Arithmetic Reasoning

Marlo pays $750 rent each month. Bea's rent is 12% higher. What is the ratio of Marlo's rent to Bea's rent? a. 5:6 b. 15:16 c. 25:28 d. 25:26

First find Bea's rent. 12% of $750 = (12/100) × 750 = $90. So Bea's rent = $750 + $90 = $840. The ratio of Marlo's rent to Bea's rent is 750:840. Dividing by the common factor 30, 750:840 = 25:28.

Matthew's dad is 5 times as old as him. If the difference of their ages is 28, how old is Matthew? a. 4 b. 5 c. 6 d. 7

Let Matthew's age be x. Then Matthew's dad is 5x years old. The difference of their ages is 28. Therefore 5x - x = 28. Solving this equation we get, 4x = 28; x = 7. So Matthew is 7 years old.

Mr. Vlasic needs to buy 2 pens each for the 17 students in his class. If pens come in packs of 6 and each pack costs $2.35, what is the minimum amount that Mr. Vlasic must spend? a. $11.75 b. $14.10 c. $7.05 d. $15.00

Mr. Vlasic needs to but 34 pens in all. Since the pens come in packs of 6, Mr. Vlasic must buy at least 6 packs (36 pens) in order to have enough pens for all his students. So Mr. Vlasic must spend at least 6 × $2.35 = $14.10.

The scale of the model of a car is 1:24. If the full-size car is 12 ft long, how long is the model? a. 4 inches b. 5 inches c. 6 inches d. 7 inches

Set up the proportion 1/24 = x/12. To solve for x, multiply both sides of the equation by 24 to get 1 = 2x. So x = 1/2 ft = 6 inches.

A cake recipe calls for 5 cups of flour to bake 2 cakes. How many cups of flour will be needed to bake 7 cakes? a. 35 b. 24.5 c. 17.5 d. 12

Set up the proportion 5/2 = x/7. To solve for x, multiply both sides of the equation by 14 to get 35 = 2x. So x = 17.5.

300 school children went on a field trip. 30% of them were first graders, 45% second graders, and the rest were third graders. How many more first graders were there than third graders? a. 5 b. 15 c. 30 d. 45

Since 45% + 30% = 75%, 75% of the children were first and second graders. The percentage of third graders = 100% - 75% = 25%. The number of third graders = (25/100) × 300 = 75. The number of first graders = (30/100) × 300 = 90. So there were 90 - 75 = 15 more first graders than third graders.

A bag contains 6 black marbles and 4 white marbles. Sally takes out a black marble and does not put it back. What is the probability that the next marble she picks will also be black? a. 6/10 b. 9/25 c. 1/2 d. 5/9

Since Sally has taken out a black marble, the bag now contains 5 black marbles and 4 white marbles. So the probability of the next marble being black is 5/9.

A school garden had been divided into 7/8 square meter plots for students. If the area of the garden is 210 square meters, how many students can get plots? a. 240 b. 210 c. 184 d. 78

Since the 210 square meter garden has been divided into plots of area 7/8 square meter each, the number of plots is 210 divided by 7/8. To divide by 7/8, flip the fraction to 8/7 and multiply. 210 × (8/7) = 240. So there are 240 plots.

Rosita buys 300 feet of yarn for a craft project. If the yarn costs 12 cents a yard, how much does Rosita spend? a. $36.00 b. $1,200.00 c. $360.00 d. $12.00

Since the cost of the yarn is given in yards, first convert the length of yarn Rosita bought into yards. Since 3 feet = 1 yard, 300 feet = 300/3 = 100 yards. Rosita spent 100 × 12 cents = 1200 cents = $12.00.

Mangoes are sold at $8.40 a dozen. How much will 15 mangoes cost? a. $12.60 b. $11.50 c. $10.70 d. $10.50

The cost of one mango = $8.40/12 = $0.70. The cost of 15 mangoes = $0.70 × 15 = $10.50.

A dress that costs $155.00 is on sale with a discount of 25%. What is the sale price of the dress? a. $38.75 b. $116.25 c. $130.00 d. $122.50

The discount amount is 25% of $155 = (25/100) × $155 = $38.75. So the sale price of the dress = $155 - $38.75 = $116.25.

Dana and Megan have to fill 500 envelopes for a charity. At the end of the morning Dana has filled 3/20 of the envelopes and Megan has filled 1/4 of them. How many envelopes have they filled together? a. 75 b. 125 c. 200 d. 50

The fraction of envelopes Dana and Megan have filled together = 3/20 + 1/4. Expressing this sum in terms of the common denominator 20, 3/20 + 1/4 = 3/20 + 5/20 = 8/20 = 2/5. 2/5 of 500 = (2/5) × 500 = 200. So Dana and Megan have filled 200 envelopes together.

Family Video stocks 1003 drama movies, 518 science fiction movies and 253 children's movies. How many more drama titles than children's titles does Family Video have in stock? a. 750 b. 1003 c. 485 d. 265

There are 1003 drama movies and 253 children's movies. So Family Video has 1003 - 253 = 750 more drama titles than children's titles.

Brandon earns $1,050 a week and Brad earns $160 a day. If both of them work 8 hours a day, 5 days a week who earns a higher hourly wage? How much higher is it? a. Brad; $6.25 b. Brandon; $6.25 c. Brad; $10.00 d. Brandon; $10.00

To find out who earns more and by how much, find out each person's hourly wage. Brandon earns $1,050 for 8 × 5 = 40 hours of work. So his hourly wage is $1,050/40 = $26.25. Brad earns $160 for 8 hours of work. So his hourly wage is $160/8 = $20. Therefore, Brandon earns $26.25 - $20.00 = $6.25 more an hour.

Mrs. Lafferty's 5 children are 6, 8, 14, 15, and 17 years old. What is their average age? a. 14 b. 13 c. 12 d. 11

To find the average age, add the ages of all the children and divide by the number of children. The sum of the ages of the children = 6 + 8 + 14 + 15 + 17 = 60. So their average age = 60/5 = 12

On the throw of a six-sided die, what is the probability that you will roll a number less than 3? a. 1/2 b. 1/6 c. 1/3 d. 2/3

To find the probability, divide the number of acceptable outcomes by the total number of possible outcomes. The acceptable outcomes are 1 and 2, so there are 2 of them. The total number of possible outcomes is 6. So the probability of rolling a number less than 3 is 2/6 which reduces to 1/3.