take a few examples. Say the set of (m + 1) is: {12, 15, 18, 21, ... 96, 99}; thus, the set of m is: {11, 14, 17, 20, ..., 95, 98}. I each case, m divided by 3 leaves a remainder of 2.

Another way: Say m + 1 = 3x; where x is any integer

Thus, m = 3x - 1

=> m/3 = (3x - 1)/3 = x - 1/3

=> Remainder = -1; since remainder cannot be negative, the remainder = 3 - 1 = 2.

(2) m is positive, and the sum of its two digits is 8.

We know that if a number is divisible by 3, the sum of its two digits is divisible by 3; thus, the remainder when m is divided by 3 is given by when the sum is divided by 3. Thus, the remainder = remainder when 8 is divided by 3 = 2. Sufficient.

On the same line, we can conclude that since the sum of the two digits of m is 8, the sum of the two digits of (m+1) is 9, which is divisible by 3. Thus, the situation is the same as that in Statement 1. Sufficient.

The correct answer: D

SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  m is a two-digit number   We are asked the remainder when m is divided by 3

Statement 1:   m+1 is divisible by 3.
  According to this statement,  m+1=3k 
 ⇒m=3k-1 
 ⇒m=3k-3+2 
 ⇒m=3(k-1)+2  
 So, when m is divided by 3, the remainder is 2 
 Thus,  statement 1 alone is sufficient and we can eliminate options B, C and E

Statement 2:   m is positive, and the sum of its two digits is 8
  This statement is essentially the same as statement 1 
 Sum of digit of m is 8. So,  m+1 will be divisible by 3  
 Thus,  statement 2 alone is also sufficient

Hence the right answer is    Option D

If m is a two-digit number, what is the remainder when m is divided by

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