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Taller and Heavier (Posted on 2013-12-06) Difficulty: 2 of 5
In a certain island, there are precisely 1000 married couples.
  1. Two thirds of the husbands who are taller than their wives are also heavier and:
  2. Three quarters of the husbands who are heavier than their wives are also taller.
If there are 120 wives who are taller and heavier than their husbands, how many husbands are taller and heavier than their wives?

No Solution Yet Submitted by K Sengupta    
Rating: 2.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Using Algebra, not logic (spoiler) | Comment 1 of 2
The only way to solve this is using the proven fact that no two people weigh EXACTLY the same, or are EXACTLY the same height.

Let x = husbands that are both taller and heavier.

From fact 1, husbands that are taller but lighter is x/2.
From fact 2, husbands that are heavier but shorter are x/3.

Then, x + x/2 + x/3 + 120 = 1000
         11x/6 = 880
         x = 480.   Final answer.

Checking:
Husbands taller and heavier = 480
Husbands taller but lighter = 240
Husbands shorter but heavier = 160
Husbands shorter and lighter = 120
Total couples = 1000

720 taller husbands, of whom 480 (2/3) are also heavier.
640 heavier husbands, of whom 480 (3/4) are also taller

Edited on December 6, 2013, 12:50 pm
  Posted by Steve Herman on 2013-12-06 10:31:47

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