5 Girls (named Alice, Betty, Carol, Diane, Emily) visit a mall to shop. They come upon a clothing shop and they decide to buy clothing.

But, for some strange reason, different colored shirts cost different amounts, which now came in increments of 10 dollars. (Every shirt of the same color costs the same amount.) This store doesn't carry very many shirts; the most expensive one is 50 dollars, and they only come in red, green, blue, yellow, and orange.

Each girl goes into the store and finds two different shirts. No two girls got the same pair of shirts, and no girl got a shirt for free. It ended up that each color shirt was bought exactly twice.

Using the following clues, can you figure out the two colors of shirts each girl bought, and how much each color bought, as well as how much each girl spent?

1) When the 5 girls were comparing their purchases, they found that Diane spent the most money, 2 girls tied for second most money spent, and the other 2 girls spent the same amount of money as well.

2) When Carol bought the blue shirt, she was mad that the it was more expensive than the 10-dollar price it was last week, and didn't buy the green shirt because of this.

3) Diane's and Emily's different styles resulted in them not buying any shirts the same color as each other's.

4) Alice and Emily both decided not to buy the orange shirt, but instead, Alice went with Carol to pick out the same color shirt to buy, noting that it didn't cost 20 dollars like last week.

5) As Betty was waiting to buy a red shirt (which she did end up buying), she saw Carol buy a shirt that cost 40 dollars.

$80 - Diane: green ($50) and orange ($30)
$60 - Emily: blue and red ($20)
$60 - Alice: green ($50) and yellow ($10)
$50 - Betty: orange ($30) and red ($20)
$50 - Carol: blue and yellow ($10)

There are five colors of shirts in $10 increments, with the most expensive costing $50, meaning that they cost 10, 20, 30, 40 and 50 dollars in some order. Since each girl bought two different shirts, possible totals are:

$30 = 10 + 20
$40 = 10 + 30
$50 = 10 + 40
$50 = 20 + 30
$60 = 10 + 50
$60 = 20 + 40
$70 = 20 + 50
$70 = 30 + 40
$80 = 30 + 50
$90 = 40 + 50

Since Diane spent the most, and the other two pairs of girls spent the same amounts [1], possible triples of the amounts spent are, at first glance:

50, 60, 70 (10,40;20,30;10,50;20,40;20,50)
50, 60, 70 (10,40;20,30;10,50;20,40;30,40)
50, 60, 80 (10,40;20,30;10,50;20,40;30,50)
50, 60, 90 (10,40;20,30;10,50;20,40;40,50)
50, 70, 80 (10,40;20,30;20,50;30,40;30,50)
50, 70, 90 (10,40;20,30;20,50;30,40;40,50)
60, 70, 80 (10,50;20,40;20,50;30,40;30,50)
60, 70, 90 (10,50;20,40;20,50;30,40;40,50)

However, we are also told that two of each color shirt were bought, eliminating most of the above combinations (the underlined priced appear three times, and the italicized values appear only once in the invalid combinations). The only valid result (in bold), then, is that Diane spent $80, while the other pairs of girls spent $50 and $60 on their clothes, respectively:

80 = 30 + 50 (Diane)
60 = 20 + 40
60 = 10 + 50
50 = 20 + 30
50 = 10 + 40

We know that Diane spent $80 on thirty- and fifty-dollar shirts, and Emily did not buy any shirts of the same colors as she did [3]. Thus, Emily either spent $10 and 40 or $20 and 40, and we know for sure that she did buy a forty-dollar shirt. Also, we are told that Carol bought the other forty dollar shirt [5]:

80 = 30 + 50 (Diane)
60 = 20 + 40 (Emily/Carol)
60 = 10 + 50 (Alice/Betty)
50 = 20 + 30 (Alice/Betty)
50 = 10 + 40 (Emily/Carol)

Carol didn't buy a twenty-dollar shirt with Alice [4]; it must have cost ten dollars [4], and by elimination, we know what price shirts everyone bought:

80 = 30 + 50 (Diane)
60 = 20 + 40 (Emily)
60 = 10 + 50 (Alice)
50 = 20 + 30 (Betty)
50 = 10 + 40 (Carol)

Now, to match prices to colors:

Carol's blue shirt was not ten dollars [2]; it must have been forty dollars. The ten-dollar shirt was not green [2], orange [4], or red [5]; it must have been yellow:

$10: yellow
 20
 30
 40: blue
 50

Alice and Betty did not buy any shirts in common [above], so Alice's fifty-dollar shirt was not yellow [$10], blue [$40], orange [4], or red [5]; it was green.

$10: yellow
 20
 30
 40: blue
 50: green

By elimination, Betty's twenty- and thirty-dollar shirts were red and orange, in some order. Emily bought a twenty-dollar shirt, but it was not orange [4]; it must have been red. That leaves the orange shirt at $30:

$10: yellow
 20: red
 30: orange
 40: blue
 50: green

So, to recap:

$80 - Diane: green ($50) and orange ($30)
$60 - Emily: blue and red ($20)
$60 - Alice: green ($50) and yellow ($10)
$50 - Betty: orange ($30) and red ($20)
$50 - Carol: blue and yellow ($10)

Posted by DJ on 2004-03-13 22:36:21