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# |x+y|=?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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17 Feb 2016, 23:01
1
4
00:00

Difficulty:

25% (medium)

Question Stats:

68% (00:50) correct 33% (00:50) wrong based on 130 sessions

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|x+y|=?

1) xy=7
2) x and y are integers

* A solution will be posted in two days.

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17 Feb 2016, 23:05
1
1
IMO :C
STATEMENT 1 : X * Y =7 ,1*7 ,-1*-7 , 49*(1/7)
Lot of possibility. Hence insufficient
Statement 2 : NS when stand alone

Combined: only two cases 1*7 * -1*-7

So C
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19 Feb 2016, 00:10
1
|x-y|=?

If we get the value of x and y we can solve the que.

from equ i
XY=7
i.e. X=1,Y=7 or X=-1,Y=-7 or X=7/2 and Y=2 so many more values are possible.As,it is not mentioned that X and Y are integers.

From equ. ii

we get X and Y are integers.Now,only two values are possible i.e 7 and 1 with both same signs

we will get ans as 8
so combining both we will be able to solve the que.
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20 Feb 2016, 23:30
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

|x+y|=?

1) xy=7
2) x and y are integers

In the original condition, there are 2 variables(x,y), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), they become (x,y)=(7,1),(1,7),(-7,-1),(-1,-7). In total, |x+y|=8, which is unique and sufficient. Therefore, the answer is C.

 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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25 Feb 2016, 19:41
[quote="MathRevolution"]|x+y|=?

1) xy=7
2) x and y are integers

statement 1:XY=7

it means both x and y have same signs
i.e xy could be 3.5*2 or -1*-7
not suff.

satement 2: X & Y are integers
so x & Y could be any integer.
Not suff.

consider both statements
As 7 is prime ,it has only 2 factors i.e 1& 7
either 1 and 7 both are +ve or -ve
in any case Ix+yI equals 8.
hence C ans.
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11 Aug 2017, 22:39
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Re: |x+y|=?   [#permalink] 11 Aug 2017, 22:39
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