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Intern  Status: Yes. It was I who let the dogs out.
Joined: 03 Dec 2012
Posts: 38
H: B
Concentration: General Management, Leadership
GMAT Date: 08-31-2013
Is x - y > r - s ? (1) x > r and y < s (2) y = 2, s = 3, r = 5, and  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 71% (01:13) correct 29% (01:34) wrong based on 292 sessions

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Project DS Butler: Day 42: Data Sufficiency (DS84)

Is x - y > r - s ?

(1) x > r and y < s
(2) y = 2, s = 3, r = 5, and x = 6

Disclaimer: I have used the Search Box Before Posting. I used the first sentence of the question or a string of words exactly as they show up in the question below for my search. I did not receive an exact match for my question.
Source: Veritas Prep; Book 04
Chapter: Lesson
Topic: Algebra
Question: 19
Question: Page 131
Solution: Page 132
Edition: Third

My Question: Please provide an explanation on how to arrive at the answer.

Solution:
Statement 2. 4 > 2. Hence Sufficient. Eliminate A, C, E

Statement 1. Fact x > r and y < s
What do i do here ? I am confused.

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Originally posted by hb on 24 Jul 2013, 12:33.
Last edited by gmatbusters on 17 Dec 2018, 07:31, edited 4 times in total.
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Joined: 02 Sep 2009
Posts: 58427
Re: Is x - y > r - s ? (1) x > r and y < s (2) y = 2, s = 3, r = 5, and  [#permalink]

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3
7
Is x - y > r - s ?

(1) x > r and y < s. You can subtract inequalities if their signs are in the opposite directions (> <): x-y>r-s. Sufficient.

(2) y=2, s=3, r=5, and x=6. We have the exact values of each unknown, thus we can answer whether x-y>r-s. Sufficient.

You can only add inequalities when their signs are in the same direction:

If $$a>b$$ and $$c>d$$ (signs in same direction: $$>$$ and $$>$$) --> $$a+c>b+d$$.
Example: $$3<4$$ and $$2<5$$ --> $$3+2<4+5$$.

You can only apply subtraction when their signs are in the opposite directions:

If $$a>b$$ and $$c<d$$ (signs in opposite direction: $$>$$ and $$<$$) --> $$a-c>b-d$$ (take the sign of the inequality you subtract from).
Example: $$3<4$$ and $$5>1$$ --> $$3-5<4-1$$.

RAISING INEQUALITIES TO EVEN/ODD POWER:

A. We can raise both parts of an inequality to an even power if we know that both parts of an inequality are non-negative (the same for taking an even root of both sides of an inequality).
For example:
$$2<4$$ --> we can square both sides and write: $$2^2<4^2$$;
$$0\leq{x}<{y}$$ --> we can square both sides and write: $$x^2<y^2$$;

But if either of side is negative then raising to even power doesn't always work.
For example: $$1>-2$$ if we square we'll get $$1>4$$ which is not right. So if given that $$x>y$$ then we can not square both sides and write $$x^2>y^2$$ if we are not certain that both $$x$$ and $$y$$ are non-negative.

B. We can always raise both parts of an inequality to an odd power (the same for taking an odd root of both sides of an inequality).
For example:
$$-2<-1$$ --> we can raise both sides to third power and write: $$-2^3=-8<-1=-1^3$$ or $$-5<1$$ --> $$-5^3=-125<1=1^3$$;
$$x<y$$ --> we can raise both sides to third power and write: $$x^3<y^3$$.

For multiplication check here: help-with-add-subtract-mult-divid-multiple-inequalities-155290.html#p1242652

THEORY ON INEQUALITIES:

x2-4x-94661.html#p731476
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html
everything-is-less-than-zero-108884.html
graphic-approach-to-problems-with-inequalities-68037.html
inequations-inequalities-part-154664.html
inequations-inequalities-part-154738.html

QUESTIONS:

All DS Inequalities Problems to practice: search.php?search_id=tag&tag_id=184
All PS Inequalities Problems to practice: search.php?search_id=tag&tag_id=189

700+ Inequalities problems: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope it helps.
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Re: Is x - y > r - s ? (1) x > r and y < s (2) y = 2, s = 3, r = 5, and  [#permalink]

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fozzzy wrote:
Is $$x-y > r-s$$?

1) $$x > r$$ and $$y < s$$
2) $$y=2,s=3,r=5 and x=6$$

So for statement 1 we can conclude that x-r is positive and y -s is negative so its sufficient is that the best approach or do we use numerical examples? Statement 2 is easy

FOR STATEMENT 1
X>R
-Y>-S
X-Y>R-S (NOTE: Always make sure inequalities have same sign before adding or subtracting)
hope it helps
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Re: Is x - y > r - s ? (1) x > r and y < s (2) y = 2, s = 3, r = 5, and  [#permalink]

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2
I didn't add the inequalities I manipulated the original question

Given x-y > r-s

We can than write this as x-r > y-s

FS 1 says X-r > 0 ( positive) and y-s<0 ( negative)
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Is x - y > r - s ? (1) x > r and y < s (2) y = 2, s = 3, r = 5, and  [#permalink]

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Project DS Butler: Day 42: Data Sufficiency (DS84)

Bumping for DS Butler project:

Is x - y > r - s ?

(1) x > r and y < s
(2) y = 2, s = 3, r = 5, and x = 6
_________________ Is x - y > r - s ? (1) x > r and y < s (2) y = 2, s = 3, r = 5, and   [#permalink] 17 Dec 2018, 07:32
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