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Is x - y > r - s ? (1) x > r and y < s (2) y = 2, s = 3, r = 5, and

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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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New post Updated on: 07 Feb 2018, 20:28
1
1
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A
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D
E

Difficulty:

  35% (medium)

Question Stats:

66% (00:51) correct 34% (01:02) wrong based on 174 sessions

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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 Bunuel on 07 Feb 2018, 20:28, edited 3 times in total.
Edited the question.
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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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New post 24 Jul 2013, 12:40
2
2
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.

Answer: D.

ADDING/SUBTRACTING INEQUALITIES:


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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New post 26 Sep 2013, 08:17
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
ADD THESE
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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New post 26 Sep 2013, 08:30
1
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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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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Re: Is x - y > r - s ? (1) x > r and y < s (2) y = 2, s = 3, r = 5, and &nbs [#permalink] 07 Feb 2018, 16:11
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