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Math Expert V
Joined: 02 Aug 2009
Posts: 7757
Is x divisible by 3?  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 38% (01:24) correct 62% (01:26) wrong based on 217 sessions

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Is x divisible by 3?

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

_________________

Originally posted by chetan2u on 10 Dec 2016, 05:18.
Last edited by Bunuel on 10 Dec 2016, 06:03, edited 1 time in total.
RENAMED THE TOPIC AND EDITED THE QUESTION!
Retired Moderator B
Joined: 05 Jul 2006
Posts: 1664
Is x divisible by 3?  [#permalink]

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1
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

Sent from my iPhone using GMAT Club Forum mobile app
Intern  B
Joined: 09 Nov 2015
Posts: 27
GMAT 1: 640 Q49 V29 GMAT 2: 720 Q50 V38 Re: Is x divisible by 3?  [#permalink]

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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.

Math Expert V
Joined: 02 Aug 2009
Posts: 7757
Re: Is x divisible by 3?  [#permalink]

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1
1
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..
_________________
Intern  B
Joined: 09 Nov 2015
Posts: 27
GMAT 1: 640 Q49 V29 GMAT 2: 720 Q50 V38 Is x divisible by 3?  [#permalink]

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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
Intern  B
Joined: 09 Nov 2015
Posts: 27
GMAT 1: 640 Q49 V29 GMAT 2: 720 Q50 V38 Re: Is x divisible by 3?  [#permalink]

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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.
Manager  G
Joined: 30 Mar 2017
Posts: 132
GMAT 1: 200 Q1 V1 Re: Is x divisible by 3?  [#permalink]

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1
(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.
Manager  B
Joined: 23 Oct 2017
Posts: 62
Re: Is x divisible by 3?  [#permalink]

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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
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7465
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Is x divisible by 3?  [#permalink]

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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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Manager  B
Joined: 29 Nov 2016
Posts: 116
Re: Is x divisible by 3?  [#permalink]

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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..

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
Math Expert V
Joined: 02 Sep 2009
Posts: 55668
Re: Is x divisible by 3?  [#permalink]

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Mudit27021988 wrote:
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..

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

Check the topics below:
How to Do Math on the GMAT Without Actually Doing Math
The Power of Estimation for GMAT Quant
How to Plug in Numbers on GMAT Math Questions
Number Sense for the GMAT
Can You Use a Calculator on the GMAT?
Why Approximate?
GMAT Math Strategies — Estimation, Rounding and other Shortcuts
The 4 Math Strategies Everyone Must Master, Part 1 (1. Test Cases and 2. Choose Smart Numbers.)
The 4 Math Strategies Everyone Must Master, part 2 (3. Work Backwards and 4. Estimate)
Intelligent Guessing on GMAT
How to Avoid Tedious Calculations on the Quantitative Section of the GMAT
GMAT Tip of the Week: No Calculator? No Problem.
The Importance of Sorting Answer Choices on the GMAT
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Manager  B
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Re: Is x divisible by 3?  [#permalink]

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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
_________________
" Can't stop learning and failing"
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Joined: 22 Aug 2013
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Re: Is x divisible by 3?  [#permalink]

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loserunderachiever wrote:
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
Director  P
Joined: 21 May 2013
Posts: 656
Re: Is x divisible by 3?  [#permalink]

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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..

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
SVP  V
Joined: 26 Mar 2013
Posts: 2231
Is x divisible by 3?  [#permalink]

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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 Is x divisible by 3?   [#permalink] 06 Mar 2018, 04:38
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