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If xy = 12, what is the value of x – y? [#permalink]
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14 Apr 2015, 04:02
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Re: If xy = 12, what is the value of x – y? [#permalink]
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14 Apr 2015, 04:48
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Bunuel wrote: If xy = 12, what is the value of x – y?
(1) x > y (2) x + y = 7
Kudos for a correct solution. xy=12 xy=? 1. xy>0 Not Sufficient 2. x+y=7 x=12/y 12+y^2=7y y^27y+12=0 (y3)(y4)=0 y=3 OR 4 x=4 OR 3 xy=1 OR 1 Not Sufficient 1 and 2: x>y Therefore x=4; y=3 xy=1 Sufficient Answer: C



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If xy = 12, what is the value of x – y? [#permalink]
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14 Apr 2015, 07:27
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xy = 12 #1 x > y: 1: x = 4, y = 3, xy = 12, x  y = 1 2: x = 6, y = 2, xy = 12, x  y = 4 insufficient
#2  x+y = 7: x = 4, y = 3, xy = 12, x  y = 1 x = 3, y = 4, xy = 12, x  y = 1
insufficient
#1+#2 the system of equations xy = 12 and #2 yields 2 pairs of (x;y), namely (3;4) and (4;3). If we add the condition #1, we'll have only 1 pair remaining which is (4;3) which explicitly lets us answer our question.
C is the answer
Last edited by Zhenek on 19 Apr 2015, 08:31, edited 2 times in total.



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Re: If xy = 12, what is the value of x – y? [#permalink]
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14 Apr 2015, 10:45
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X will have only one value. But stat 2 gives us two values, stat 1 help us to discard one and keep one. Ans:C



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Re: If xy = 12, what is the value of x – y? [#permalink]
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14 Apr 2015, 13:03
St 1) X>Y > 6X2 ; 4X3 etc.. NS St 2) X+Y = 7 > from ques X=12/Y; 12/Y+Y=7 So 12+Y^2=7Y > Y=4 OR Y=3 Hence X=3 OR X=4 Combining 1&2 Only one unique value of X = 4 Answer C



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Re: If xy = 12, what is the value of x – y? [#permalink]
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19 Apr 2015, 06:13
I've picked B, here is why,
In 2] X+Y=7
Then X=7Y
Then XxY= 12 becomes [7Y]xY= 12
The only solution is Y=3
If Xx3=12 then X = 4
XY=1.
Correct me if i'm wrong



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Re: If xy = 12, what is the value of x – y? [#permalink]
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19 Apr 2015, 07:04
mike34170 wrote: I've picked B, here is why,
In 2] X+Y=7
Then X=7Y
Then XxY= 12 becomes [7Y]xY= 12
The only solution is Y=3
If Xx3=12 then X = 4
XY=1.
Correct me if i'm wrong mike34170 When we take [7Y]xY= 12, this can be expanded as \(y^2\)7y+12=0 (y3)(y4)=0 Therefore, y can be 3 OR 4. Replacing the values of y in the initial equation of xy=12 or x+y=7, If y=3 then x=4 and xy=1 If y=4 then x=3 and xy= 1 Since there can be 2 possible values of xy, namely 1 and 1, statement 2 is insufficient. When we take both the statements together we know for sure that the instance 1 is true. That is, If y=3 then x=4 and xy=1 Since we need both the statements to get a unique value of xy, answer is C.



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Re: If xy = 12, what is the value of x – y? [#permalink]
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19 Apr 2015, 07:22
AmoyV wrote: mike34170 wrote: I've picked B, here is why,
In 2] X+Y=7
Then X=7Y
Then XxY= 12 becomes [7Y]xY= 12
The only solution is Y=3
If Xx3=12 then X = 4
XY=1.
Correct me if i'm wrong mike34170 When we take [7Y]xY= 12, this can be expanded as \(y^2\)7y+12=0 (y3)(y4)=0 Therefore, y can be 3 OR 4. Replacing the values of y in the initial equation of xy=12 or x+y=7, If y=3 then x=4 and xy=1 If y=4 then x=3 and xy= 1 Since there can be 2 possible values of xy, namely 1 and 1, statement 2 is insufficient. When we take both the statements together we know for sure that the instance 1 is true. That is, If y=3 then x=4 and xy=1 Since we need both the statements to get a unique value of xy, answer is C. Hello AmoyV. Thanks for you reply. Exact, Y has two roots 3 and 4.



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Re: If xy = 12, what is the value of x – y? [#permalink]
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20 Apr 2015, 05:46
Bunuel wrote: If xy = 12, what is the value of x – y?
(1) x > y (2) x + y = 7
Kudos for a correct solution. MAGOOSH OFFICIAL SOLUTIONIn this case, the question includes an “if” statement, xy = 12. Once again there is no obviously useful way to rephrase the question. We could, say, use the “if” equation to solve for y in terms of x, and substitute the resulting expression for y in the question. That’s not vey promising, though, so let’s turn to (1). Even if we restrict ourselves to positive integers, the “if” statement and (1) together allow a number of solutions, each of which yields a different value for x – y. Specifically, x and y could be 12 and 1, 6 and 2, or 4 and 3, and could therefore be 11, 4, or 1. Eliminate A and D. Statement (2) and the “if” statement together might seem to allow just one solution, x=4, y=3, and xy=1. In fact, though, (2) and the “if” statement also allow x=3, y=4, =1. So (2) is also not sufficient. Eliminate B. Together (1) and (2) (along with the “if” statement) allow just one solution, x=4, y=3, and xy=1. The correct answer is C.
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Re: If xy = 12, what is the value of x – y? [#permalink]
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02 Jul 2015, 10:57
My first though was Option C is correct But then it struck me that there is nowhere mentioned that x& y are integer so how can we choose c IMO E is correct Experts please correct my reasoning Bunuel



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Re: If xy = 12, what is the value of x – y? [#permalink]
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02 Jul 2015, 11:06



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Re: If xy = 12, what is the value of x – y? [#permalink]
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02 Jul 2015, 11:16
Bunuel wrote: kanigmat011 wrote: My first though was Option C is correct But then it struck me that there is nowhere mentioned that x& y are integer so how can we choose c IMO E is correct Experts please correct my reasoning Bunuelxy = 12 and x + y = 7 gives x = 3 and y = 4 OR x = 4 and y = 3 but since it's given that x > y, then the first case is out and x  y = 1. Thanks Bunuel Got it Maybe i over exercised my brain on this one!



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Re: If xy = 12, what is the value of x – y? [#permalink]
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03 Jul 2015, 08:53
Would it be enough to know that the equation out of 2 is a quadratic and will therefore almost always yield two different results? Bc. then xy could be two different things.
or would you proceed and calculate it out? thx



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If xy = 12, what is the value of x – y? [#permalink]
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03 Jul 2015, 09:11
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noTh1ng wrote: Would it be enough to know that the equation out of 2 is a quadratic and will therefore almost always yield two different results? Bc. then xy could be two different things.
or would you proceed and calculate it out? thx No, you should atleast look at the discriminant of a quadratic equation. D (discriminant) = \({b^24ac}\), where a,b,c are coefficients of the quadratic equation, \(ax^2+bx+c=0\) D can be <0, >0 or =0 Now, for 2 UNIQUE (or unequal real roots), D should be >0 For 2 EQUAL roots, D=0 For complex roots (not applicable for GMAT) , D<0 Thus, just knowing that an equation is quadratic IS NOT sufficient to say that you will get 2 different roots. Example, \(x^2+5x+6=0\) has 2 unique roots, x=2, x=3, D = \({6^24*1*6}\) = 12 >0 But, \(x^2+6x+9=0\), has 2 EQUAL roots and thus only 1 value, x=3, D = \({6^24*1*9}\) = 0 Another thing to look at in questions like these is whether the question stems prohibit 1 of 2 values that you obtain from a quadratic equation. In this case, although you did get 2 values, only 1 is allowed and this quadratic equation will thus be sufficient.



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Re: If xy = 12, what is the value of x – y? [#permalink]
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01 Mar 2017, 22:04
HI, couldn't I just isolate "y" in the second statement, so that y=7x, and then calculate the so asked "xy" as: x(7x)=7? so that statement 2 is actually sufficient? thank you



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Re: If xy = 12, what is the value of x – y? [#permalink]
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21 Mar 2017, 06:30
Juliaz wrote: HI, couldn't I just isolate "y" in the second statement, so that y=7x, and then calculate the so asked "xy" as: x(7x)=7? so that statement 2 is actually sufficient? thank you x(7x) = x7(x) = x7+x = 2x7 .
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Re: If xy = 12, what is the value of x – y? [#permalink]
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21 Mar 2017, 06:36
The answer will be C... x.y=12 ; also both x and y have to be a factor of 12... Sent from my GTI9060I using GMAT Club Forum mobile app




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