Arithmetic Reasoning Test Improvement

! Sample Test Breakdown

These are the skills and questions for some sample tests.

!! Peterson's Test #1
# take percentage; avoid confusion (negation) - "53% of the 1000 students at Barnett High are girls. How many boys are there in the school?"
# cross-multiply - "If four bananas cost 72¢, how many dozen bananas can be bought for $5.40?"
# cross-multiply (with 1) - "Limes are on sale at a price of 8 limes for $1. How much do two limes cost?"
# distributive property - "Which quantity is NOT equal to 75(32 + 88)?"
# avoid confusion - "A truck with room for 200 bales of hay has room for how many more bales if it is one-half full already?"
# make change (long subtraction) - "Bob buys popcorn for $4.65 using a five-dollar bill. How much change will he receive?"
# cross-multiply (with 1) - "How many 1.5-inch thick boards will fit into a box that is 18 inches tall?"
# cross-multiply - "If potting soil is sold in 20-pound bags for $5.20 each, the price of 160 pounds of potting soil is"
# ignore distractions; reduce fraction; convert units - "A man bought 3 dozen eggs at the store. There are a dozen eggs in each carton. When he got home, he discovered that 2 eggs in each of the cartons were broken. What part of the eggs was not broken?"
# calculate discount - "A jacket costing $96 is discounted by 20 percent. What is the discounted price of the jacket?"
# cross-multiply - "On a house plan on which 2 inches represents 5 feet, the length of a room measures 7 1/2 inches. The actual length of the room, in feet, is"
# calculate discount (compound) - "An appliance store gives a 15% discount off the list price of all of its merchandise. The store gives an additional 30% discount for a floor model. A television set that has a list price of $300 and is a floor model sells for"
# packing - "Craig spent exactly one dollar to buy 3-cent stamps and 5-cent stamps. The number of 5-cent stamps that he could NOT have bought is"
# cross-multiply (with 1) - "A machine punches cards at a rate of 400 per hour. How many hours has the machine been working if it has already punched 1,800 cards?"
# rate arithmetic - "A teacher has 200 tests to grade. If he can grade 40 tests per hour, the number of tests remaining to be graded after he has worked for 3 hours is"
# calculate price increase - "The sticker price of a car is $19,800. If the tax increases the price by 11% and the title increases it by $480, what is the total cost of the car?"
# cross-multiply - "Two inches of track on a scale model railroad represents 20 real miles. On the same model, a distance of 55 real miles is represented by how much track?"
# time arithmetic - "A nurse worked a double shift from 8:45 a.m. Thursday to 3:15 p.m. the next day. If she is paid $20 per hour worked, how much money did she make on this double shift?"
# calculate percentage - "A retailer pays $120 for a stereo and sells it for $195. The retailer's profit is what percent of the price he paid for the stereo?"
# cross-multiply; convert units - "Roy needs to carpet a room that measures 12 feet wide and 15 feet long. What will it cost to carpet the room if carpeting costs $20.80 per square yard?"
# rate arithmetic - "A car that averages 21 miles to the gallon starts a trip with a full 10-gallon tank of gas. If the car travels 150 miles, how many more miles can it go before the tank is empty?"
# profit - "If a man buys lemons at 3 for 30 cents and intends to sell them at 5 for 60 cents, how many lemons does he have to sell in order to make a profit of 50 cents?"
# calculate percentage - "The price of an Allen wrench was reduced from 31 cents to 28 cents. The percent of decrease is approximately"
# unit cost ($) - "Ms. Smith wants to buy 72 ounces of canned corn for the least possible cost. Which of the following should she buy?"
# know ounces in quarts; reduce fractions - "Four fluid ounces is what fractional part of one quart?"
# cross-multiply - "At a price of 99 cents per dozen eggs, the cost of 16 eggs is"
# simple interest; avoid confusion - "A man invests $10,000 in a bond that pays him $5.12 annually for every $100 he invests. How much is he paid at the end of the year?"
# packing - "A plumber needs eight pieces of pipe, each 3 feet 2 inches long. If pipe is sold only in sections of 10 feet each, how many sections must he buy?"
# average two different rates - "A truck driver travels a certain distance at 60 miles per hour and returns over the same road at 40 miles per hour. What is her average rate for the round trip?"
# work equation (cross-multiply) - "Six tractors can plow a cornfield in 8 hours if the farmers all work together. How many hours will it take 4 tractors to do the job?"
!! Peterson's Test #2
# converting fraction to decimal; multiplying decimals - "If a recipe for a cake calls for 2 1/2 cups of flour, and Mary wishes to make three cakes, she must use how many cups of flour?"
# packing; common sense reasoning - "The toll on the Prospect Street Bridge is $1.00 for car and driver and $.75 for each additional passenger. How many people were riding in a car for which the toll was $3.25?"
# time calculation - "Yesterday morning, Janette got up at 7:42 A.M. and went to bed at 10:10 P.M. How much time went by between her getting up and going to bed?"
# calculating discount - "A woman wins a contest prize of $1,000. If 20 percent of the prize is withheld for taxes, the amount the woman actually receives is"
# money math - "A change machine dispensed 25 quarters, 12 dimes, 15 nickels, and 50 pennies. What is the total value of the change dispensed?"
# cross-multiply (with 1) - "A box of 24 nectarines costs $6.00. How much does each nectarine cost?" (good example of with-1, also reverse-plugging and multiply-is-easier-than-divide)
# calculate percent; simple interest - "A company borrows $10,000 from a bank at an annual rate of 8 percent. How much interest will the company owe after one year?"
# avoid confusion; convert units; reduce fractions - "A case of water bottles consists of 4 dozen bottles. If 7 basketball players each drank 6 bottles of water, what part of a dozen was left?"
# geometry (calculate perimeter) - "The side of a square is 20 cm. Find its perimeter."
# multiply; common sense - "Fifteen books with widths of 2 cm each can be arranged on a shelf with no room left over. Find the length of the shelf."
# calculate profit; avoid confusion; money math - "If a muffin is bought at $1.00 and resold at $1.20, find the profit made on 12 dozen muffins."
# convert units (tons to pounds) - "The weight of the load carried by a truck is 15.26 tons. What is the weight of the load in pounds?"
# cross-multiply - "A cake requires two ingredients in the ratio 2:3. If the requirement of the first ingredient is 20 ounces, find the requirement of the second ingredient in ounces."
# geometry (calculate volume) - "Find the volume of a rectangular solid that is 12 meters long, 9 meters wide, and 8 meters high."
# cross-multiply - "In a town, 30% of the members of the population are school-going children. If the number of school-going children is 4,500, find the population of the town."
# calculate percentage - "The local government decides to spend 10% of the budget on education, 30% on healthcare, 20% on municipal facilities, and the remaining money on public transport. If the total budget is $100,000, find the amount spent on public transportation."
# calculate perimeter; money math - "If fencing costs $9.00 per yard, what would be the total cost of the fencing needed to enclose a rectangular area that measures 46 feet by 34 feet?"
# d=rt formula - "Riding a bike to school takes 25 minutes. Coming home only takes 20 minutes. If the trip to school is 3 miles long, what is the average speed, in miles per hour, for the whole trip?"
# cross-multiply; avoid confusion (add $15 to the 80%) - "If a discount of 20% off the marked price of a jacket saves a man $15, how much did he pay for the jacket?"
# cross-multiply - "A graph shows a company's progress toward a sales goal. If 2 inches on the graph represents $10,000 in sales, how much does 19 inches represent in sales?"
# calculate percentage - "Jeanette's salary was increased from $24,000 to $26,000. The percent increase was most nearly"
# algebra - "Judy is three times her daughter's age. If the difference between their ages is 30, how old is the daughter?"
# work formula - "Pipe M can fill a tank in 36 hours, and pipe N can fill it in a certain time. If both pipes are opened simultaneously, the tank gets filled in 24 hours. Find the time it takes pipe N alone to fill the tank."
# simple interest - "A principal of $500, kept at a 4% annual rate of interest, earns $40 as interest. Find the number of years for which the principal was kept."
# geometry; algebra; reasoning - "A farmer owns two rectangular fields. The length of the larger field is twice the length of the smaller field, and the width of the larger field is four times the width of the smaller field. If the smaller field has an area of 1 acre, what is the area of the larger field?"
# money math - "Pencils are bought at 35 cents per dozen. If every lot of 3 pencils is sold for 10 cents, find the total profit on 5.5 dozen pencils."
# divide decimal; ratio/reduce fraction - "The price of a candy bar is $1.00. The price of a pack of a dozen of the same candy bars is $9.60. What is the ratio of the amount saved in buying a dozen pack to the amount spent in buying 12 candy bars individually?"
# reasoning; reduce fraction - "In a group of 15 students, 7 can speak Spanish, 8 can speak French, and 3 can speak neither of the two languages. What fraction of the group can speak both French and Spanish?"
# cross-multiply; convert units - "If 48 feet are represented by 12 inches on a scale drawing, how many feet are represented by 1/4 inch on the drawing?"
# reasoning; work formula - "If four women can wallpaper 2 rooms in 1 day, how many women, working at the same uniform rate, can wallpaper 12 rooms in 2 days?"

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Arithmetic Reasoning Test Improvement