is a + b a multiple of 3?

[gmatnmein2010]

If a and b are both single-digit positive integers, is a + b a multiple of 3?

(1) The two-digit number "ab" (where a is in the tens place and b is in the ones place) is a multiple of 3.

(2) a - 2b is a multiple of 3.

[ajith]

If a and b are both single-digit positive integers, is a + b a multiple of 3?

(1) The two-digit number "ab" (where a is in the tens place and b is in the ones place) is a multiple of 3.

(2) a - 2b is a multiple of 3.

1) if two-digit number "ab" is a multiple of 3; a+b is a multiple of 3, sufficient
2) a-2b is a multiple of 3; 3b is a multiple of 3 ; a-2b+3b is a multiple of 3 ; a+b is a multiple of 3; sufficient

[harsh.champ]

If a and b are both single-digit positive integers, is a + b a multiple of 3?

(1) The two-digit number "ab" (where a is in the tens place and b is in the ones place) is a multiple of 3.

(2) a - 2b is a multiple of 3.

Important Note:-This question tests our knowledge of divisibility test of 3.
Divisibility Test of 3 is that "sum of the digits should be a multiple of 3"

Statement 1:- ab is a multiple of 3 only when a+b is a multiple of 3.
Hence,it is alone sufficient.

For statement 2,I got very confused.
But I saw ajith's solution and liked it very much.

a-2b is a multiple of 3;
3b is a multiple of 3 ;
a-2b+3b is a multiple of 3(We have to remember the addition rule of divisibility in this case-If x is divisible by a and y is divisible by a ,then x+y is also divisible by 3 .Similarly it applies for subtraction and multiplication but don't use it in division(Always to be remembered) );
a+b is a multiple of 3

Hence the answer would be C.

[thephoenix]

If a and b are both single-digit positive integers, is a + b a multiple of 3?

(1) The two-digit number "ab" (where a is in the tens place and b is in the ones place) is a multiple of 3.

(2) a - 2b is a multiple of 3.

(1) SUFFICIENT: The two-digit number "ab" can be represented by the expression 10a + b. Since 10a + b is a multiple of 3, 10a + b = 3k, where k is some integer.
This can be rewritten as 9a + (a + b) = 3k
a + b = 3k - 9a.

3k - 9a can be factored to 3(k - 3a).
Since both k and a are integers, 3(k - 3a) must be a multiple of 3.
Therefore a + b is also a multiple of 3.

(2) SUFFICIENT: Since a - 2b is a multiple of 3, a - 2b = 3k, where k is some integer.
This can be rewritten as a + b - 3b = 3k
a + b = 3k + 3b .

3k + 3b can be factored to 3(k + b).
Since both k and b are integers, 3(k + b) must be a multiple of 3.
Therefore a + b is also a multiple of 3.

The correct answer is D.

[shashank.ism]

If a and b are both single-digit positive integers, is a + b a multiple of 3?

(1) The two-digit number "ab" (where a is in the tens place and b is in the ones place) is a multiple of 3.

(2) a - 2b is a multiple of 3.

St.1 : As per the divisiblity rule of 3 , ab will be divisible by 3 only if A+b is a multiple of 3 .... so sufficient...
St.2: a-2b is multiple of 3
an assumption {{also taking a+b a multiple of 3 ...hence 2a+2b is multiple of 3}}
we add both
a-2b + 2a +2b should also be multiple of 3
--> 3a should be multiple of 3 which is true for all a and b
hence our assumption is correct and a+b is multiple of 3 ...sufficient ....

Ans D