Math Problem Statement

Solution

Let's analyze and solve the two questions from the image:

Question 77:

Problem: Examine (A), (B), and (C) and find the best answer.

  • (A) has more circles than (B).
  • (B) and (C) have the same number of circles.
  • (C) (B) and (C) each have more circles than (A).
  • (D) (A) and (C) each have fewer circles than (B).

Solution:

  • (A) has 11 circles.
  • (B) has 16 circles.
  • (C) has 14 circles.

From the options:

  • Option A: Incorrect, (A) has fewer circles than (B).
  • Option B: Incorrect, (B) and (C) do not have the same number of circles.
  • Option C: Correct, both (B) and (C) have more circles than (A).
  • Option D: Incorrect, (A) has fewer circles, but (C) has more than (B).

Answer: C

Question 78:

Problem: Examine (A), (B), and (C) and find the best answer.

  • (A) (C) is more shaded than (B).
  • (B) (A) and (C) are equally shaded, and both are more shaded than (B).
  • (C) (B) is more shaded than (A) and less shaded than (C).
  • (D) (A), (B), and (C) are equally shaded.

Solution:

  • (A) has 3 out of 6 parts shaded.
  • (B) has 4 out of 6 parts shaded.
  • (C) has 3 out of 6 parts shaded.

From the options:

  • Option A: Incorrect, (C) and (A) are equally shaded, (B) is more shaded.
  • Option B: Correct, (A) and (C) are equally shaded.
  • Option C: Incorrect, (B) is more shaded than (A) and (C).
  • Option D: Incorrect, (A) and (C) are equally shaded, but (B) is more shaded.

Answer: B

Would you like any more details or have any questions? Here are some related problems to think about:

  1. How many circles would (C) have if it had the same number as (B)?
  2. If (A) had one more circle, how would that affect the comparison?
  3. What if (B) had fewer shaded parts than (A) and (C), what would the correct answer be then?
  4. How would your answer change if (A) had an additional shaded region?
  5. What would be the effect on question 77 if (B) had fewer circles than (A)?
  6. What is the ratio of shaded parts to unshaded parts in (B)?
  7. If (C) had two more shaded parts, what would be the correct answer for question 78?
  8. How would you compare the shading if each shape had 8 parts instead of 6?

Tip: Always carefully count elements and compare them step by step for each option to ensure accuracy when answering visual or pattern recognition questions.

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Math Problem Analysis

Mathematical Concepts

Geometry
Visual Pattern Recognition

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9