How many pairs of integers (x, y) with x y can be selected from the

Question

How many pairs of integers (x, y) with x > y can be selected from the range -5 to 4, inclusive?

A. 15
B. 18
C. 36
D. 45
E. 90

This is a  PS Butler Question

Check the links to other Butler Projects: 
 
   Data Sufficiency Butler 
   Critical Reasoning Butler  
   Sentence Correction Butler  
   Reading Comprehension Butler  
   Integrated Reasoning Butler

If two integers x,y (x>y) are selected from -5 to 4(inclusive), how many cases are there?

ramiav · Answer

we need to find the sorted pairs between

for -5 we have 9 ( (-5,-4).. (-5,4) )
-4, 8 ...
-3, 7 ...

So we have a sequence from 9 to 1 and we need to know the sum of that:
(First element + last element )*Number of elements / 2 => 
(9+1)*9/2 = 45

VivekSri · Answer

OA is D

Aryaa03 · Answer

Sol:  IMO-Option-D

Between -5 to 4, total no.of Integers = 4-(-5)+1 = 10
Any pair selected from the 10 nos. will have one of the numbers greater than the other. 
To count it once (for x > y) , take combination (rather than all arrangements)

Total no. of ways to select 2 nos. out of 10 = 10C2 = 10!/(10-2)!2! = 45

sachi-in · Answer

An Simple solution would be:

If we choose any two different numbers one will be greater another will be less .

So X > Y and Y > X are equally probable and distributed

There are total of 100 pairs of numbers (X , Y) i.e 10 * 10

Of those 10 pairs i.e (-5, -5) , (-4, -4) ... ( 4,4 ) are equal pairs
Out of 90 that are left they will be equally probable to be either X > Y or x < Y.

Hence 45 satisfy X > Y condition.

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

How many pairs of integers (x, y) with x > y can be selected from the

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions