Why you use 1/2 for x and y? when you substruct them you wont get 5. Can you please explain? Thank you

For (x^2 - y^2) = (x+y)(x-y) (Square of differences) and since we know that x-y = 5
We can replace (x+y)(5)

Now according to the first statement x-y = 5
So both cannot be negative or it will result into a negative number. X must positive and y can be negative ( e.g. 2 - (-3)which gave us 5) or both can be positive with x>y or it will give a negative result (e.g.7 -2 = 5)
We can use the aforementioned values:
1) X postive Y negative
(x+y)(5)= (3 + (-2))(5) = (1)(5) so answer C
Now test the other case
2) X and Y positive
(7 + 2)(5) = (9)(5) Greater than B

So the answer is D.

But Carcass I am a bit confused with the 1/2? Or did I get it wrong?

The stem does not specify any number you could pick. As suc, pick a wise numebr to prove or disprove the quantities and see which answer is wrong or right.

\(\frac{1}{2}\) is just a wise number. This is the way to tackle a question like this as fast as possible.

hope is clear now

Regards

\(5* (x + y) = 5 * (\frac{1}{2} + \frac{1}{2}) = 5*1 = 5\)

\(1/2 + 1/2 = 0.5 + 0.5 = 1\)

Hope now is clear

Regards

good question

We can solve this question using matching operations
Given:
Quantity A: x² - y²
Quantity B: 5

Factor Quantity A to get:
Quantity A: (x - y)(x + y)
Quantity B: 5

Since, we're told that x - y = 5, we can rewrite Quantity A as:
Quantity A: 5(x + y)
Quantity B: 5

Divide both quantities by 5 to get:
Quantity A: x + y
Quantity B: 1

At this point, we might TEST some values of x and y
NOTE: The values must satisfy the condition that x - y = 5

Try x = 7 and y = 2
We get:
Quantity A: 7 + 2
Quantity B: 1
Quantity A is greater

Try x = 1 and y = -4
We get:
Quantity A: 1 + (-4)
Quantity B: 1
Quantity B is greater

Answer: D

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I thought it does restrict the numbers for x and y because (x-y) must equal 5 ( you therefore cannot pick 0.5 for both x and y because it would equal 0 if subtracted from one another)

The trick is to see that y can be negative (e.g. -4) while x positive (e.g. 1). This gives (x-y) = 5 and (x+y) = -3, multiplied gives -15 such that A would be smaller than B.
Now just picking two positive numbers to get (x-y) = 5 (e.g. x = 7 and y = 2) gives (x+y= = 9 and multiplied by 5 makes A larger than B.
Thus, answer D is correct
It's important to know that x²-y² can be rewritten to (x+y)(x-y).

I would personally try to fill following variables to check the possibilities:

Positive integers
Negative integers
Positive Fractions
Negative fractions

We just need to prove that any 2 of these variable values would give option D as answer

Just keep in mind that testing values only provides conclusive results when the correct answer is D.

More on this drawback here (starting at 2:50):

I support to Answer: D

Can i re-write the stem as x-y=5 to x=5+y, I then substitute it into the simplified expression "x+y" to become "5+y+y" which in turns simply to 5+2y". I then minus 5 on both columns and divide by 2 which results in column A becoming "y" and column B becoming "-2". I then plug in numbers to test if there is a consistent relationship between column A and B, in which case there isn't.

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