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OG Quant (Green Book) DS #80

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OG Quant (Green Book) DS #80

by navalpike » Mon Jun 22, 2009 2:36 pm
Hi all,
Would love to hear an expert’s opinion but all are welcome.

If xy>0, does (x-1)(y-1) = 1
1. x+y = xy
2. x=y

we can obviously conclude that 1. Is sufficient by re-writing the problem
xy-x-y+1=1……..which is the same as 1.
However, I would like to see where my thinking is wrong for the 2nd one because I concluded that it was sufficient.

If x=y, then
(y-1)(y-1)=1
Y^2-2y=0
Y(y-2)=0
Either y=0 or y=2.
Now, the stem mentions that xy>0, thus y cannot be 0, thus y=2
(x-1) (2-1)=1
(x-1)=1
x=2
We know both x & y and thus can solve the problem.

The OG explanation stops at y^2-2y=0, but can we not continue?
Would love to hear your opinion, thanks!
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Source: — Data Sufficiency |
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by navalpike » Mon Jun 22, 2009 2:42 pm
OA is A
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plug in some answer choices:

by jtjang99 » Mon Jun 22, 2009 3:22 pm
if xy>0, and x=y (from statement 2), then let's plug in 1 for x and y into the formula that is in the question stem. This yields 0=1, so the answer is no. Now let's plug in 2 for x and y (doing so still fulfills xy>0, and point 2) x=y). Plugging in 2 to the equation in the question stem yields 1=1, so the answer is yes. Because we get conflicting answers ("no" when we plug in 1 for x and y, and "yes" when we plug in 2 for x and y), point 2 (x=y) is insufficient.
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by navalpike » Mon Jun 22, 2009 7:56 pm
never mind. I think I figured out the problem.

I had already plugged in the info. from 2. into the question stem. It gave two choices for y. I wasn't allowed to plug it back into the stem a second time.
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by joymukhi » Tue Jun 23, 2009 1:55 am
Guys to help me understand ..what is the approach that we should we taking while solving such problems because going by the equation approach we would get y & x as 2 and the result 1. Going by substitution approach we get conflicting answers which makes the answer choice different. Appreciate if someone could shed some light on this. I went by y = 0 & y = 2 and got stumped. (2-1) (2-1) = 1 ..so why is it incorrect? Still not clear.
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by rah_pandey » Tue Jun 23, 2009 4:18 am
Use value plugging only when you want to prove that the statement given is false.

The equation approach is always the best approach mathematically but it takes time and you should be comfortable working with variables and inequalities

in the question asked using second condition we know

x=y so (x-1)*(y-1)=(x-1)^2

it can take any values and one of them can be 2 so II by itself is not sufficient. The approach used by Navalpike is wrong as he finds out for what x if any is (x-1)^2=1 but we need to tell if (x-1)^2=1 for all values of x>0
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by carpe_diem » Thu Jun 25, 2009 1:50 pm
(x - 1) (y - 1) = 1 ?
xy - (x+y) + 1 = 1
xy - (x+y) = 0
so does xy = (x+y) ?

state 1: x + y = xy ; Sufficient
state 2: x = y
Substitute this in original equation :
xy = (x+y)
x^2 = 2x
x^2 - 2x = 0
This equation will give 2 value of x and hence Not Sufficient.
OG wants to say that after the equation y^2 - 2y = 0 will give 2 value of y and hence inconclusive. Therefore Insufficient.
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