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

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If m is a two-digit number, what is the remainder when m is divided  [#permalink]

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30 Sep 2015, 11:32
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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.

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If m is a two-digit number, what is the remainder when m is divided  [#permalink]

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18 Mar 2016, 22:19
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Can someone please address why we must ASSUME that m is positive here? If m can be negative, A is not sufficient and the answer is B!

Hi,

But even if I take it as a negative number, it will give the same remainder as a positive number..
---a) say m<0.. so m+1 is div by 3.. say m+1=-12 or m=-13
=> Remainder : m=3x+R
..... -13= 3*(-5) +2= -15+2, so R=2
REMEMBER R can never be -ive

---b) say m>0.. m+1 is div by 3.. say m+1=12 or m=11
=> 11= 3*3+2, here too R is 2

so R will be 2 in each case
Suff

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Re: If m is a two-digit number, what is the remainder when m is divided  [#permalink]

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02 Oct 2015, 21:06
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s1: If m+1 is divisible by 3, then m will give (3-1 =2) remainder when divided by 3. So, sufficient.

s2: m>0, The sum of the digits of the number is 8. So, the remainder that we get by dividing 8 by 2 will be the same for m. So sufficient.

Therefore, D
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Re: If m is a two-digit number, what is the remainder when m is divided  [#permalink]

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04 Oct 2015, 04:19
s1: If m+1 is divisible by 3, then m will give (3-1 =2) remainder when divided by 3. So, sufficient.

s2: m>0, The sum of the digits of the number is 8. So, the remainder that we get by dividing 8 by 2 will be the same for m. So sufficient.

Therefore, D

S1: If m < 0, e.g. m=-13 (remainder is 1 when divided by 3) and m+1=-12 (which is divisible by 3)
If m > 0, remainder is 2
Hence, not sufficient. Ans=B
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Re: If m is a two-digit number, what is the remainder when m is divided  [#permalink]

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04 Oct 2015, 21:14
m is a two digit number. We cannot take integers (as in m<0)

Hope it helps!
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Re: If m is a two-digit number, what is the remainder when m is divided  [#permalink]

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10 Oct 2015, 23:20
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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.

There is one variable (m) in the original condition, and 2 equations are provided by the conditions; the answer is likely to be (D).
The remainder from a number divided by 3 or 9 is equal to the remainder of the sum of the digits in the number divided by 3 or 9. It is also fastest to directly substitute in values when solving remainder problems.
For condition 1, m+1=3p, m+1=3,6,9,.... m=2,5,8,... If we divide these values of m by 3, the remainder is always 2, so this is a sufficient condition
For condition 2, as the sum of the two digits is 8, 8=3*2+2. The remainder is 2, so m divided by 3 also leaves a remainder of 2. This is also a sufficient condition, so the answer becomes (D).

Normally for cases where we need 1 more equation, such as original conditions with 1 variable, or 2 variables and 1 equation, or 3 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore D has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) separately. Here, there is 59 % chance that D is the answer, while A or B has 38% chance. There is 3% chance that C or E is the answer for the case. Since D is most likely to be the answer according to DS definition, we solve the question assuming D would be our answer hence using 1) and 2) separately. Obviously there may be cases where the answer is A, B, C or E.
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Re: If m is a two-digit number, what is the remainder when m is divided  [#permalink]

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18 Mar 2016, 09:19
Can someone please address why we must ASSUME that m is positive here? If m can be negative, A is not sufficient and the answer is B!
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Re: If m is a two-digit number, what is the remainder when m is divided  [#permalink]

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23 Mar 2017, 08:45
s1: If m+1 is divisible by 3, then m will give (3-1 =2) remainder when divided by 3. So, sufficient.

s2: m>0, The sum of the digits of the number is 8. So, the remainder that we get by dividing 8 by 2 will be the same for m. So sufficient.

Therefore, D

Thanks for the explanation. Though for s1, I'm not sure I follow. Are you basically saying that (m+1)/3 = integer (let's assume it equals 1 for simplicity). Therefore,

m+1=3
m=3-1
m=2, where 2 is a remainder for all values of m? Cheers
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Re: If m is a two-digit number, what is the remainder when m is divided  [#permalink]

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24 Mar 2017, 09:07
s1: If m+1 is divisible by 3, then m will give (3-1 =2) remainder when divided by 3. So, sufficient.

s2: m>0, The sum of the digits of the number is 8. So, the remainder that we get by dividing 8 by 2 will be the same for m. So sufficient.

Therefore, D

I don't understand how statement 2 is sufficient. Could you please elaborate some more and explain the rule used?
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Re: If m is a two-digit number, what is the remainder when m is divided  [#permalink]

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26 May 2017, 09:38

I did the following way to prove if Statement 2 was sufficient -

Since, the sum of the digits is 8, possible solutions are 17, 26, 35 , 44 or the reverse of these nos. And each of them when divided by 3 will give a remainder of 2, a unique value. Hence, sufficient.
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Re: If m is a two-digit number, what is the remainder when m is divided  [#permalink]

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09 Jul 2017, 05:48
s1: If m+1 is divisible by 3, then m will give (3-1 =2) remainder when divided by 3. So, sufficient.

s2: m>0, The sum of the digits of the number is 8. So, the remainder that we get by dividing 8 by 2 will be the same for m. So sufficient.

Therefore, D

"So, the remainder that we get by dividing 8 by 2 will be the same for m" ...means what ...?
division of 8 by 2 produces no remainder...? please make it clear to me ....

thanks in advance ...
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Re: If m is a two-digit number, what is the remainder when m is divided  [#permalink]

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31 Jul 2018, 06:28
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Re: If m is a two-digit number, what is the remainder when m is divided &nbs [#permalink] 31 Jul 2018, 06:28
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# If m is a two-digit number, what is the remainder when m is divided

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