Math and Logic Problems for 10th Class

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Questions and Answers

What is 58 hundreds rounded to the nearest thousands?

6000

What is 10,000 less than 3 million?

2,990,000

Which number when rounded to the nearest millions becomes 8,000,000?

  • 8.909010 (correct)
  • 7499999
  • 7.099999
  • 8010000

What is the least number which when rounded to the nearest hundredths gives 51.64?

<p>51.636 (D)</p> Signup and view all the answers

What number subtracted from 450 so that the difference is equal to the sum of 2.73 and 8.0361?

<p>39.2339</p> Signup and view all the answers

What is the result when 3.07 is added to itself 12 times?

<p>36.84</p> Signup and view all the answers

The result when the cube of 5.1 is increased by 0.032 is

<p>132.683</p> Signup and view all the answers

When two ratios are equivalent they are called

<p>Proportion (D)</p> Signup and view all the answers

What is the Least Common Multiple (LCM) of 3 and 18?

<p>18</p> Signup and view all the answers

Which of the following is divisible by 17?

<p>1517 (D)</p> Signup and view all the answers

What is the numerical value of 5 ÷ 5 + 5.5 - 5?

<p>2.5</p> Signup and view all the answers

Remove the grouping symbols and simplify: 5 + (7 + 8 - 3)?

<p>17</p> Signup and view all the answers

Simplify the following: -8 - (3 + 10 - 9)?

<p>-12</p> Signup and view all the answers

Remove the symbols of grouping and simplify: (-x² + 3x - 3)?

<p>-x² + 3x - 3</p> Signup and view all the answers

Give the ratio of 18 Clinical Instructors to 12 Nursing Students?

<p>3:2</p> Signup and view all the answers

How many hectares are there in a rectangular field measuring 750m wide and 800m long?

<p>60</p> Signup and view all the answers

What is the difference between 109 and 49?

<p>60</p> Signup and view all the answers

Melchor played basketball for the College Varsity Team. He attempted 45 free throws and shot 85% of these. How many free throws did he make?

<p>38</p> Signup and view all the answers

How much is 25% of 55% of 350?

<p>48.13</p> Signup and view all the answers

A certain number doubled and increased by 15 is 29. What is the number?

<p>7</p> Signup and view all the answers

What is the floor area of a 5 storey building whose each floor measures 15m x 22.5?

<p>1687.50 sq. m.</p> Signup and view all the answers

In the series of 1, 5, 10, 16, 23,..., the 8th term is?

<p>50</p> Signup and view all the answers

What is the remainder of the division 5100÷7?

<p>2</p> Signup and view all the answers

How many factors of 2000 are perfect squares?

<p>6</p> Signup and view all the answers

How many odd integers are there in 10/4 and 71/3?

<p>11</p> Signup and view all the answers

If the sum of four different prime numbers is an odd number, what is the smallest of the four?

<p>5 (D)</p> Signup and view all the answers

Charice weighs 94 kilos. How much is her weight in pounds?

<p>206.13</p> Signup and view all the answers

How many ribbons, each at 12 3/4 cm long, can be obtained from a roll of 6.63 meters long?

<p>51</p> Signup and view all the answers

Change the following percent to decimals: 25%, 5.5%, 4%, and 35.5%

<p>0.25,; 0.055,; 0.04,; 0.355 (A)</p> Signup and view all the answers

Express in Scientific Notation: .000435

<p>4.35 x 10⁻⁴ (C)</p> Signup and view all the answers

Which of the following gives the sum of the polynomials by a monomial? (x + 2y) (3x² – 5xy + y²)

<p>3x³ + x²y - 9 xy² + 2y³ (A)</p> Signup and view all the answers

Find the products of two binomials with similar terms? (x – 4y) (x + 7y)

<p>x² + 3xy - 28y² (B)</p> Signup and view all the answers

Which of the following equation has the LEAST value?

<p>6 + 2 x 2 = (C)</p> Signup and view all the answers

There are two numbers whose sum is 48. One of the numbers is greater by 6. What are the numbers?

<p>21, 27 (B)</p> Signup and view all the answers

If MANILA can be written as NBOJMB, then how would you write BAGUIO?

<p>CBHVJP (B)</p> Signup and view all the answers

Which of the figures, you think best fits the series below?

<p>↑ (A)</p> Signup and view all the answers

Which of the figures can be used to continue the series given below?

<p>◇ (A)</p> Signup and view all the answers

Which completes the pattern?

<p>.... (A), .... (B), .... (C), .... (D)</p> Signup and view all the answers

Identify the figure that completes the pattern.

<p>4 (D)</p> Signup and view all the answers

If you begin to fold along the dotted line, which of the following figures would follow the figure given below?

<p>▽ (B)</p> Signup and view all the answers

Which figure is next in the series?

<p>3 (C)</p> Signup and view all the answers

What completes the following pattern?

<p>↑ (B), ↑ (D)</p> Signup and view all the answers

AB, AC, AD, A

<p>AE (A)</p> Signup and view all the answers

A17, B34, D51, E

<p>68 (B)</p> Signup and view all the answers

A, B35, C40, D45

<p>34 (B)</p> Signup and view all the answers

What is the total number of students in the class?

<p>27 (B)</p> Signup and view all the answers

How many students learn piano not guitar?

<p>17 (B)</p> Signup and view all the answers

How many students learn just the guitar?

<p>8 (D)</p> Signup and view all the answers

How many students learn just the piano or the guitar?

<p>17 (C)</p> Signup and view all the answers

Which store gave the worst value of money?

<p>Store V (B)</p> Signup and view all the answers

Which two shops charged the same price per kilogram?

<p>Store V and W (A)</p> Signup and view all the answers

At which store should you go get three times the amount of sugar for the same price as store 7?

<p>Store Y (A)</p> Signup and view all the answers

Which department has the most number of enrollees?

<p>Education (A)</p> Signup and view all the answers

What is the approximate enrollment in the Business Administration department?

<p>8,000 (C)</p> Signup and view all the answers

What is the approximate enrollment of the College of Business Administration and Liberal Arts Departments?

<p>10,000 (D)</p> Signup and view all the answers

What percent is spent on food?

<p>35% (A)</p> Signup and view all the answers

How much money was spent for clothing?

<p>10% (C)</p> Signup and view all the answers

How much is their savings?

<p>15% (B)</p> Signup and view all the answers

On which item is the budget spent most?

<p>Food (B)</p> Signup and view all the answers

What is the total percentage of the expenses for savings, insurance and other expenses?

<p>35% (A)</p> Signup and view all the answers

From the statement "all politicians are liars", which of the following can be immediately inferred?

<p>Some liars are politicians. (A)</p> Signup and view all the answers

What is wrong with the following argument. “All men are banana-eaters, but all monkeys are also banana-eaters; therefore, all men are monkeys.”

<p>No class of men and monkeys follows under the same category (A)</p> Signup and view all the answers

From the statement, "if you study hard, you will pass the Civil Service Exams", which of the following can be immediately inferred?

<p>Studying hard is a sufficient condition for passing the Civil Service Commission Exams. (C)</p> Signup and view all the answers

Flashcards

Rounding 58 hundreds

58 hundreds rounded to the nearest thousand is 6000.

3 million minus 10,000

10,000 less than 3 million equals 2,990,000.

Rounding to millions

The number that rounds to 8 million is between 7.5 million and 8.5 million.

Least number for rounding

The least number that rounds to 51.64 is 51.635.

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Subtracting for a sum

To find what number subtracted from 450 equals the sum of 2.73 and 8.0361, the answer is 39.2339.

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Adding multiple times

Adding 3.07 to itself 12 times gives you 36.84.

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Cube and increase

The cube of 5.1, increased by 0.032, is approximately 132.683.

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Equivalent ratios

When two ratios are equivalent, they are termed as Proportion.

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Finding LCM

The Least Common Multiple (LCM) of 3 and 18 is 18.

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Divisibility check

1547 is divisible by 17.

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Numerical expression evaluation

5÷5 + 5.5 - 5 equals 25.

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Simplifying expressions

5 + (7 + 8 - 3) simplifies to 17.

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Negative simplification

Simplify -8 - (3 + 10 - 9) to -12.

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Group symbols simplification

Removing grouping symbols from (-x² + 3x - 3) keeps it as -x² + 3x - 3.

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Ratio of instructors to students

The ratio of 18 Clinical Instructors to 12 Nursing Students is simplified to 3:2.

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Area calculation

A 750m by 800m field has an area of 60 hectares.

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Difference between numbers

The difference between 109 and 49 is 60.

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Basketball free throw success

Melchor made 38 out of 45 free throws, lacking 85%.

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Percentage calculations

25% of 55% of 350 is approximately 48.13.

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Solving equations

The equation 2x + 15 = 29 solves to x = 7.

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Floor area of building

Each floor area of a 5-storey building measuring 15m x 22.5m results in 1,688.75 sq. m.

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Finding series terms

In the series 1, 5, 10, 16, 23, the 8th term is 61.

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Dividing with a remainder

The remainder of 5100 ÷ 7 is 2.

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Perfect square factors

There are 6 factors of 2000 that are perfect squares.

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Counting odd integers

There are eleven odd integers between 10/4 and 71/3.

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Smallest prime number

The smallest prime number in a set summing to an odd number must be 5.

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Study Notes

Math Problems

  • Rounding: 58 hundreds rounded to the nearest thousand is 6000.

  • Subtraction: 10,000 less than 3 million is 2,990,000.

  • Rounding to Millions: A number rounded to 8,000,000 in the millions place must end in 000,000 to the specified range for example: 7,999,999. A number when rounded to nearest millions would in this case 8,000,000 be 8,000,000 if rounding 7,099.999 - 7,999,999

  • Rounding to Hundredths: The least number that rounds to 51.64 when rounded to the nearest hundredth is 51.636.

  • Subtraction and Sum: Subtracting a number from 450 to equal the sum of 2.73 and 8.0361 results in 41.9639.

  • Multiplication: 3.07 added to itself 12 times is 36.84.

  • Cube of a Number Increased The result of 5.1 cubed with an extra 0.032 added is 132.777

  • Ratios Two equal ratios are called a proportion.

Logic Problems

  • LCM: The least common multiple of 3 and 18 is 18.

  • Division by 17: From the given options, 1547 is divisible by 17.

  • Numerical Value: The numerical value of 5 ÷ 5 + 5.5 - 5 is 25.

  • Simplifying Expressions: Simplifying 5 + (7 + 8 − 3) equals 17.

  • Simplifying Expressions With Parentheses: Simplifying -8 - (3 + 10 - 9) results in -12

  • Simplifying Grouping Symbols: Removing grouping symbols and simplifying (-x² + 3x – 3) yields (-x² + 3x − 3).

  • Ratio: The ratio of 18 clinical instructors to 12 nursing students is 3:2.

  • Area (Hectares): A rectangular field that is 750m wide and 800m long translates to 60 hectares.

  • Difference: The difference between 109 and 49 is 60.

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