Properties and Problems in Mathematics

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Questions and Answers

What is the original price of the item if the price increased by the same rate results in Php 3,100 and decreased results in Php 1,900?

Php 2,500 (correct)

Php 1,200

Php 2,800

Php 200

How much must one invest in corporate bonds paying 9.6% to earn a Php 12,000 income per annum?

Php 11,520

Php 125,000

Php 23,040

Php 250,000 (correct)

What needs to be cut from a piece of glass 16 1/8 cm wide to fit into a 14 ¾ cm wide opening?

2 3/8 cm (correct)

1 7/8 cm

1 3/8 cm

2 5/8 cm

If a race car traveled for 2 ½ hours at an average speed of 132 5/8 km per hour, what total distance did it cover?

331 9/16 km Signup and view all the answers

What will be the weight of a freight car that weighs 241 kg and increases 3 1/8 times when fully loaded?

824 3/8 kg Signup and view all the answers

How many liters will remain in a 1,000-liter tank if 8.2% of its liquid has evaporated?

991.8 Signup and view all the answers

How much did Dante receive for his stock that increased in value by 116% from his original purchase price of Php 358?

Php 773.28 Signup and view all the answers

What is Mr. Manny Vargas's commission if he sold a building for Php 175M at a commission rate of 5.5%?

Php 9.625M Signup and view all the answers

If 8 less than the product of a number and -3 is greater than 7, which number could it be?

-5 Signup and view all the answers

Solve for the number if the difference between 8 times a number and 17 is 231.

37 Signup and view all the answers

What is the perimeter of a parking lot if four times the perimeter is 16 less than 2,000 meters?

504 m Signup and view all the answers

Calculate the amount of last month’s telephone bill if it decreased by the product of 3 and Php30.00, resulting in Php1,319.50.

Php1,289.50 Signup and view all the answers

Eighteen less than seven times the number of sandwiches is 269. How many sandwiches are there?

44 Signup and view all the answers

If a house and lot cost Php 14M, and the house costs 1.5 times as much as the lot, what is the cost of the lot?

Php8.4M Signup and view all the answers

Find the regular price of a television set sold at Php 7,200 after a 40% discount.

Php12,000 Signup and view all the answers

What is the length of the longest side of a triangle with sides represented by three consecutive integers and a perimeter of 96 cm?

32 Signup and view all the answers

What best describes a 'ruffian' as mentioned in the context?

a brutal person Signup and view all the answers

Which word is the opposite of 'accompanied' as used in the sentence about Hanna and her sister?

let go on one’s own Signup and view all the answers

What does 'augment' mean in the context of the policemen's income?

increase Signup and view all the answers

What does 'effaced' indicate regarding the footprints?

erased Signup and view all the answers

What is the meaning of 'topsy-turvy' as used in the description of the room?

disorderly Signup and view all the answers

What does 'calumniate' mean in relation to a person's reputation?

slander Signup and view all the answers

What does 'ruined' imply about the state of the room?

damaged Signup and view all the answers

What best describes the act of 'rumaging' through clothes?

searching through Signup and view all the answers

What is incorrect about the phrase 'The news are written immediately to meet the previous deadline'?

The verb 'are' should be 'is'. Signup and view all the answers

Which phrase contains a grammatical error related to subject-verb agreement?

Great literary works enriches the vocabulary. Signup and view all the answers

Identify the erroneous phrase in the statement, 'Either Prof. Teodoro Agoncillo or Dr. Gregorio F. Zaide affirm the history of our flag.'

'Affirm' should be 'affirms'. Signup and view all the answers

Which statement correctly addresses the error in 'One of the machines in the printing press weren’t functioning properly'?

'Were' should be 'was'. Signup and view all the answers

What is incorrect in the sentence 'All children has inherent rights that must be protected'?

'Has' should be 'have'. Signup and view all the answers

Which phrase in 'Have either of the books been returned?' is not likely correct?

There are no errors in this sentence. Signup and view all the answers

What is wrong with the phrase 'The number of readers continually rise each year'?

'Rise' should be 'rises'. Signup and view all the answers

Identify the grammatical error in 'One hundred fifty pesos are the average selling price of one textbook.'

The verb 'are' should be 'is'. Signup and view all the answers

How many shirts remained unsold when the shop opened last Saturday?

112 Signup and view all the answers

What can be concluded about the number of boys and girls in the room based on the statements provided?

The number of boys equals square of the number of girls. Signup and view all the answers

Which statement alone is sufficient to determine in what year David was born?

Only statement (2) is sufficient. Signup and view all the answers

How many blue balls remain in the box after 16 balls are removed?

6 Signup and view all the answers

What was Mrs. Lim's average speed during her trip?

80 km/h Signup and view all the answers

Which statements are needed to determine if Lorna's dentist appointment was on a Friday?

Both statements together are needed. Signup and view all the answers

What can be inferred about the number of girls if there are 56 children total?

There can be 48 boys and 8 girls. Signup and view all the answers

What is the specific number of red balls that could have been removed if the ratio of red to blue is 5:3?

15 Signup and view all the answers

Study Notes

Properties of Mathematics

Distributive property: states that a(b + c) = ab + ac, emphasizing multiplication over addition.
Commutative property of addition: a + b = b + a, showcasing the ability to swap terms.
Associative property: (a + b) + c = a + (b + c), highlighting the grouping of terms.
Transitive property of equality: If a = b and b = c, then a = c, establishing equality among variables.

Algebraic Problems and Solutions

For the inequality of a number and -3, solutions can include various integers such as -6, -5, 5, or 6.
Problem: The equation relating to 8 times a number, resulting in a difference of 231, leads to a solution of 31, 37, 48, or 1,984.
A parking lot's perimeter calculated through the equation yields options such as 496 m, 504 m, 992 m, or 1,008 m.
A telephone bill after deducting a specific amount equals Php1,319.50, leading to possible amounts like Php1,229.50, Php1,289.50, Php1,310.50, or Php1,409.50.
Sandwiches problem finds the quantity of sandwiches based on an equation leading to options like 32, 41, 44, or 45.

Financial and Real Estate Calculations

Sale of a house and lot totaling Php14M, with the house costing 1.5 times as much as the lot, hints at cost options like Php5.6M, Php8.4M, Php10.5M, or Php21M.
The regular price of a TV discounted to Php7,200 at a 40% rate, calculated to find original prices such as Php4,320, Php12,000, Php6,800, or Php10,000.
The triangle's side lengths add to a perimeter of 96 cm to find the longest side, which could be 28, 32, 33, or 36 cm.
A rectangle's dimensions determined by given perimeter and dimensional ratio leading to area options like 16 m, 24 m, 28 m², or 640 m².

Age and Investment Scenarios

Paula's age related to Queenie's through a past scenario solves to Queenie's current age options of 8, 10, 16, or 20.
An item's price increase and decrease associated with a specific rate leads to a calculation of its original price, revealing options like Php1,200, Php200, Php2,500, or Php2,800.
Investment of Php12,000 as income from corporate bonds at 9.6% gives options including Php11,520, Php23,040, Php125,000, or Php250,000.

Measurement and Miscellaneous Problems

A piece of glass must be reduced in width with calculated measures to fit different opening sizes.
A race car's total distance calculated from speed and travel time yields figures such as 264 5/16 km, 331 9/16 km, 330 5/16 km, or 135 1/8 km.
Weight calculations regarding freight car loading gives potential weight options like 750 3/8 kg, 824 3/8 kg, 720 5/8 kg, or 753 1/8 kg.
Remaining liquid in a storage tank after evaporation, leading to remaining amounts such as 918, 991.8, 999.18, or 998 liters.
Stock value increase shown through percentage calculations leads to potential values received including Php678.27, Php772, Php773.28, or Php778.

Real Estate Transactions and Commission

Earnings from selling a building at Php175M with a commission rate yielding options like Php9.5M, Php9.7M, Php9.625M, or Php180.5M.
Career Service exam passing percentage calculated from total examinees and successful candidates resulting in a variety of passing rates.

Reasoning and Logical Deductions

Deductions based on provided statements about unknown quantities, requiring combined or singular interpretations to solve.
Various logic problems regarding the number of participants or inventory evaluated through provided statements, with conclusions drawn about adequacy and sufficiency of information.

Vocabulary and Language Understanding

Understanding of antonyms and context within sentences to connect meaning with words.
Examples of vocabulary to improve comprehension including synonyms and antonyms for clarified understanding of terms in context.

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Description

Explore the essential properties of mathematics including distributive, commutative, associative, and transitive properties. This quiz also covers various algebraic problems and solutions, helping to reinforce your understanding of mathematical concepts and equations.