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1.  
The largest four-digit number exactly divisible by 88 is:

Correct Answer: E [9,944]

Explanation:

9,999 ÷ 88 leaves 55; 9,999 − 55 = 9,944 (= 88 × 113).

2.  
The least number that must be added to 2,000 to make it a perfect square is:

Correct Answer: A [25]

Explanation:

44² = 1,936 < 2,000 < 45² = 2,025 → add 25.

3.  
The least number by which 1,323 must be multiplied to make it a perfect cube is:

Correct Answer: B [7]

Explanation:

1,323 = 3³ × 7² → one more 7 → 9,261 = 21³.

4.  
How many perfect squares lie between 1,000 and 2,000?

Correct Answer: C [13]

Explanation:

32² = 1,024 to 44² = 1,936 → 44 − 32 + 1 = 13.

5.  
If the number 6,7*,452 is divisible by 9, the digit * is:

Correct Answer: A [3]

Explanation:

6 + 7 + 4 + 5 + 2 = 24; 24 + * must be a multiple of 9 → * = 3.

6.  
1,04,976 is the square of:

Correct Answer: D [324]

Explanation:

Ends in 6 → 4 or 6; 1,049 → 32_; 325² = 1,05,625 is larger → 324.

7.  
Is the three-digit number 7A4 (A is a digit) divisible by 11?
I. A = 1.
II. 7A4 is divisible by 3.

Correct Answer: C [Either statement alone is sufficient]

Explanation:

I: 714 → 7 − 1 + 4 = 10 → No.

8.  
Quantity I: ∛10,648 × √1,764
Quantity II: 31 × 29 + 25

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

Explanation:

I: 22 × 42 = 924. II: (30² − 1²) + 25 = 899 + 25 = 924.

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