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# What is the sum of positive integers x and y ? (1) 2x - 6y -

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VP
Joined: 18 Nov 2004
Posts: 1406
What is the sum of positive integers x and y ? (1) 2x - 6y - [#permalink]

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14 Mar 2005, 22:11
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1. What is the sum of positive integers x and y ?
(1) 2x - 6y - 1 = 3
(2) 5x - 3 = 15y + 7

2. What is the sum of positive integers x and y ?
(1) 3x + 2y = 14 - x
(2) 2x + 3y = 15 - x

3. What is the sum of positive integers x and y ?
(1) 3x + y = 6
(2) 4x + y = 7

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VP
Joined: 13 Jun 2004
Posts: 1100
Location: London, UK
Schools: Tuck'08

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14 Mar 2005, 22:53
the key word is POSITIVE INTEGER
I remind you that 0 is neither positive nor negative so it is not a potential value

1.E (1 and 2 are coming from the same equation : x-3y=2)

2.C

1) 2x+y=7 -> could be 1,5 or 3,1 or 2,3
2) x+y = 5 -> could be 2,3 or 3,2 or 1,4 or 4,1

3.D (it can only be 1,3)
Director
Joined: 21 Sep 2004
Posts: 591

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15 Mar 2005, 07:53
1. E
both equations come out to be the same. nothing can be said.

2. B
A is 2x+y=7. doesn't help as we want the sum of x and y where as B directly gives us x+y=5. we don't care what individual values are if i am reading the question right.

3. C.
solving both the equations give us the value for this one.
Manager
Joined: 13 Oct 2004
Posts: 236

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15 Mar 2005, 08:40
EBD as x and y are positive integers.
VP
Joined: 18 Nov 2004
Posts: 1406

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15 Mar 2005, 09:10
OA is EBD......let's make sure we understand why the OA for # 3 is "D" and not "C", I think this type of ques is very likely in GMAT.
Manager
Joined: 11 Jan 2005
Posts: 56
Location: Mexico City

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15 Mar 2005, 09:21
I got E C D but i see how the second is B. What a pain to give different values that yield the same result.

Good to see it here and be ready for it on Test Day (8 days away)
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 4971
Location: Singapore

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15 Mar 2005, 11:32
ah.. number properties..

1. What is the sum of positive integers x and y ?
(1) 2x - 6y - 1 = 3
(2) 5x - 3 = 15y + 7

(1) 2x-6y=4 --> x-3y=2 --> x+2 = 3y
So x+2 is a multiple of 3, and could be 3,6,9,12 etc. So we don't know x+y

(2) 5x-3=15y+7 --> 5x-15y=10 --> x-3y=2 (same thing).

E it is for question 1.

2. What is the sum of positive integers x and y ?
(1) 3x + 2y = 14 - x
(2) 2x + 3y = 15 - x

(1) 3x+2y=14-x --> 4x+2y=14 --> 2x+y=7 --> 2x=y+7
y + 7 is even since 2x is even. Therefore y must be odd. But that's all we know. Therefore not sufficient.

(2) 2x+3y=15-x --> 3x+3y=15 --> x+y=5
Suffcient.

B it is for question 2.

3. What is the sum of positive integers x and y ?
(1) 3x + y = 6
(2) 4x + y = 7

(1) 3x+y=6 --> x cannot be 2 since y canot be 0 (we're told they're positive). So x must be 1, and y must be 3, so x+y=4

(2) 4x+y=7 --> same thing, x cannot be 2 that would make the LHS of the equation wrong. So x must be 1, y must be 3 and again x+y=4

D it is for question 3.
Manager
Joined: 15 Feb 2005
Posts: 242
Location: Rockville

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15 Mar 2005, 14:31
Awesome question i got EBD also
Director
Joined: 21 Sep 2004
Posts: 591

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15 Mar 2005, 14:33
wow. the last one messed me.. anyways.. i get it now.. +Ve doesn't include zero's..
VP
Joined: 13 Jun 2004
Posts: 1100
Location: London, UK
Schools: Tuck'08

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15 Mar 2005, 17:39
Antmavel wrote:
2.C

I was too focused on finding x and y, instead of x+y, that's why I missed that one...
Non-Human User
Joined: 09 Sep 2013
Posts: 7295
Re: What is the sum of positive integers x and y ? (1) 2x - 6y - [#permalink]

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16 Sep 2017, 03:13
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: What is the sum of positive integers x and y ? (1) 2x - 6y -   [#permalink] 16 Sep 2017, 03:13
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