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# x - y =5

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x - y =5 [#permalink]  07 Dec 2017, 03:08
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57% (00:51) correct 42% (00:35) wrong based on 117 sessions
$$x - y =5$$

 Quantity A Quantity B $$x^2 - y^2$$ 5

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: x - y =5 [#permalink]  08 Dec 2017, 00:13
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waiting for someone's explanation on this one! thanks
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Re: x - y =5 [#permalink]  08 Dec 2017, 02:15
Expert's post

tricky question.

Quantity A is $$(x^2 - y^2) = (x-y)(x+y)$$. Now we do from the stem that $$(x-y)=5$$.

So we do have $$5(x+y)$$. x and y can be any value for instance $$\frac{1}{2} >>>> 5(\frac{1}{2} + \frac{1}{2}) = 5*1 = 5$$ and the two quantities are equal.

But if x and y are zero A is $$5(0+0)= 0$$ and B is greater.

So two different values. The answer is D
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Re: x - y =5 [#permalink]  16 Dec 2017, 20:01
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Why you use 1/2 for x and y? when you substruct them you wont get 5. Can you please explain? Thank you
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Re: x - y =5 [#permalink]  16 Dec 2017, 22:33
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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

But Carcass I am a bit confused with the 1/2? Or did I get it wrong?
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Re: x - y =5 [#permalink]  17 Dec 2017, 01:25
Expert's post
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
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Re: x - y =5 [#permalink]  17 Dec 2017, 01:28
Expert's post
550542 wrote:
Why you use 1/2 for x and y? when you substruct them you wont get 5. Can you please explain? Thank you

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

$$1/2 + 1/2 = 0.5 + 0.5 = 1$$

Hope now is clear

Regards
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Re: x - y =5 [#permalink]  30 Dec 2017, 10:55
good question
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Re: x - y =5 [#permalink]  09 Jan 2018, 12:37
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Expert's post
Carcass wrote:
$$x - y = 5$$

 Quantity A Quantity B $$x^2 - y^2$$ 5

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

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Re: x - y =5 [#permalink]  30 Jan 2018, 03:25
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Carcass wrote:
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

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.
It's important to know that x²-y² can be rewritten to (x+y)(x-y).
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Re: x - y =5 [#permalink]  30 Jan 2018, 04:43
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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
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Re: x - y =5 [#permalink]  30 Jan 2018, 07:02
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Expert's post
mohan514 wrote:
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):

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Re: x - y =5 [#permalink]  07 Feb 2018, 04:46
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Re: x - y =5 [#permalink]  12 Aug 2018, 23:17
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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.
Re: x - y =5   [#permalink] 12 Aug 2018, 23:17
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