Tough and Tricky questions: Remainders.

If x and y are integers, is xy + 1 divisible by 3?

(1) When x is divided by 3, the remainder is 1.
(2) When y is divided by 9, the remainder is 8.

Kudos for a correct solution.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Given x and y are integers. We have to find out whether xy+1 is divisible by 3 ?

Statement 1: When x is divided by 3, the remainder is 1

Therefore, x can be represented as 3*a+1 ( where a is an integer)
therefore, xy+1 => (3*a+1)*y+1

Since 3*a*y is divisible by 3, we have to find out whether (y+1) is divisible by 3.


Statement 2:
When y is divided by 9, the remainder is 8. Clearly insufficient, since we don't know the value of x.
But, we can say that y => 9*b+8 ( where b is an integer)

Combining 1) and 2), we can say y+1 = 9*b + 9 is divisible by 3. Hence the answer should be C

If x and y are integers, is xy + 1 divisible by 3?

(1) When x is divided by 3, the remainder is 1.
(2) When y is divided by 9, the remainder is 8.

Statement 1
x = 3m+1; m is an integer
no information on y, hence insufficient.

Statement 2
y= 9n +8; n is an integer
no information on x, hence insufficient.

Combining statements (1) and (2) and substituting x and y as (3m+1) and (9n+8)
xy +1 = (3m+1)(9n+8)+1 = 27mn+24m+9n+9 = 3*(9mn+8m+3n+3) --> xy+1 is divisible by 3
Hence, both statements together are sufficient

Answer: C