Tag: math & puzzles

Questions Related to math & puzzles

After how many days will half of the pool be covered by the water-lily?

general knowledge math & puzzles

  1. 10

  2. 19

  3. 15

  4. 11

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Correct Option: B

How old are John and Julia?

general knowledge math & puzzles

  1. 40 and 30

  2. 30 and 40

  3. 80 and 60

  4. 60 and 80

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Correct Option: B

111,111,111 * 111,111,111 = 12,345,678,987,654,321
general knowledge math & puzzles

  1. True

  2. False

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Correct Option: B

A company makes a profit equal to 25% of its sales. The profit is shared equally among the 4 owners of the company. If the company generates sales of $5,000,000, how much money does each one of the owners get?

general knowledge math & puzzles

  1. 12,500

  2. 312,500

  3. 500,000

  4. 1,250,000

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Correct Option: B

The two legs of a right triangle measure 6 and 8 inches respectively. What is the area of the circle that contains all 3 vertices of the triangle?

general knowledge math & puzzles

  1. 24Pi

  2. 25Pi

  3. 36Pi

  4. 64Pi

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Correct Option: B

A cylinder of radius 5 cm is inserted within a cylinder of radius 10 cm. The two cylinders have the same height of 20 cm. What is the volume of the region between the two cylinders?

general knowledge math & puzzles

  1. 100Pi

  2. 500Pi

  3. 1000Pi

  4. 1500Pi

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Correct Option: D

A cone made of cardboard has a vertical height of 8 cm and a radius of 6 cm. If this cone is cut along the slanted height to make a sector, what is the central angle, in degrees, of the sector?

general knowledge math & puzzles

  1. 216

  2. 180

  3. 90

  4. 36

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Correct Option: A

As x increases from Pi/4 to 3Pi/4, |sin(2x)|

general knowledge math & puzzles

  1. always increases

  2. always decreases

  3. increases then decreases

  4. decreases then increases

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Correct Option: D

AI Explanation

To answer this question, let's analyze the given expression |sin(2x)| as x increases from π/4 to 3π/4.

The function sin(2x) is an oscillating function with a period of π. That means it completes one full cycle from 0 to 2π.

When x increases from π/4 to 3π/4, we can see that the values of 2x also increase. Let's consider the values of 2x within the given range:

When x = π/4, 2x = 2(π/4) = π/2 When x = 3π/4, 2x = 2(3π/4) = 3π/2

Now, let's evaluate the absolute value of sin(2x) at these two points:

|sin(π/2)| = 1 |sin(3π/2)| = |sin(π + π/2)| = |sin(π/2)| = 1

We can observe that the absolute value of sin(2x) is equal to 1 at both x = π/4 and x = 3π/4.

Therefore, as x increases from π/4 to 3π/4, |sin(2x)| does not always increase or always decrease. Instead, it remains constant at 1 throughout this interval.

Hence, the correct answer is D) decreases then increases.

If the sum of the repeating decimals 0.353535... + 0.252525... is written as a fraction in lowest terms, the product of the numerator and denominator is
general knowledge math & puzzles

  1. 2475

  2. 680

  3. 670

  4. 660

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Correct Option: D

The price x of a t-shirt was first reduced by 10%. Then the new price was reduced by a further 20%. The price of the T-shirt after the two reductions is given by
general knowledge math & puzzles

  1. x - 0.3x

  2. x - 30

  3. x - 0.3x + 0.02x

  4. x + 0.02x

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Correct Option: C