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# If x-y = 8, which of the following must be true?

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Intern
Joined: 08 Oct 2011
Posts: 43
If x-y = 8, which of the following must be true? [#permalink]

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18 Oct 2013, 11:30
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74% (00:46) correct 26% (00:52) wrong based on 245 sessions

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If x-y=8, which of the following must be true?

I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative

A) I only
B) II only
C) III only
D) I and II
E) II and III

I am having difficulty reaching at the correct answer choice. Please support!
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 43892
Re: If x-y = 8, which of the following must be true? [#permalink]

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18 Oct 2013, 11:39
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This post was
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If x-y=8, which of the following must be true?

I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative

A) I only
B) II only
C) III only
D) I and II
E) II and III

Given that: $$x=y+8$$.

I. Both x and y are positive. Not necessarily true. Consider x=7 and y=-1.

II. If x is positive, y must be positive. Not necessarily true. Consider the same numbers.

III. If x is negative, y must be negative. If x is negative, then we have that $$x=negative=y+8$$ --> y cannot be a positive number, because in this case $$y+8$$ would be $$positive+positive=positive\neq{negative}$$. Thus, in this case y must be a negative number.

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Re: If x-y = 8, which of the following must be true? [#permalink]

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18 Oct 2013, 11:42
Bunuel wrote:
If x-y=8, which of the following must be true?

I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative

A) I only
B) II only
C) III only
D) I and II
E) II and III

Given that: $$x=y+8$$.

I. Both x and y are positive. Not necessarily true. Consider x=7 and y=-1.

II. If x is positive, y must be positive. Not necessarily true. Consider the same numbers.

III. If x is negative, y must be negative. If x is negative, then we have that $$x=negative=y+8$$ --> y cannot be a positive number, because in this case $$y+8$$ would be $$positive+positive=positive\neq{negative}$$. Thus, in this case y must be a negative number.

Similar question to practice: if-x-and-y-are-integers-and-x-y-5-which-of-the-followin-107199.html

Hope it helps.
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Re: If x-y = 8, which of the following must be true? [#permalink]

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18 Oct 2013, 11:45
aakrity wrote:
If x-y=8, which of the following must be true?

I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative

A) I only
B) II only
C) III only
D) I and II
E) II and III

I am having difficulty reaching at the correct answer choice. Please support!

Is this actually 600-700 level? Could you please elaborate why this tag was used.
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Math Expert
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Posts: 43892
Re: If x-y = 8, which of the following must be true? [#permalink]

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18 Oct 2013, 11:48
2
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Expert's post
kvazar wrote:
aakrity wrote:
If x-y=8, which of the following must be true?

I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative

A) I only
B) II only
C) III only
D) I and II
E) II and III

I am having difficulty reaching at the correct answer choice. Please support!

Is this actually 600-700 level? Could you please elaborate why this tag was used.

The author of the post tagged it that way. I think it's ~550 level question.
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Re: If x-y = 8, which of the following must be true? [#permalink]

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18 Oct 2013, 12:11
It's a tricky question. I hadn't even considered negative numbers
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Re: If x-y = 8, which of the following must be true? [#permalink]

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22 May 2015, 11:03
Hi All,

Roman Numeral questions are relatively rare on Test Day (you'll probably see just 1 in the Quant section), and they're typically designed to take longer to solve than average. However, there is usually at least one built-in design "shortcut" so that you can avoid doing some of the work.....

Here, we're told that X-Y = 8. We're asked which of the following MUST be true (which really means "which of the following is ALWAYS true no matter how many different examples we can come up with?"). In these situations, it's usually easier to try to prove that a Roman Numeral is NOT true, so that we can eliminate it from the answer choices...

If X - Y = 8

I. Do BOTH X and Y have to be POSITIVE?

IF...
X = 8, then Y = 0
Then Roman Numeral 1 is NOT true.

II. If when X is POSITIVE, does Y have to be POSTIVE?

We can use the same example that we used in Roman Numeral 1....
IF....
X = 8, then Y = 0
Then Roman Numeral 2 is NOT true.

There's only 1 answer remaining, so we don't even have to check Roman Numeral 3.

[Reveal] Spoiler:
C

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Re: If x-y = 8, which of the following must be true? [#permalink]

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27 May 2015, 12:52
If x-y=8, which of the following must be true?

I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative

1. x and y can be negative, for instance, -2 - (-10) = 8 =>Eliminate A and D
2. x can be positive and y can be negative, for instance, 2 - (-6) = 8 => Eliminate B and E

A) I only
B) II only
C) III only
D) I and II
E) II and III
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Re: If x-y = 8, which of the following must be true? [#permalink]

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28 May 2015, 04:35
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Expert's post
Quote:
If x-y=8, which of the following must be true?

I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative

A) I only
B) II only
C) III only
D) I and II
E) II and III

Here's an alternate approach to evaluating the three statements:

I. Both x and y are positive

x- y = 8
=> y = x - 8

It's clear that for some positive values of x (like x = 2), y will be negative. Since we have found a case where St. I doesn't hold true, it is not a MUST BE TRUE statement.

II. If x is positive, y must be positive
Again, by the same example as above (when x = 2), we see that St. II is not always true either.

Since we know by now that St. I and II are not MUST BE TRUE statements, we are sure that the correct answer is D. Still, for the sake of completeness, I'll elaborate how we can evaluate St. III using this algebraic approach.

III. If x is negative, y must be negative
Again, using y = x - 8

We can see that if x is negative, then y = (negative) - 8 = (negative)

Hence St. III is a MUST BE TRUE statement.

Hope this was useful!

Best Regards

Japinder
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Re: If x-y = 8, which of the following must be true? [#permalink]

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28 May 2015, 05:00
Hello all

I believe its important to approach questions visually. In the attached diagram we can easily see that only III holds true. We must not every time delve into algebra or for a question such as this even use the pen.

Point to note is that one must know how to plot graphs. For GMAT linear graphs are very easy just know how to put the equation into intercept form of
$$x/a + y/b = 1$$
where $$a$$ is the intercept on $$X$$ axis and $$b$$ is the intercept on $$Y$$ axis.

Similarly know how to plot other degree equations but I don't think it is absolutely necessary as is the case with modulus functions, nevertheless very useful to know these techniques.

Attachments

Slide1.JPG [ 31.36 KiB | Viewed 2203 times ]

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Regards
J

Do consider a Kudos if you find the post useful

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Re: If x-y = 8, which of the following must be true? [#permalink]

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11 Nov 2016, 07:27
aakrity wrote:
If x-y=8, which of the following must be true?

I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative

A) I only
B) II only
C) III only
D) I and II
E) II and III

We are given that x - y = 8 and need to determine which of statement(s) must be true. Let’s analyze each Roman numeral answer choice.

I. Both x and y are positive

Both x and y DO NOT have to be positive. For instance if x = -1 and y = -9, then:

-1 - (-9) = -1 + 9 = 8

II. If x is positive, y must be positive

If x is positive, y DOES NOT have to be positive. For instance, if x = 7 and y = -1, then:

7 - (-1) = 7 + 1 = 8

III. If x is negative, y must be negative

If x is negative, it is true that y must also be negative to produce a positive difference between x and y. For instance, if x = -1 and y = -9, then:

-1 - (-9) = -1 + 9 = 8

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Re: If x-y = 8, which of the following must be true? [#permalink]

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21 Feb 2017, 12:38
aakrity wrote:
If x-y=8, which of the following must be true?

I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative

A) I only
B) II only
C) III only
D) I and II
E) II and III

I am having difficulty reaching at the correct answer choice. Please support!

I. 10-2=8 ok
but, 6-(-2)=8 also ok. So, eliminate it.

II. same logic like above example.

III. if x is negative, then y must be negative otherwise we'll not get the positive result. So, C is the correct choice to me.
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Re: If x-y = 8, which of the following must be true?   [#permalink] 21 Feb 2017, 12:38
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