ACT and SAT Math Tips: Holiday Dilemmas

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We have a special SAT Math and ACT MathHow to hone your SAT and ACT Math skills over Winter Break (Christmas present) post today from our senior curriculum developer (and VP!), Jon Denning. He'll help you get into the test prep spirit with a little winter break math.

Everyone at PowerScore wishes you a happy holiday!  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 little 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 74th ring be?

A)  red

B)  blue

C)  yellow

D)  green

E)  purple

 Bragging Lights

Your parents 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 your mom insists 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, your dad has hung the lights himself, taking 8 hours. Last year he threw his back out, and your mom hung the lights in 6 hours. This year, how long will it take them to hang the lights if they 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

seats1

 

 

 

 

 

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

cyl1

 

 

 

 

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

71st ring = red

72nd ring = blue

73rd ring = yellow

74th ring = green

The 74th ring is green.

 

Bragging Lights Solution: A

Your mom can do the whole house by herself in 6 hours, but now she has help, so she’ll be done before 6 hours. This eliminates (D) and (E). How much can each person do in ONE hour? Dad does all the lights in 8 hours, so he can do 1/8 of the lights in one hour. Similarly, your mom can do all of the lights in 6 hours, so she can finish 1/6 of the lights in one hour. This is their rate. Now find their rate together:  1/8 + 1/6 = 3/24 + 4/24 = 7/24.

The time it takes them together is an inverse of their 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

seats2

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.

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