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A comprehensive overview of solving various types of math word problems, including problems involving speed, distance, and time calculations, as well as problems involving the sale of used and new cars, and problems involving the baking of pizzas. A range of mathematical concepts and problem-solving strategies, making it a valuable resource for students preparing for exams or seeking to improve their problem-solving skills. Detailed step-by-step solutions to the problems, as well as explanations of the underlying mathematical principles and reasoning. Overall, this document is a comprehensive and informative resource for anyone interested in improving their math problem-solving abilities.
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The eleventh month of the year is: A. January B. November C. October D. May The correct answer is (B). The eleventh month of the year is November. A shop owner bought some shovels for $5,500. The shovels were sold for $7,300, with a profit of $50 per a shovel. How many shovels were involved? A. 18 B. 36 C. 55 D. 73 E. 90 F. None of these The correct answer is (B). The total profit from the sale is the selling price minus the cost of purchase, which is $7300-$5500= $1800.If the total profit is $1800 and each shovel accounts for $50 profit, the amount of shovels is 1800/50=36. How many states are there in the U.S.A? A. 20 B. 30 C. 40 D. 50 E. 60 The correct answer is (D). The USA has 50 states.
There are three times elephants compared to giraffes in the safari. If there is a total of 88 elephants and giraffes, how many elephants are there in the safari? A. 22 B. 31 C. 43 D. 59 E. 66 F. None of these The correct answer is (E). If there are 3 times as many elephants as there are giraffes, giraffes can be defined as X, and elephants as 3X, and build the following equation: 3X + X = 88 4X = 88 X = 88/ X = 22 As stated above, X stands for the number of giraffes. Thus, there are 22 giraffes. As mentioned in the problem, there are three times as many elephants as there are giraffes in the safari. Thus, to find how many elephants there are in the safari, multiply the number of giraffes by 3: 22 * 3 = 66 66 is the number of elephants in the safari. What is the next number in the series? 5, 15, 10, 13, 15, 11, A. 9 B. 13 C. 10 D. 20 E. 15 F. None of these
First of all, in order to simplify the calculations we can divide all the numbers by a common denominator: 1000, in that way we can get rid of all those annoying zeroes. Now we define the used cars as U (with a price of 7 each) and the new cars as N (with a price of 16 each) Now we can build two equations, the first representing the total price and the second the total amount of cars: a. 7U+16N= b. N+U= 17 So according to the second equation N = 17 - U, and we can now substitute N in the first equation: 7U+16(17-U)=191 ; 7U+272-16U=191 ; 9U=81 ; U=9. 9 used cars were sold. Solving Tip: You could try solving this question by elimination. For starters, since 191 is an odd number and 16 is an even number, then the number of used cars must be odd (even+odd=odd) - which means we can eliminate answers A, D & E. Now that we are left only with B and C, let's try to calculate it for each of these options:
. 37 + 16(17-3) = 245, which means we can eliminate B as an answer. . 57 + 16(17-5) = 227, which means we can eliminate C as an answer. Therefore, the only possible answer is F - none of the above. Joey got a 25% raise to his salary. If his original salary was $1,200, how much was it after the raise was implemented? A. $ B. $ C. $ D. $ E. $ F. None of these The correct answer is (B). 25% equals one quarter and a quarter of 1200 is 1200/4=300. Therefore, an addition of a quarter to 1200 equals 1200+300=1500.
Arrange the following words so that they make a complete sentence. Is the rearranged sentence true or false? Triangle A sides three has A. True B. False The sentence is: A triangle has three sides, which is true. is to JUICE as WHEAT is to BREAD A. Water B. Pitcher C. Supermarket D. Soda E. Orange The correct answer is (E). An orange is used to produce juice like wheat is used to produce bread. In addition, both wheat and oranges must be processed to produce the final product. This eliminates answer (A). Does FAQ mean "frequently asked questions"? A. Yes B. No Yes, FAQ is the acronym for "frequently asked question". ATTRACTION is the opposite of:
There are 2 exact duplicates: 6845 and 45641 If the first two statements are true, is the final statement true? Dave spoke with Sally. Sally spoke with John. Dave did not speak with John. A. Yes B. No C. Uncertain The correct answer is (C) - It is uncertain whether the last statement is true. The first 2 statements do not tell us anything about Dave talking to John, therefore we cannot know if it is true or not. In the following set of words, which word does not belong? A. Affirmation B. Designation C. Approval D. Authorization E. Permission The correct answer is (B). Designation is the act of indicating, while the other words mean confirmation.
is to CLEANING as MEDICINE is to CURING A. Chore B. Dirt C. Soap D. Germs E. Shiny The correct answer is C). Soap is used for cleaning as medicine is used for curing Which one has the biggest diameter? A. The sun B. The moon C. Earth D. Venus E. A basketball The correct answer is (A). The sun has a diameter over than 100 times larger than earth, which has a diameter larger than the all the other answers. Sam and Edna have 56 marbles together. Edna has 6 times more marbles than Sam. How many marbles does Sam have? A. 8 B. 12 C. 32 D. 46 E. 49 F. None of these The correct answer is (A). If Edna has 6 times more marbles than Sam, we can define Sam as X and Edna as 6X, and build the following equation: X+6X=56, therefore X=8.
START is the opposite of... A. Source B. Inception C. Conclusion D. Initiation E. Origin The correct answer is (C). Start means "to begin," so the antonym is conclusion. Inception and origin are synonyms. Source is not related. Therefore, the correct answer is conclusion. IMPERIOUS is the opposite of... A. Arrogant B. Moody C. Subservient D. Quiet E. Stormy The correct answer is (C). The word imperious describes an arrogantly domineering or overbearing person while a subservient person is extremely compliant and submissive. How many of the six pairs listed below are exact duplicates? 3356 3356 87878 87978 909152 989152 7776145 7776145 865656 865656 71829 71829 A. 1 B. 2
The correct answer is (D). The exact duplicates are: 3356; 7776145; 865656; 71829 In the following set of words, which word is different from the others? A. Solemn B. Archaic C. Grave D. Mirthless E. Serious The correct answer is (B). Archaic is a word used to describe something that belongs to an earlier period of time, while the other words are used to describe sad and gloomy states of mind or facial expressions. How many of the five pairs listed below are exact duplicates? 123A3 122A LLO8761 LLO KKA3213 KKA ORR13726B ORR13726B 12AB12AB1 12AB1AB A. 1 B. 2 C. 3 D. 4 E. 5 The correct answer is (B). The exact duplicates are: LLO8761, ORR13726B
Answers A and B can definitely be eliminated as they are too low. Since we only rounded down by 0.05, know that the correct answer will only be slightly larger than 4900. We can therefore conclude with fair certainty that C is the correct answer. An oven can bake 8 pies of thin crust pizza per hour, or 2 pies of deep dish pizza pies per hour. How many hours will it take to prepare an order of 16 thin crust pies and 4 pies of deep dish? A. 4 hours B. 2.5 hours C. 2 hours D. 1 hours The correct answer is (A). Time = work/rate In order to calculate how long it would take to prepare 16 thin crusts, we need to divide 16 by the rate of thin crusts per hour. 16 thin crust pies/8 thin crust pies per hour = 2 hours Similarly, to calculate how long it would take to prepare 4 deep dish pies, we need to divide 4 by the rate of deep dish pies per hour. 4 deep dish pies/2 deep dish pies per hour = 2 hours The number of hours it will take to complete the order is 2 hours + 2 hours = 4 hours John's gross pay for the past month is $4687.24. If $421.78 was deducted from John's gross pay, how much take-home pay did John earn this past month? A. $ 421.
The correct answer is (B). If John's gross pay was $4687.24 and $421.78 was deducted from that amount, John's take-home pay was: $4687.24 - $421.78 = $4265.46. A motorcyclist rode between Flibbertown and Guinevill at a steady pace of 60 miles per hour for 2 hours. After two hours she accelerated to 65 miles per hour for another full hour. What is the distance between those cities? A. 150 miles B. 180 miles C. 165 miles D. 185 miles E. None of the above The correct answer is (D). In order to solve the question, we need to separate the two stages. The first stage is: the two-hour ride at a rate of 60 mph; the second stage is the one- hour ride at a rate of 65 mph. Time (hours) Speed Distance Stage 1 3 X 3X Stage 2? 2X 3X If we sum up the distance of both stages, we will find the distance between the cities. The first stage is calculated using the formula Time * Speed = Distance: 2 hours X 60 miles per hour=120 miles The second stage is calculated using the same formula:
The average of the 4 stock prices is $100, and therefore the sum of the stock prices is $400. If the value of the Drone stock is $70, we can conclude that the sum of the remaining three stock prices is $330. If the value of three of them is $330, the average price is $110. Quick tip: If an average is provided followed by the number of values, the sum of the values can be calculated. The sum is calculated as follows: Number of values X Average=Sum of the values. The volume of a rectangle prism is 100 cubic inches. Which of the alternatives is its greatest possible length? A. 100 B. 10 C. 20 D. 60 E. 50 The correct answer is (A). In order to answer the question correctly, we need to understand it. In order to find out the greatest possible size, we have to think in extremes. The volume formula of a rectangular prism is: Length Width Depth = Volume. If the volume is already set at 100 cubic inches, we can obtain from the formula the greatest value for length if we set the lowest values for width and depth. Theoretically, both the width and depth may each be 1 inch, and the length 100 inches; thus the correct answer is A. Which THREE of the following words have similar meanings? A. Rapidly B. Exceedingly C. Hastily D. Eventually E. Swiftly
The correct answers are: (A) rapidly, (C) hastily, and (E) swiftly. All three words are adverbs that mean "quickly." "Exceedingly" does not belong because it means "extremely." "Eventually" is not related to speed but to chronological order; therefore, it does not belong. In the following set of words, which word is different from the others? A. Inflation B. Interest C. Debt D. Budget E. Drought The correct answer is (E). All of the other answers are closely related to money, while drought is related to the weather/climate. This question is confusing because a drought can bring on financial difficulties to a country, causing inflation and debt, but a drought is simply a period of dry weather. Which alternative includes all the states that border Oklahoma? A. Texas, New Mexico, Arkansas, Missouri, Kansas, Colorado B. Texas, Arkansas, Missouri, Kansas, Louisiana, Colorado C. Texas, New Mexico, Mississippi, Missouri, Kansas, Colorado D. Texas, New Mexico, Kansas E. Texas, Arkansas, Missouri, Kansas, Colorado The correct answer is A. Six states border Oklahoma: In the north - Kansas and Colorado In the south - Texas In the east - Arkansas and Missouri In the west - New Mexico
A. Ample B. Meager C. Sufficient D. Overflowing E. Lavish The correct answer is (B). "Abundant" is an adjective meaning "plentiful" while "meager" is an adjective meaning "not enough." Therefore, the words are opposite in meaning. Answers (A), (D), and (E) are synonyms of "abundant." While answer (C) is related to "abundant," it is neither a synonym nor an antonym of it. Oranges are to fruits as are to shapes. A. Angles B. Dimensions C. Dots D. Rulers E. Triangles The correct answer is (E). To solve this questions correctly, it is necessary to understand the relationship between X and Y (oranges and fruits). Creating a sentence with the first pair of words and applying it to the second pair is a useful method for solving this type of question. Thus, we should phrase a sentence to define what X is to Y. Oranges are a specific kind of fruit. Now, we can try to apply this relation to shapes: A. Angles are a specific kind of shape. B. Dimensions are a specific kind of shape. C. Dots are a specific kind of shape. D. Rulers are a specific kind of shape. E. Triangles are a specific kind of shape.
Options B, dimensions, can be eliminated because it is a characteristic of a shape, not a type of one. Option D, rulers, can also be eliminated as rulers may assist us in creating shapes, but they are not a shape. Angles, dots, and triangles are the only options left. Although angles and dots are a part of shapes, they do not constitute as shapes. Thus, the correct answer is E. If the first two statements are true, is the final statement true? Some officers carry a gun. Most officers carry a club. The chances of finding an officer who carries both a gun and a club are high. A. Yes B. No C. Cannot say The correct answer is (C), cannot say. Although most officers carry a club, we do not know how many of them carry a gun. Therefore, we cannot reach any conclusions about the probability of finding an officer carrying both a gun and a club. What is the following number in the series? 0.18 -- 0.36 -- 0.72 --? -- 2. A. 0. B. 1. C. 1. D. 1. The correct answer is (C). Each term is double the previous term.