All triangles are shapes. Some shapes are colored. No colored things are invisible. Which conclusion is valid?

The correct answer is C: Some triangles may not be invisible. Triangles are shapes. Some shapes are colored, but not all. Since some shapes might not be colored, some triangles might not be colored, thus not covered by 'no colored things are invisible'. Some triangles may not be invisible.

Three friends P, Q, and R are standing in a line. Q is to the West of P. R is to the South of Q. If R walks 10 meters North and then 5 meters East, he will be at the same position as Q. How far is P from R in the North-South direction?

The correct answer is B: 10 meters. Since R reaches Q's position by walking 10 meters North and 5 meters East, this means R was initially 10 meters South of Q and 5 meters West of Q. Given Q is West of P and they're in a line, P is East of Q. Therefore, P is 10 meters North of R in the North-South direction.

Squares in a 3×3 grid?

The correct answer is B: 14. This question asks you to count all possible squares of different sizes that can be formed in a 3×3 grid. Step 1: Count 1×1 squares In a 3×3 grid, the smallest squares are individual cells. $$1 \times 1 \text{ squares} = 3 \times 3 = 9$$ Step 2: Count 2×2 squares Larger squares formed by combining f

All A are B. All B are C. Some C are not D. No D is E. Which of the following must be true?

The correct answer is A: Some A are not D. Since all A are B, all B are C, and some C are not D, it follows that some A are not D (as some of C are not D).