What does xy>0..mean?
"xy" means x and y are multiplied. If we want to totally write "a multiplied by b" which is the same as "b multiplied by a" we write: a x b or a * b. That's a multiplication.
xy>0 means that the result is positive. For example, if x=2 and y=3 we have: 2*3=6>0
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inequalities
Source: Beat The GMAT — Data Sufficiency |
I'm not postiive on this one, but I think it's A here.
1. x+y=xy
The only way this works is if x and y both equal 2 or 0. In both cases, the stem is proven. Sufficient
2. x=y
Just picking numbers and plugging into the stem, say x, y= 3 (3-1)(3-1) does not = 1 whereas (2-1)(2-1) = 1. Insufficient.
So I think it's A. What's the OA?
1. x+y=xy
The only way this works is if x and y both equal 2 or 0. In both cases, the stem is proven. Sufficient
2. x=y
Just picking numbers and plugging into the stem, say x, y= 3 (3-1)(3-1) does not = 1 whereas (2-1)(2-1) = 1. Insufficient.
So I think it's A. What's the OA?
I would say A since,
For (x-1)(y-1)=1, there are only 2 possibilities:
1. x=0 y=0
2. x=2 y=2
In both cases x+y=xy
Option B could be anything...3=3, 4=4, 5=5....and so on..
For (x-1)(y-1)=1, there are only 2 possibilities:
1. x=0 y=0
2. x=2 y=2
In both cases x+y=xy
Option B could be anything...3=3, 4=4, 5=5....and so on..
One thing to consider is that xy>0, so both x and y are either positive or negative, but can't equal 0.
IMO A, b/c 2 is the only number that satisfies the criterion.
IMO A, b/c 2 is the only number that satisfies the criterion.
(x-1)(y-1)=1 ?
makes the questionin such way: xy=x+y ?
(1)
xy=x+y
the same as we found
SUFF
(2)
x=y
from the main statement xy=x+y we have
yy=2y
y^2=2y
y=2 so x=2
(2-1)(2-1)=1
SUFF
Answer D
If I am wrong, pls somebody correct me
makes the questionin such way: xy=x+y ?
(1)
xy=x+y
the same as we found
SUFF
(2)
x=y
from the main statement xy=x+y we have
yy=2y
y^2=2y
y=2 so x=2
(2-1)(2-1)=1
SUFF
Answer D
If I am wrong, pls somebody correct me
Ans is A
The second condition is possible only of x=y=2 but not true for any other number
Hence A is correct
The second condition is possible only of x=y=2 but not true for any other number
Hence A is correct
[quote="4meonly"](x-1)(y-1)=1 ?
makes the questionin such way: xy=x+y ?
(1)
xy=x+y
the same as we found
SUFF
(2)
x=y
from the main statement xy=x+y we have
yy=2y
y^2=2y
y=2 so x=2
(2-1)(2-1)=1
SUFF
Answer D
If I am wrong, pls somebody correct me[/quote]
The stem was xy > 0, not xy=x+y, that was statement one.
makes the questionin such way: xy=x+y ?
(1)
xy=x+y
the same as we found
SUFF
(2)
x=y
from the main statement xy=x+y we have
yy=2y
y^2=2y
y=2 so x=2
(2-1)(2-1)=1
SUFF
Answer D
If I am wrong, pls somebody correct me[/quote]
The stem was xy > 0, not xy=x+y, that was statement one.
(x-1)(y-1)=1 ?
xy-x-y+1=1
xy=1-1+x+y
xy=x+y
So, the question can be rephrased in
Does xy=x+y ?
(1) Directly gives you the answer
(2) x=y
sustitute yy=y+y
y^2 = 2y
y = 2
2*2 = 2+2 or (2-1)(2-1)=1
According to xy>0? 2*2 > 0
Answer D
xy-x-y+1=1
xy=1-1+x+y
xy=x+y
So, the question can be rephrased in
Does xy=x+y ?
(1) Directly gives you the answer
(2) x=y
sustitute yy=y+y
y^2 = 2y
y = 2
2*2 = 2+2 or (2-1)(2-1)=1
According to xy>0? 2*2 > 0
Answer D
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Ian Stewart
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You are doing the math correctly, but you're answering a different question from the one that's being asked here. The question is:4meonly wrote:(x-1)(y-1)=1 ?
xy-x-y+1=1
xy=1-1+x+y
xy=x+y
So, the question can be rephrased in
Does xy=x+y ?
(1) Directly gives you the answer
(2) x=y
sustitute yy=y+y
y^2 = 2y
y = 2
2*2 = 2+2 or (2-1)(2-1)=1
According to xy>0? 2*2 > 0
Answer D
Is (x-1)(y-1) = 1 ?
As you've done, you can rephrase the question:
Is xy = x + y ?
Still, that's the question. It's not a fact. Do not assume the answer to the question is 'yes', and use it as if it were a fact. This is crucially important, and it's a common trap people fall into when they first start doing DS questions.
So, you aren't trying to find x or y here; you are trying to decide, from Statement 2, whether xy = x+y must be true. If we know statement 2, we know that x = y, so we need to know whether x*x = x+x, that is whether x^2 = 2x. Well, x could be 2, and then x^2 = 2x, or x could be 3, and x^2 does not equal 2x. So we can't answer the question by only using 2) alone. As demonstrated above, Statement 1) is sufficient.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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I agree with your explanation IAN but if an equation is simplified and found to be true, shouldlnt the un simplified equation be true also?
GMAT/MBA Expert
-
Ian Stewart
- GMAT Instructor
- Posts: 2623
- Location: Montreal
- Thanked: 1090 times
- GMAT Score:780
Yes, but I'm afraid I don't see the relevance of that to this question. We can rewrite or simplify the equation in the question all we want; using Statement 2 alone, we can't prove that it's true.sumithshah wrote:I agree with your explanation IAN but if an equation is simplified and found to be true, shouldlnt the un simplified equation be true also?
