All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Counting Quadruplets II (Posted on 2010-09-21) Difficulty: 3 of 5
Each of A, B, C and D is a positive integer with the proviso that A ≤ B ≤ C ≤ D ≤ 20

Determine the total number of quadruplets (A, B, C, D) such that: A*B + C*D > 300.

What is the total number of quadruplets (A, B, C, D) such that: A*B - C*D > 100?

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
precedence / solution | Comment 1 of 2

If one assumes the normal operator precedence rules (i.e. when not overrides by parentheses) for such expressions, e.g. multiplications and divisions before additions and subtractions, ----- then:

(a) A * B + C * D is read as (A*B) + (C*D).  There are 3254 quadruplets evaluating 300 or greater.

(b) A * B - C * D is read as (A*B) - (C*D).  There are obviously no evaluations greater than 100, since (C*D) will always be greater than (A*B) unless ABCD are all the same in which case also an evaluation of zero is less than 100.

If some different interpretation was the intent, the text  expression should be fully parenthesized. 


  Posted by ed bottemiller on 2010-09-21 14:05:30
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information