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1.  
113 × 108 = ?

Correct Answer: A [12,204]

Explanation:

+13, +8 → left 121, right 104 → 12,100 + 104 = 12,204.

2.  
√9,409 = ?

Correct Answer: C [97]

Explanation:

Ends in 9 → 3 or 7; 94 lies between 9² and 10² → 9_; 95² = 9,025 < 9,409 → 97.

3.  
What is the smallest digit that can replace * in 3,5*6 so that the number is divisible by 8?

Correct Answer: E [3]

Explanation:

Last three digits 5*6: 506, 516, 526 fail; 536 = 8 × 67 → 3.

4.  
Quantity I: 45² − 35²
Quantity II: 26 × 31

Correct Answer: B [Quantity I < Quantity II]

Explanation:

I: (45 + 35)(45 − 35) = 800.

5.  
Is the positive whole number N divisible by 12?
I. N is divisible by 4.
II. N is divisible by 6.

Correct Answer: D [Both statements together are needed]

Explanation:

I alone: 8 no, 24 yes. II alone: 6 no, 12 yes.

6.  
What is the remainder when 8,47,326 is divided by 9?

Correct Answer: B [3]

Explanation:

Digit sum 8 + 4 + 7 + 3 + 2 + 6 = 30 → 3.

7.  
324 ÷ 0.0625 = ?

Correct Answer: D [5,184]

Explanation:

0.0625 = 1/16, so ÷ 0.0625 = × 16 → 5,184.

8.  
Trick Spotter: which is the fastest correct way to find 482 × 125?

Correct Answer: B [482 × 1,000 ÷ 8]

Explanation:

125 = 1,000/8: 4,82,000 ÷ 8 = 60,250 in one step.

9.  
Spot My Mistake: "96 × 103: deviations −4 and +3; left part 96 + 3 = 99; right part (−4) × 3 = −12; answer 9,912." Which statement is correct?

Correct Answer: C [The last step is wrong: 9,900 − 12 = 9,888]

Explanation:

99 | −12 means 9,900 − 12 = 9,888; the student added.

10.  
Which of the following is/are correct?
I. 27³ = 19,683
II. 1/19 ≈ 0.0526
III. 1,331 is a perfect square

Correct Answer: C [Only I and II]

Explanation:

I true; II true (1/19 = 0.05263…); III false – 1,331 = 11³, and 36² = 1,296, 37² = 1,369.

11.  
Which one of the following divides 3,97,834 exactly?

Correct Answer: C [17]

Explanation:

17-test: 39,783 − 5 × 4 = 39,763 → 3,976 − 15 = 3,961 → 396 − 5 = 391 = 17 × 23 ✓.

12.  
Reverse question: the square of a number ending in 5 is 30,625. The number is:

Correct Answer: A [175]

Explanation:

306 = 17 × 18, so the number is 175 (Five-Tail Square in reverse).

13.  
57² − 43² = ?

Correct Answer: B [1,400]

Explanation:

(57 + 43)(57 − 43) = 100 × 14 = 1,400.

14.  
999 × 47 = ?

Correct Answer: E [46,953]

Explanation:

47,000 − 47 = 46,953.

15.  
Odd one out – which product is WRONG?

Correct Answer: D [62 × 68 = 4,226]

Explanation:

Same front digit, last digits adding to 10: 6 × 7 = 42 | 2 × 8 = 16 → 4,216, not 4,226.

16.  
4,785 × 11 = ?

Correct Answer: D [52,635]

Explanation:

Sandwich: 4 | 11 | 15 | 13 | 5 → with carries 52,635.

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