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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Momsspaghetti · Answer

(1) m+1 is divisible by 3.
M can be infinite numbers.  Not Sufficient

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

1+7 = 8 
7+1 = 8
3+5 = 8
5+3 = 8 
.......  Not Sufficient

Together :

From 1) m is not divisible by 3
From 2) Sum is 8

1+7 = 8 
7+1 = 8
.....

Not Sufficient

Option E.

Sushil117 · Answer

m is two digit number. so can be between 10 to 99

(1) m+1 is divisible by 3.
first can be 11 as 11+1=12 and last can be 98 in same way..
11/3 remainder 2...14/3 remainder ...17/3...same all the way up to 98...
suff
always 2

(2) m is positive, and the sum of its two digits is 8
8,0
1,7
2,6
3,5
4,4
80/3 remainder 2..can't reverse the digit as it'll be 08
17/3....remainder 2...71/3..remainder 2
26/3 & 62/3 same remainder
35/3 ,53/3 & 44/3 all have same remainder 2
suff

IMO D

gmatophobia · Answer

Statement 1

(1) m+1 is divisible by 3.

If m + 1 is divisible by 3, then the remainder when m is divided by 3 will be 2.

This statement is sufficient, hence we can eliminate B, C and E.

Statement 2

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

We can use the properties / concept of divisibility.

The remainder of a number when divided by 3 is same as the remainder obtained by dividing sum of digits by 3.

Hence remainder when m is divided by 3 = Remainder when 8 is divided by 3

= 2

Hence, this statement is also sufficient.

Option D

Maria240895chile · Answer

in (I) just try some numbers and you'll see that there is pattern
m+1 must be a multiple of 3
m+1=3 -> m=2
m+1=6 -> m=5
m+1=9 -> m=8
m+1=12 -> m=11
.
.
m+1=30 m=29

and each of those values gives a reminder of 2 SUFFICIENT

(II)
1+7= 8 17/3=3(5)+ 2
6+2=8 62/3= 3(20) + 2
5+3 =8 53/3= 3(17)+ 2
4+4= 8 44/3= 3(14)+2

SUFFICIENT

Correct answer D

ileoboi · Answer

What if m is a negative number in statement (1)?

e.g. if m=11, (11+1)/3 OK, and remainder is 2/3, while if m=-10, (-10+1)/3 OK, and remainder is 1/3

Bunuel · Answer

Yes, it would be better if the question mentioned that m is a positive integer because all GMAT divisibility/remainder questions are limited to positive integers only. Having said that, the answer would still remain D. The point is -10 divided by 3 gives the remainder of 2, not 1 (-10 is 2 greater than -12, which is the closest multiple of 3 to -10).

Hope it's clear.

bumpbot · Answer

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

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GMAT Data Sufficiency (DS) Questions

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

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