A math question that is so hard, nobody can solve it.

[luvya]

Ok, here is one I couldn't understand..
What is the value of x^2 - y^2?

1. x-y = y+2
2. x-y = 1/x+y

Answer:
a. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
b. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
c. Both statements together are sufficient, but neither statement alone is sufficient.
d. Each statement alone is sufficient.
e. Statement (1) and (2) together are not sufficient.

The correct answer is B. I choose C because I thought statement 1 gives you a good idea of what X and Y are if u isolate one of them and then apply that to statement 2.....but I am wrong again

 

[rgwalt]

Statement one tells us that there are at least 17 employees currently at the company. If the current employees remain, and three are hired, there will be AT LEAST 20, which means that there are at least 17 to begin with (20-3=17). It does not tell us any more than that.

Statement two tells us that there are no more than 17 employees currently at the company. If the company doesn't hire anyone, and 3 leave, there will be FEWER THAN 15 employees (this means that there are 14 or fewer after 3 leave). This means that at most, there can be 17 employees to begin with (14+3=17).

Neither statement gives enough info to determine the number of employees by itself, but together they tell you the exact number of employees.

Hope that helps.

Ryan

 

[luvya]

Oh yeah! Thanks...I think I got confused by the sentence "at least 20"...I forgot it could be 20 as well...Mmmm

 

[RossGr]

If you set up the inequalites the necessity of both is clear

the first statement gives

x+3>=20 or x>=17


The second statement gives

x-3<15 or x < 18

the key here is the absence of the equal sign in the second statement. The number of employees cannot be 18 it must be less then 18.

The first statement tells us that there can be 17 or more employees. The ONLY number which satisfies BOTH inequalites is 17, thus both statements are required and uniquely determine a answer. c is the correct responce.

 

[luvya]

^

 

[luvya]

Anyone?

 

[luvya]

 

[JayHu]

Originally posted by: luvya
Ok, here is another one I couldn't understand..
What is the value of x^2 - y^2?

1. x-y = y+2
2. x-y = 1/x+y

Answer:
a. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
b. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
c. Both statements together are sufficient, but neither statement alone is sufficient.
d. Each statement alone is sufficient.
e. Statement (1) and (2) together are not sufficient.

The correct answer is B. I choose C because I thought statement 1 gives you a good idea of what X and Y are if u isolate one of them and then apply that to statement 2.....but I am wrong again

is that x-y=1/x + y
or x-y = 1/(x+y)?

 

[luvya]

x-y=1/x + y is correct, I didn't mistype.
But what's the difference?

 

[luvya]

Ahh..after-meal-bump

 

[her209]

Originally posted by: luvya
Ok, here is one I couldn't understand..
What is the value of x^2 - y^2?

1. x-y = y+2
2. x-y = 1/x+y

Answer:
a. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
b. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
c. Both statements together are sufficient, but neither statement alone is sufficient.
d. Each statement alone is sufficient.
e. Statement (1) and (2) together are not sufficient.

The correct answer is B. I choose C because I thought statement 1 gives you a good idea of what X and Y are if u isolate one of them and then apply that to statement 2.....but I am wrong again

I guess I missed the question.

From what I see (1) and (2), you can make x = .5 and y can be anything. Is that what you are asking about?

 

[aux]

you did mistype it;
(2) should be x-y = 1/(x+y)
then x^2-y^2=(x-y)*(x+1)=1
therefore (2) is sufficient
(1) is obviously not sufficient

note that 1/x+y = (1/x) + y != 1/(x+y)

 

[aux]

Originally posted by: luvya
x-y=1/x + y is correct, I didn't mistype.
But what's the difference?

the difference is that (say x=1, y=5)
1/x + y = 1/1 + 5 = 1+5 = 6 and
1/(x+y) = 1/(1+5) = 1/6 which is quite of a difference

btw (see my previous post) if it was 1/x+y, the answer would not be B)

 

[CSMOOTH]

Ok, here is one I couldn't understand..
What is the value of x^2 - y^2?

1. x-y = y+2
2. x-y = 1/x+y

Answer:
b. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

The correct answer is B. I choose C because I thought statement 1 gives you a good idea of what X and Y are if u isolate one of them and then apply that to statement 2.....but I am wrong again

Here is something to think about:

1 goes like this:
x-y = y+2 multiply both sides by (x+y)
x^2 - y^2 = xy + 2x + y^2 + 2y
There is not much more that you can do on the right side so you look at this and it doesn't strike me as anything that can be solved unless you are given the values of x and y somewhere. But if you have the values, the left side is trivial.

2 goes like this:
x-y = 1/x+y get a common denominator on the right side
** = (1+xy)/x multiply both sides by x+y
x^2 - y^2 = (1 + xy)(x+y)/x
*** = (x+y+x^2 * y + x*y^2)/x
*** = (x+x^2 * y + x*y^2)/x + y/x
*** = x(1+xy+y^2)/x + y/x
*** = 1+xy+y^2 + y/x
*** = (1+y^2) + xy + y/x
*** = (1+2y+y^2) - 2y + xy + y/x
*** = (1+y)^2 + (x-2)y + y/x
This is the same as the first case.

Now if the 2nd equation was x-y = 1 / (x+y) like it should be for an SAT or something like that
Then the answer is trivial.
x-y = 1 / (x+y) multiply both sides by (x+y)
x^2 - y^2 = 1
and you are done. So I am pretty sure that you just wrote the problem down wrong. If not, what kind of math are you in???