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This is the pretest for the 2014-2015 Oak Hill Math Bowl team. Do your best!
Questions and Answers
1.
I'm thinking of a number with 3 digits. The first digit is odd. The last two digits are even. The sum of the first and last digits is 13. The product of the last two digits is 8. The difference of the first and last digits is 5.What is my secret number?
A.
924
B.
742
C.
518
D.
524
Correct Answer A. 924
Explanation The secret number is 924. The first digit is odd, which means it can only be 9. The last two digits are even, and their product is 8, so the possibilities are 28, 48, 68, and 88. However, the sum of the first and last digits is 13, so the only possible combination is 92. Lastly, the difference between the first and last digits is 5, confirming that the secret number is indeed 924.
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2.
Solve for x: x/200 = 42%
A.
4.2
B.
8.4
C.
42
D.
84
Correct Answer D. 84
Explanation To solve for x, we can start by multiplying both sides of the equation by 200 to get rid of the fraction. This gives us x = 200 * 42%, which simplifies to x = 200 * 0.42. Multiplying 200 by 0.42 gives us 84, so the value of x is 84.
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3.
While walking on the beach, Ken finds 1 seashell on the 1st day. He finds 2 seashells on the 2nd day, 5 seashells on the 3rd day, 14 seashells on the 4th day, and 41 seashells on the 5th day. If the pattern continues, how many seashells will Ken find on the 6th and 7th days?
A.
122 shells on the 6th, 365 shells on the 7th
B.
81 shells on the 6th, 243 shells on the 7th
C.
77 shells on the 6th, 122 shells on the 7th
D.
36 shells on the 6th, 45 shells on the 7th
Correct Answer A. 122 shells on the 6th, 365 shells on the 7th
Explanation The pattern in the number of seashells Ken finds each day follows a sequence where each term is obtained by multiplying the previous term by 3 and then subtracting 1. On the 6th day, Ken will find 41 * 3 - 1 = 122 seashells. On the 7th day, he will find 122 * 3 - 1 = 365 seashells.
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4.
Chris went to the grocery store to buy 3 items. Indiana charges a 7% sales tax on nonfood items. Chris bought 2 food items costing $1.21 and $1.94. He bought 1 nonfood item for $2.57. How much will he spend at the store?
A.
$5.72
B.
$5.89
C.
$5.90
D.
Not given
Correct Answer C. $5.90
Explanation Chris bought 2 food items costing $1.21 and $1.94, which adds up to $3.15. He also bought 1 nonfood item for $2.57. The total cost of the items before sales tax is $3.15 + $2.57 = $5.72. Indiana charges a 7% sales tax on nonfood items, so the sales tax on the nonfood item is $2.57 * 0.07 = $0.18. Therefore, the total amount Chris will spend at the store, including sales tax, is $5.72 + $0.18 = $5.90.
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5.
For plumbing repairs in the home, Mr. Fix-it charges $35 an hour plus a service-call charge. After working 3 hours in Mrs. Plummer’s house, he charged her $130. How much does Mr. Fix-it charge for a service call?
A.
$20
B.
$25
C.
$30
D.
Not given
Correct Answer B. $25
Explanation Based on the given information, Mr. Fix-it charges $35 an hour plus a service-call charge. After working 3 hours and charging $130, we can subtract the cost of the hours worked ($35 x 3 = $105) from the total charged to find the service-call charge. $130 - $105 = $25. Therefore, Mr. Fix-it charges $25 for a service call.
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6.
Which of the following sets of fractions are equivalent to 6/8?
A.
21/28, 6/10, 5/55, 21/35, 24/40
B.
1/2, 1/5, 4/20, 12/36, 4/12
C.
3/4, 9/12, 12/16, 15/20, 18/24
D.
36/48, 12/16, 9/81, 2/3, 12/16
Correct Answer C. 3/4, 9/12, 12/16, 15/20, 18/24
Explanation The fractions in the set 3/4, 9/12, 12/16, 15/20, 18/24 are equivalent to 6/8 because they can all be simplified to the same value. When we simplify each fraction, we find that 3/4, 9/12, 12/16, 15/20, and 18/24 are all equal to 3/4. Therefore, this set of fractions is equivalent to 6/8.
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7.
Jason enrolled in the U Drive It driving school. He drove 2,890 miles the first week of June. He drove 3,223 miles the second week and 4,998 miles the third week. His goal is to drive 12,000 miles in June. How many more miles does he have to drive to reach his goal in June?
A.
500 miles
B.
889 miles
C.
900 miles
D.
700 miles
Correct Answer B. 889 miles
Explanation Jason drove a total of 2,890 + 3,223 + 4,998 = 11,111 miles in the first three weeks of June. His goal is to drive 12,000 miles in June. Therefore, he still needs to drive 12,000 - 11,111 = 889 miles to reach his goal.
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8.
If the clock tower chimes twice every 15 minutes, how many times will it chime in one day?
A.
96
B.
192
C.
360
D.
720
Correct Answer B. 192
Explanation The clock tower chimes twice every 15 minutes, which means it chimes 4 times every 30 minutes. In one hour, it will chime 8 times. Since there are 24 hours in a day, the clock tower will chime 8 times per hour multiplied by 24 hours, which equals 192 times in one day.
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9.
There are 84 legs in a dog show ring that has an equal number of people and dogs. How many dogs are there?
A.
14 dogs
B.
21 dogs
C.
28 dogs
D.
42 dogs
Correct Answer A. 14 dogs
Explanation Since there are an equal number of people and dogs in the dog show ring, we can assume that each person has 2 legs and each dog has 4 legs. Therefore, the total number of legs in the ring would be twice the number of people plus four times the number of dogs. If there are 84 legs in total, and each person has 2 legs, then the number of people would be 84/2 = 42. Since there are an equal number of dogs and people, there must be 42 dogs as well. Therefore, the correct answer is 14 dogs.
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10.
For Christmas gifts, Dave made and delivered slide show DVDs to his friends. He delivered ½ of the DVDs on Friday and 1/3 of the DVDs on Saturday. On Sunday, he delivered the last 2 DVDs. In all, how many DVDs did he make and deliver?
A.
6 DVDs
B.
9 DVDs
C.
11 DVDs
D.
12 DVDs
Correct Answer D. 12 DVDs
Explanation Dave delivered half of the DVDs on Friday and one-third on Saturday. This means that the remaining DVDs were delivered on Sunday. Since he delivered 2 DVDs on Sunday, it means that the remaining DVDs must be 2 as well. Therefore, the total number of DVDs that Dave made and delivered is 2 (Sunday) + 2 (remaining) + 6 (Friday) + 3 (Saturday) = 12 DVDs.
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11.
What is 13.7% of 500?
A.
6.85
B.
68.5
C.
685
D.
6,850
Correct Answer B. 68.5
Explanation To find 13.7% of 500, we can multiply 500 by 0.137. This gives us 68.5, which is the correct answer.
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12.
The average monthly temperature in Indianapolis during April is 12.2 degrees Celsius. Find the average temperature in degrees Fahrenheit using C=12.2 in the expression 1.8C + 32.
A.
21.9 degrees F
B.
33.9 degrees F
C.
42.2 degrees F
D.
53.96 degrees F
Correct Answer D. 53.96 degrees F
Explanation To convert Celsius to Fahrenheit, we use the formula F = 1.8C + 32. Plugging in the given average temperature of 12.2 degrees Celsius, we get F = 1.8(12.2) + 32 = 21.96 + 32 = 53.96 degrees Fahrenheit. Therefore, the average temperature in degrees Fahrenheit is 53.96 degrees F.
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13.
The scale of a map is 1 inch = 50 miles. If the distance between two cities is 5 ½ inches, what is the actual mileage?
A.
50 miles
B.
100 miles
C.
250 miles
D.
275 miles
Correct Answer D. 275 miles
Explanation The scale of the map is 1 inch = 50 miles. If the distance between two cities is 5 Â½ inches, we can calculate the actual mileage by multiplying the distance on the map by the scale. Therefore, 5 Â½ inches multiplied by 50 miles per inch equals 275 miles.
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14.
Liesel read 4 books over Spring Break. The first book had 98 pages, the second had 102 pages, the third had 54 pages, and the fourth had x pages. The mean number of pages was 90. Find x. (Hint: The mean of a set of items is determined by findingtheir sum, then dividing by the numbers of items.)
A.
106 pages
B.
90 pages
C.
85 pages
D.
64 pages
Correct Answer A. 106 pages
15.
Bob needs four pieces of wire each 218 inches long. Wire at the hardware store is sold only by the foot. How many feet of wire does Bob need?
A.
70 ft.
B.
72 ft.
C.
73 ft.
D.
75 ft.
Correct Answer C. 73 ft.
Explanation Bob needs four pieces of wire, each 218 inches long. Since wire is sold by the foot, we need to convert inches to feet. There are 12 inches in a foot, so each piece of wire is 218/12 = 18.17 feet long. Since Bob needs four of these pieces, he needs a total of 4 * 18.17 = 72.68 feet of wire. Rounding up to the nearest whole number, Bob needs 73 feet of wire.
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16.
Some veterinarians find a dog’s “dog age” by assigning 12 dog years for each of the dog’s first two people years; after that, each human year adds 4 dog years. Using that information, what is the “dog age” of a terrier who has lived 13 human years?
A.
52 dog years
B.
64 dog years
C.
68 dog years
D.
156 dog years
Correct Answer C. 68 dog years
Explanation According to the given information, for the first two human years of a dog, each year is equivalent to 12 dog years. After that, each human year is equivalent to 4 dog years. Therefore, for the first two human years, the dog would be 24 dog years old (2 human years x 12 dog years per year). For the remaining 11 human years, the dog would be 44 dog years old (11 human years x 4 dog years per year). Adding these two values together, the dog would be 68 dog years old.
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17.
Susan and friends bought 5 hamburgers, 2 hotdogs, 3 salads, 7 fries, and 7 drinks. If the sales tax is 5%, plus they then leave a 15% tip on the amount before tax, what is the total cost? The menu is shown below.Food PriceHamburgers $2.50Hotdogs $1.75French Fries $1.65Chili $1.25Salad $1.00All drinks $1.35
A.
$40
B.
$42
C.
$46
D.
$48
Correct Answer D. $48
Explanation The total cost can be calculated by adding up the cost of each item and then adding the sales tax and tip. The cost of 5 hamburgers is 5 * $2.50 = $12.50. The cost of 2 hotdogs is 2 * $1.75 = $3.50. The cost of 3 salads is 3 * $1.00 = $3. The cost of 7 fries is 7 * $1.65 = $11.55. The cost of 7 drinks is 7 * $1.35 = $9.45. The total cost before tax is $12.50 + $3.50 + $3 + $11.55 + $9.45 = $40. The sales tax is 5% of $40, which is $2. The total cost after tax is $40 + $2 = $42. The tip is 15% of $42, which is $6.30. The final total cost is $42 + $6.30 = $48.
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18.
Kiley left home at 6:00 A.M. Her flight leaves at 8:00 A.M. She has to be at a meeting at 10:00 A.M. Her flight lands at 9:26 A.M. How long was her flight?
A.
1 hour
B.
1 1/2 hours
C.
1 hour 26 minutes
D.
4 hours
Correct Answer C. 1 hour 26 minutes
Explanation Kiley left home at 6:00 A.M and her flight landed at 9:26 A.M. To find the duration of her flight, we subtract the departure time from the arrival time. The difference between 9:26 A.M and 6:00 A.M is 3 hours and 26 minutes. Therefore, her flight lasted for 3 hours and 26 minutes, which is equivalent to 1 hour and 26 minutes.
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19.
Maria is 10 years older than Jared. Next year, she will be twice as old as Jared. How old are Maria and Jared now?
A.
Maria is 20 years old; Jared is 10
years old.
B.
Maria is 19 years old; Jared is 9
years old.
C.
Maria is 15 years old; Jared is 5
years old.
D.
Maria is 10 years old; Jared is 20
years old.
Correct Answer B. Maria is 19 years old; Jared is 9
years old.
Explanation Maria is 10 years older than Jared, so if Jared is 9 years old, Maria must be 19 years old. Next year, Jared will be 10 years old and Maria will be 20 years old, which means Maria will be twice as old as Jared. Therefore, Maria is 19 years old and Jared is 9 years old now.
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20.
Trista spent 1/3 of her allowance at the fair. She lent ¼ of what she had left to her friend. She was left with $13.50. How much was her allowance?
A.
$20.00
B.
$25.00
C.
$27.00
D.
$30.00
Correct Answer C. $27.00
Explanation Trista spent 1/3 of her allowance at the fair, which means she spent 2/3 of her allowance. After spending, she lent 1/4 of what she had left to her friend. So, she was left with 3/4 of 2/3 of her allowance, which is equal to $13.50. To find her allowance, we can set up the equation (3/4) * (2/3) * allowance = $13.50. Solving this equation, we get the value of allowance as $27.00.
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