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# Is x divisible by 3?

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Math Expert
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Is x divisible by 3? [#permalink]

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10 Dec 2016, 04:18
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Is x divisible by 3?

(1) x + y is divisible by 3.
(2) x - y is divisible by 3.
[Reveal] Spoiler: OA

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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Last edited by Bunuel on 10 Dec 2016, 05:03, edited 1 time in total.
RENAMED THE TOPIC AND EDITED THE QUESTION!

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Is x divisible by 3? [#permalink]

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10 Dec 2016, 04:51
From 1

X could = y= 1.5 no
X=3,y=6 yes

Insuff

From 2

7-4 s divisible by 3 but x=7 not

9-3 is divisible by 3 and x= 9 is too insuff

2x=3 k , still x could be a fraction of integer

E

Edited answer from C to E to avoid confusion of future readers

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Re: Is x divisible by 3? [#permalink]

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21 Dec 2016, 05:28

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.

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Re: Is x divisible by 3? [#permalink]

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21 Dec 2016, 08:52
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Hi

For the members who have posted above and all others..
x and y are not given as integers

Say x is 6 and y is 3..
6-3 is div by 3 and 6+3 is div by 3 and ans is YES for "is x div by 3?"

But if x is 9/2 and y is 3/2
9/2 + 3/2 is div by 3 and 9/2 - 3/2 is also div by 3..
But x is not div by 3.. so ans is NO..

Therefore insufficient..
E

NOTE - always remember that x and y can be any value unless it is specified that they are integers..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Is x divisible by 3? [#permalink]

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21 Dec 2016, 08:59
chetan2u wrote:
Hi

For the members who have posted above and all others..
x and y are not given as integers

Say x is 6 and y is 3..
6-3 is div by 3 and 6+3 is div by 3 and ans is YES for "is x div by 3?"

But if x is 9/2 and y is 3/2
9/2 + 3/2 is div by 3 and 9/2 - 3/2 is also div by 3..
But x is not div by 3.. so ans is NO..

Therefore insufficient..
E

NOTE - always remember that x and y can be any value unless it is specified that they are integers..

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

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Re: Is x divisible by 3? [#permalink]

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21 Dec 2016, 09:25
chetan2u wrote:
Is x divisible by 3?

(1) x + y is divisible by 3.
(2) x - y is divisible by 3.

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.

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Re: Is x divisible by 3? [#permalink]

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02 Jan 2018, 16:15
(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
$$x = 3m - y$$
$$x = 3n + y$$

$$2x = 3(m + n)$$
$$x = \frac{3}{2}(m+n)$$
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.

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Re: Is x divisible by 3? [#permalink]

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02 Jan 2018, 21:22
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

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Re: Is x divisible by 3? [#permalink]

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04 Jan 2018, 22:38
chetan2u wrote:
Is x divisible by 3?

(1) x + y is divisible by 3.
(2) x - y is divisible 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.

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.
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Re: Is x divisible by 3?   [#permalink] 04 Jan 2018, 22:38
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