6

Set 1: Linear Equations (Advanced)

Explanation

Answer: C

The sum of three consecutive integers is 33. What is the middle integer?

A.

10

B.

12

C.

11

✓ Correct
D.

33

Detailed Explanation

Choice C is correct. Choice D is the correct answer. 1. Define: x,x+1,x+2x, x+1, x+2. Middle is x+1x+1. 2. Equation: x+(x+1)+(x+2)=33x + (x+1) + (x+2) = 33 3. Simplify: 3x+3=333x + 3 = 33 4. Subtract 3: 3x=303x = 30 5. Divide by 3: x=10x = 10 6. Middle: x+1=11x + 1 = 11 7. Verify: 10+11+12=3310+ 11 + 12 = 33 ✓ Choice C is incorrect because this is the smallest. Choice A is incorrect because this is the largest. Choice C is incorrect because it results from an error in the solution process.

Key Steps:

The correct answer is 11

Why others are wrong:
A: Choice A is incorrect and may result from a calculation error.
B: Choice B is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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