Is x divisible by 3?

could you please explain?
my answer is C.

Statement 1: Not Sufficient
x+y can be (1) 7+8, (2) 1+2 or (3) 6+3. It is yes or no. Hence N.S.

Statement 2: Not Sufficient
x-y can be (1) 5-2 or (2) 6-3. It is yes or no. Hence, N.S.

Putting Statement 1 and Statement 2 together.

Case 1: 4-1=3 | 4+1 not equal to multiple of 3.
Case 2: 5-2=3 | 5+2 not equal to multiple of 3.

Case 3: 6-3=3 | 6+3=multiple of 3.

Case 4: 7-1=6 | 7+1 not equal to multiple of 3.
Case 5: 8-2=6 | 8+2 not equal to multiple of 3.

Case 6: 9-3=6 | 9+3=12 both have multiples of 3.

Cases 1,2,4 and 5 cannot be possible as they all do not fulfil conditions of both Statement 1 and Statement 2.
Hence, only Cases 3 and 6 can be possible as they both fulfil conditions of Statement 1 and statement 2.
Therefore, citing cases 3 and 6, X is multiple of 3. X may be 1st or 2nd digit.

So, I marked answer C.

Thank you so much. Your posts are very helpful. I thought about integers and non-integers but somehow skipped it. Thanks again

This below mentioned question is modification of above question.

If x, y and d are integers and d is odd, are both x and y divisible by d?

(1) x+y is divisible by d.

(2) x-y is divisible by d.

(1) x + y is divisible by 3.
Written as an equation, this is
\(x + y = 3m\)
\(x = 3m - y\)
From this you can see that x is divisible by 3 only if y is a multiple of 3. E.g. if y = 3, then x is divisible by 3. If y = 2, then x is not divisible by 3.
Not sufficient.

(2) x - y is divisible by 3.
Written as an equation, this is
\(x - y = 3n\)
\(x = 3n + y\)
From this you can see that x is divisible by 3 only if y is a multiple of 3. E.g. if y = 3, then x is divisible by 3. If y = 2, then x is not divisible by 3.
Not sufficient.

Putting (1) and (2) together, we have
\(x = 3m - y\)
\(x = 3n + y\)

Adding the 2 equations gives

\(2x = 3(m + n)\)
\(x = \frac{3}{2}(m+n)\)
From this you can see that x is divisible by 3 only if (m + n) is a multiple of 2. E.g. if m = 1 and n = 1, then x is a multiple of 3. If m = 2 and n = 1, then x is not a multiple of 3.
Not sufficient.

Is x divisible by 3?
stmt 1: x+y = 3k not sufficient (as x and y can take any values eg. 1,2; 3,6 - > hence cannot comment on whether x is divisible by 3)
stmt 2: x-y = 3m not suffiecent (as x and y can take any values eg. 5,2; 6,3 > hence cannot comment on whether x is divisible by 3)

Combining both stmts: we have 2 equations, hence we can solve for x and check
x= (3/2)*(k+m)
This whether x is divisible by 3 depends on the values of k & m, which are quotients on dividing x+y & x-y by 3

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables (x and y) and 0 equations,C is most likely to be the answer. So, we should consider 1) & 2) first.

Conditions 1) & 2):
Since there is no condition that x and y are integers, x and y might be decimals.

x = 4.5, y = 1.5 : x is not divisible.
x = 6, y = 3: x is divisible.

Both conditions together are not sufficient.
Therefore, the answer is E.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

Hi chetan.

Any post that tells about the fractions you should choose for hit n trial. Most of the time I realize I need to check fractions but I am not able to choose the correct once.

Posted from my mobile device

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Went for C . But I'm still not clear on this with E. Any explanations on this ? Looks like trial n error

Hi

You should look at this solution by Chetan already posted in this thread:

https://gmatclub.com/forum/is-x-divisib ... l#p1779748

Chetan,
I understand the kind of question you are trying to frame here. But 4.5 not divisible by 3? I think it is. Divisible means something that can be divided without leaving any remainder and here there is no remainder. So answer should be C IMO

Is x divisible by 3?

(1) x + y is divisible by 3.

Let x=3 & y =0......... x + y is divisible by 3..........Answer is Yes

Let x=1/3 & y =2/3......... x + y is divisible by 3..........Answer is NO

Insufficient

(2) x - y is divisible by 3.

Let x=3 & y =0......... x - y is divisible by 3..........Answer is Yes

Let x=4 & y =1......... x - y is divisible by 3..........Answer is NO

Insufficient

Combine 1 & 2:

Sum 2 equations:

\(\frac{(x+y)}{3}\)= Integer.............1

\(\frac{(x-y)}{3}\)= Integer.............2

---------------------------------------------------------------
\(\frac{2}{3}\) x = Integer

To make our conclusion valid let's check some numbers

Let x = 3..... \(\frac{2}{3}\)* (3)= Integer .............Answer is Yes

Let x =\(\frac{3}{2}\)..... \(\frac{2}{3}\) * \(\frac{3}{2}\)= Integer .............Answer is NO

Insufficient

Answer: E

Just try to prove the statement wrong:

(1) x + y is divisible by 3.

4+2 is divisible by 3 but 4 is not. Gone.

(2) x - y is divisible by 3.

4-1 is divisible by 3 but 4 is not. Gone

Combined:
4.5 +or- 1.5 is divisible by 3 but 4.5 is not.

Answer E

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