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.
The only possible combinations for purchase are as follows:
50,40 = 90
50,30 = 80
50,20 = 70
50,10 = 60
40,30 = 70
40,20 = 60
40,10 = 50
30,20 = 50
30,10 = 40
20,10 = 30
From Clue 1, nobody spent $30 or $40, as these values do not duplicate. Eliminating these leaves only two combinations that include $10 -- 40,10 and 50,10. Since two of each were sold, both of these combinations exist in the purchases. It follows from Clue 1 that 40,20 and 30,20 are also included, as these are the only other values that reach $60 and $50. These four combinations have two of every number except 50 and 30, which is Diane's total (Clue 1). So, we know the final combinations are:
50,30 Diane
50,10
40,20
40,10
30,20
Diane and Emily bought none of the same shirt (Clue 3), so Emily cannot have the combinations of 50,10 or 30,20. Thus, she either bought the 40,20 combination or the 40,10 combination. From Clue 5, we know that Carol also bought a $40 shirt, so she is also either the $40,10 or $40,20 combination. However, Alice bought one common shirt with Carol, which did not cost $20 (Clue 4). It cannot be the $40 shirt, as Carol and Emily purchased the $40 shirts, so it has to be $10. Thus, we now know the following:
50,30 Diane
40,20 Emily
40,10 Carol
50,10 Alice
30,20 Betty
Alice and Emily did not buy Orange (Clue 4), which means that the Orange shirts do not cost 40,20,50, or 10. Thus the Orange shirts cost 30, and were purchased by Betty and Diane. Betty bought a Red shirt (Clue 5), so the red shirts cost $20, and were purchased by Betty and Emily. Carol bought a Blue shirt, which did not cost $10 (Clue 2). Thus it cost $40. Carol did not buy the green shirt (Clue 2), and from above we know that she did not purchase red or orange. Thus, the $10 shirt is yellow, and the $50 shirt is green.
The final combinations
Diane - $50 (Green) and $30 (Orange) $80
Emily - $40 (Blue) and $20 (Red) $60
Alice - $50 (Green) and $10 (Yellow) $60
Carol- $40 (Blue) and $10 (Yellow) $50
Betty $30 (Orange) and $20 (Red) $50
Solution
