On a Tuesday, an accountant has exactly seven bills -- numbered 1 through 7 -- to pay by Thursday of the same week. The accountant will pay each bill only once according to the following rules:Either three or four of the seven bills must be paid on Wednesday, the rest on Thursday.Bill 1 cannot be paid on the same day as bill 5.Bill 2 must be paid on Thursday.Bill 4 must be paid on the same day as bill 7.If bill 6 is paid on Wednesday, bill 7 must be paid on Thursday.If bill 6 is paid on Wednesday, which one of the following bills must also be paid on Wednesday?
Answer(s): B
Again, we have bill 6 on Wednesday. You can use the work from the previous question; it's the same sketch.Choice [3], which has bill 3 paid on Wednesday, is correct.
On a Tuesday, an accountant has exactly seven bills -- numbered 1 through 7 -- to pay by Thursday of the same week. The accountant will pay each bill only once according to the following rules:Either three or four of the seven bills must be paid on Wednesday, the rest on Thursday.Bill 1 cannot be paid on the same day as bill 5.Bill 2 must be paid on Thursday.Bill 4 must be paid on the same day as bill 7.If bill 6 is paid on Wednesday, bill 7 must be paid on Thursday.If bill 4 is paid on Thursday, which one of the following is a pair of bills that could also be paid on Thursday?
If bill 4 is paid on Thursday, then so is bill 7 (Rule 4). Again, that's four bills on Thursday (2, 7, 4, and 1/5), so the rest (6, 3, and 1/5) must be on Wednesday. Now we need a pair of bills that could be paid on Thursday.
On a Tuesday, an accountant has exactly seven bills -- numbered 1 through 7 -- to pay by Thursday of the same week. The accountant will pay each bill only once according to the following rules:Either three or four of the seven bills must be paid on Wednesday, the rest on Thursday.Bill 1 cannot be paid on the same day as bill 5.Bill 2 must be paid on Thursday.Bill 4 must be paid on the same day as bill 7.If bill 6 is paid on Wednesday, bill 7 must be paid on Thursday.Which one of the following statements must be true?
Answer(s): C
This question provides us with no new information, so unfortunately there's nothing for us to do but test out each choice. The choices are in if/then form, so this could take some time.
Two mannequins -- 1 and 2 -- will be dressed for display in outfits chosen from ten articles of clothing. Each article is in exactly one of three colors: navy, red, or yellow. There are three hats -- one in each color; three jackets -- one in each color; three skirts -- one in each color; and one red tie. Each mannequin wears exactly one of the hats, one of the jackets, and one of the skirts. Furthermore, their outfits must meet the following restrictions:Neither mannequin wears all three colors.Each mannequin wears a hat in a different color from the jacket it wears.Mannequin 2 wears the navy skirt.Mannequin 1 wears the tie.Which one of the following could be complete outfits for the two mannequins?
Answer(s): D
First up is a standard acceptability question, which the testmaker could have made harder by only providing information on one of the mannequins, but so be it. Our Method for acceptability questions applies here: take each rule and see which choices it eliminates.Rule 1 kills choice [mannequin 1: navy hat, red jacket, yellow skirt, red tie mannequin 2: red hat, navy jacket, navy skirt], which gives all three colors to mannequin 1.Rule 2 kills choices [mannequin 1: red hat, red jacket, yellow skirt, red tie mannequin 2: yellow hat, navy jacket, navy skirt]. and [mannequin I: yellow hat, yellow jacket, red skirt mannequin 2: red hat, navy jacket, navy skirt], which both contain a mannequin with the same color hat and jacket.Rule 3 kills choice [mannequin 1: red hat, yellow jacket, red skirt, red tie mannequin 2: yellow hat, navy jacket, yellow skirt], which gives mannequin 2 a yellow skirt, and we're done! Option [mannequin 1: yellow hat, red jacket, yellow skirt, red tie mannequin 2: red hat, navy jacket, navy skirt] remains and is correct.
Two mannequins -- 1 and 2 -- will be dressed for display in outfits chosen from ten articles of clothing. Each article is in exactly one of three colors: navy, red, or yellow. There are three hats -- one in each color; three jackets -- one in each color; three skirts -- one in each color; and one red tie. Each mannequin wears exactly one of the hats, one of the jackets, and one of the skirts. Furthermore, their outfits must meet the following restrictions:Neither mannequin wears all three colors.Each mannequin wears a hat in a different color from the jacket it wears.Mannequin 2 wears the navy skirt.Mannequin 1 wears the tie.Which one of the following could be true of the mannequins' outfits?
Answer(s): E
This one must be attacked choice by choice, and wouldn't be a bad one to postpone:
Two mannequins -- 1 and 2 -- will be dressed for display in outfits chosen from ten articles of clothing. Each article is in exactly one of three colors: navy, red, or yellow. There are three hats -- one in each color; three jackets -- one in each color; three skirts -- one in each color; and one red tie. Each mannequin wears exactly one of the hats, one of the jackets, and one of the skirts. Furthermore, their outfits must meet the following restrictions:Neither mannequin wears all three colors.Each mannequin wears a hat in a different color from the jacket it wears.Mannequin 2 wears the navy skirt.Mannequin 1 wears the tie.If mannequin 1 wears the navy jacket, which one of the following could be true?
If mannequin 1 gets the navy jacket, then mannequin 1's colors are red and navy. So [Mannequin 1 wears the yellow hat.] and [Mannequin 1 wears the yellow skirt.], which give mannequin 1 yellow clothing, are impossible.One more deduction leads to the correct answer. Mannequin 2 gets either a navy hat or a navy jacket (Key Deductions).Here, mannequin 1 gets the navy jacket, and so mannequin 2 gets the navy hat. That kills [Mannequin 2 wears the red hat.]. and [Mannequin 2 wears the yellow hat.]So [Mannequin 2 wears the yellow jacket.] is correct.
Two mannequins -- 1 and 2 -- will be dressed for display in outfits chosen from ten articles of clothing. Each article is in exactly one of three colors: navy, red, or yellow. There are three hats -- one in each color; three jackets -- one in each color; three skirts -- one in each color; and one red tie. Each mannequin wears exactly one of the hats, one of the jackets, and one of the skirts. Furthermore, their outfits must meet the following restrictions:Neither mannequin wears all three colors.Each mannequin wears a hat in a different color from the jacket it wears.Mannequin 2 wears the navy skirt.Mannequin 1 wears the tie.If all four of the red articles of clothing are included in the two mannequins' outfits, which one of the following must be true?
If there are four red items worn, then someone gets the red hat, someone gets the red jacket, and someone gets the red skirt. Since mannequin 2 gets the navy skirt, mannequin 1 gets the red skirt, but that's not one of the choices. What else do we know? We know that mannequin 2's hat and jacket are different colors (Rule 2), and that one of those colors is navy. What's the other color? It can't be yellow, since that would force mannequin 1 to have a red hat and a red jacket in violation of Rule 2. So mannequin 2's colors are red and navy, which means that mannequin 2 wears no yellow clothing, and option [Mannequin 2 wears no yellow articles of clothing.] is correct. The other choices are possible only.
Two mannequins -- 1 and 2 -- will be dressed for display in outfits chosen from ten articles of clothing. Each article is in exactly one of three colors: navy, red, or yellow. There are three hats -- one in each color; three jackets -- one in each color; three skirts -- one in each color; and one red tie. Each mannequin wears exactly one of the hats, one of the jackets, and one of the skirts. Furthermore, their outfits must meet the following restrictions:Neither mannequin wears all three colors.Each mannequin wears a hat in a different color from the jacket it wears.Mannequin 2 wears the navy skirt.Mannequin 1 wears the tie.If mannequin 2 wears the red jacket, then mannequin 1 must wear the
If mannequin 2 gets the red jacket, then mannequin 2's colors are red and navy, and so mannequin 2 must get the navy hat, which eliminates option [navy hat] and tells us that mannequin 1's hat is either red or yellow.Could it be yellow? If it were yellow, then we wouldn't be able to pick a color for mannequin 1's jacket: that jacket couldn't be yellow (Rule 2), navy (Rule 1) or red, since mannequin 2 has the red jacket. So the only option for mannequin 1's hat is red.
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