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Statement 1 gives possible values of x as -3, 0 3, 6, 9 .. out of which ... -6, 0, 6, 12 ... are the ones divisible by 6, others are not. Statement 2 gives possible values of x as ...-4 , -2, 0, 2, 4, 6 out of which 0, 6, 12 .. are divisible by 6, others are not.

Taken together, the values 0, 6, 12 satisfy both statements and are all divisible by 6, so the answer is "Yes" and i would choose option C.

Ans is C. Here is another way of solving the problem.

Question asked is IS x divisible by 6 means we need to prove that x is divisible by 2 and also x is divisible by 6. (Divisibility rule for 6)

Clue 1 - X + 3 is divisible by 3 ==> One rule is If two numbers are multiple of a number, then the sum of the two numbers is also multiple of that number. Here it is said that x + 3 is divisible by 3 in other words, x + 3 is a multiple of 3. Of the two numbers, 3 is multiple of 3 and also x should be multiple of 3 to satisfy the condition that x + 3 is a multiple of 3. This concludes that x is divisible by 3. One part of the divisibility rule is satisfied. But we don't know anything whether x is divisible by 2 or not.

Clue 2 - x + 3 is Odd. The sum of two numbers is odd only when both the numbers one is odd and the other is even. Here 3 is already odd, so x should be even in other words, x is divisible by 2. But we don't know if still x is divisible by 3.

Now combining Clue 1 and 2, x is even and is divisible by 3. Hence both clues are needed to solve the problem.

Is the integer x divisible by 6? (1) x + 3 is divisible by 3 (2) x + 3 is an odd number.

Answer choices: (a) Statement 1 alone is sufficient, but Statement 2 alone is not sufficient. (b) Statement 2 alone is sufficient, but Statement 1 alone is not sufficient. (c) Either statements are NOT sufficient, but BOTH together are sufficient. (d) Each statement ALONE is sufficient. (e) Neither statement Alone is sufficient.

(1) x+3/ 3 = k (integer) x/3+1=k --> x is multiple of 3 not sufficient (2)x + 3 is an odd number -->.. x must be even integer. not sufficient combine ( x=6k..

C
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to be x divisible by 6, it should be divisible by 2 and 3

Statement 1 says that X+3 is divisible by 3, it means both x and 3 are divisible by 3 , but we dont know if x is divisible by 2. so this statement is not sufficient.

Statement 2 says that x+3 is odd. It means x is an even number which is divisible by 2(because even+odd can only give odd value). but here we dont know if x is divisible by 3. So this statement is not sufficient.

now consider both the statements together we can say that x is divisible by 6,Statement 1 says that x is divisible by 3 and statement 2 says that x is divisible by 2. Thats what we wanted to know.

(1) x + 3 is divisible by 3. This basically means that x is divisible by 3 (x = {a multiple of 3} - 3 = {a multiple of 3}), which is not sufficient to say whether it's divisible by 6.

(2) x + 3 is an odd number. This means that x is even (\(x=odd-3=odd-odd=even\)). Not sufficient.

(1)+(2) x is an even multiple of 3, hence it's a multiple of 6. Sufficient.

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