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1.  
3 3/4 + 5 1/6 − 2 5/12 = ?

Correct Answer: A [6 1/2]

Explanation:

Wholes 3 + 5 − 2 = 6; fractions (9 + 2 − 5)/12 = 1/2 → 6 1/2.

2.  
216 ÷ 1/3 of 54 + 12 = ?

Correct Answer: E [24]

Explanation:

"Of" first: 1/3 of 54 = 18; 216 ÷ 18 = 12; 12 + 12 = 24.

3.  
(0.35 × 0.35 − 0.15 × 0.15) ÷ (0.35 − 0.15) = ?

Correct Answer: C [0.5]

Explanation:

(a² − b²)/(a − b) = a + b = 0.35 + 0.15 = 0.5.

4.  
24.98% of 1,601 + 18.97 × 7.02 ≈ ?

Correct Answer: D [530]

Explanation:

≈ 1/4 of 1,600 + 19 × 7 = 400 + 133 = 533 → 530.

5.  
0.(45) + 0.(54) = ?

Correct Answer: B [1]

Explanation:

45/99 + 54/99 = 99/99 = 1 exactly.

6.  
√(0.0169 × 0.36) = ?

Correct Answer: D [0.078]

Explanation:

√0.0169 = 0.13, √0.36 = 0.6 → 0.078.

7.  
Quantity I: (√7 + √3)(√7 − √3)
Quantity II: 2^(3/2) × 2^(1/2)

Correct Answer: E [Quantity I = Quantity II or relation cannot be established]

Explanation:

I: 7 − 3 = 4. II: 2^(3/2 + 1/2) = 2² = 4.

8.  
What is the value of x ÷ y (y ≠ 0)?
I. x = 0.75y
II. x + y = 35

Correct Answer: A [Statement I alone is sufficient]

Explanation:

I: x/y = 0.75 – sufficient.

9.  
Trick Spotter: the fastest correct way to find 997² − 9 is:

Correct Answer: A [(997 + 3)(997 − 3) = 1,000 × 994]

Explanation:

9 = 3², so a² − b² = (a + b)(a − b) = 1,000 × 994 = 9,94,000.

10.  
Spot My Mistake: "5 + 3 × 2² = (5 + 3) × 4 = 32." Which statement is correct?

Correct Answer: B [Multiplication comes before addition, so the answer is 5 + 12 = 17]

Explanation:

Power first (2² = 4), then 3 × 4 = 12, then 5 + 12 = 17.

11.  
Which of the following is/are correct?
I. 2⁻³ = 1/8
II. ∛(−8) = −2
III. 5⁰ = 0

Correct Answer: C [Only I and II]

Explanation:

I and II are true; 5⁰ = 1, not 0.

12.  
?² + 24² = 25². The positive value of ? is:

Correct Answer: A [7]

Explanation:

?² = 625 − 576 = 49 → ? = 7.

13.  
1 + 1/(2 + 1/(1 + 1/3)) = ?

Correct Answer: C [15/11]

Explanation:

Bottom up: 1 + 1/3 = 4/3; 2 + 3/4 = 11/4; 1 + 4/11 = 15/11.

14.  
1/(√8 + √7) + 1/(√8 − √7) = ?

Correct Answer: B [4√2]

Explanation:

Conjugate Flip (8 − 7 = 1): (√8 − √7) + (√8 + √7) = 2√8 = 4√2.

15.  
√(9 + 2√14) = ?

Correct Answer: E [√7 + √2]

Explanation:

Two numbers with sum 9 and product 14 are 7 and 2 → √7 + √2.

16.  
√626 × 3.98 + 5.02² ≈ ?

Correct Answer: D [125]

Explanation:

≈ 25 × 4 + 25 = 125.

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