Quantitative: Holiday Dilemmas

Gift Wrapping Wringer

Your dad loves sushi, so you bought him some 10-inch personalized chopsticks for Hanukkah. You want to wrap them in a cylindrical box, which you are shopping for online. All of the cylinders have a base diameter of 6 inches, but they come in various heights, listed in the answer choices below. You want the shortest cylinder that will completely contain the chopsticks. What is the shortest cylinder you can buy?

A)  7 inches

B)  8 inches

C)  9 inches

D)  10 inches

E)  11 inches

Garland Grief

You and your sister are creating a chain of paper rings to hang on the Christmas tree. She is adamant that you must follow her specific color pattern: red—blue—yellow—green—purple—red—blue—yellow—green—purple—etc. If you start with a red ring, what color will the 74^th ring be?

A)  red

B)  blue

C)  yellow

D)  green

E)  purple

Bragging Lights

You  go a little overboard with the Christmas light display in the front yard. Mr. Jones, across the street, uses 50,000 lights in his display. So you nsists that your yard has 50,001 lights (it’s rumored that the astronauts on the International Space Station can see your street from space). In the past, you have hung the lights yourself, taking 8 hours. Last year you threw your back out, and your brother hung the lights in 6 hours. This year, how long will it take you and your brother to hang the lights if you work together?

A)  3  3/7 hours

B)  3  7/9 hours

C)  4  2/5 hours

D)  7 hours

E)  14 hours

New Year’s Eve Dinner Dilemma

Your dad has invited his mother to New Year’s Eve dinner, despite the fact that she does not get along with your mom. He’s asked you to select everyone’s seat at the dinner table using the diagram above; you have to place your parents, your grandma, your brother, your sister, and you. Your parents have to sit at the heads of the table, and your grandma cannot sit on either side of your mom or they might bicker. How many different arrangements are possible?

A)  12

B)  24

C)  48

D)  96

E)  1944

Photo: “Christmas present” courtesty of mac2416

Answer Key

Gift Wrapping Wringer Solution: B

This is a right triangle question. The base of the triangle is 6 (the diameter of the base of the cylinder). The hypotenuse of the triangle is 10 (the length of the chopsticks). PowerScore test takers should recognize the 6:8:10 triangle, but those who do not can perform the Pythagorean Theorem.

a² + b² = c²

6² + b² = 10²

36 + b² = 100

b² = 64

b = 8

The shortest cylinder that will fit the chopsticks is 8 inches.

Garland Grief Solution: D

Every fifth ring is purple. So the 10^th, 15^th, 20^th, 25^th, etc. ring will be purple. That means all multiples of 5 are purple, including the 70^th ring. Therefore:

71^st ring = red

72^nd ring = blue

73^rd ring = yellow

74^th ring = green

The 74^th ring is green.

Bragging Lights Solution: A

Your brother can do the whole house by himself in 6 hours, but now he has help, so he’ll be done before 6 hours. This eliminates (D) and (E). How much can each person do in ONE hour? You do all the lights in 8 hours, so you can do 1/8 of the lights in one hour. Similarly, your brother can do all of the lights in 6 hours, so he can finish 1/6 of the lights in one hour. These are your individual rates. Now find your rate together:  1/8 + 1/6 = 3/24 + 4/24 = 7/24.

The time it takes you together is an inverse of your rate: the inverse of 7/24 is 24/7 or 3 3/7 hours.

New Year’s Eve Dinner Dilemma Solution: B

Draw a diagram and label the people at dinner:

D = dad

M = mom

Y = you

S = sister

B = brother

G = grandma

Start with the heads of the table. On the left side, there are two people who can sit there: M and D. We selected D to sit there, so that means M must sit at the head of the table on the right side.

Since G cannot sit next to M, that leaves Y, S, and B for the top right chair. We put you in that seat, leaving S and B for the bottom right chair. We put S there. Now G enters back into the mix, and either she or B can sit in the top left seat. Ladies first, so we give it to G. That leaves one person—B—for the bottom left chair.

Now multiply the number of possibilities for each seat: 2 x 2 x 3 x 1 x 2 x 1 = 24. There are 24 possible arrangements.