1. The number of digits in 416 525 is
- (A) 31
- (B) 30
- (C) 29
- (D) 28
- (E) 27
2. The number 2564 ∙ 6425 is the square of a positive integer N. In decimal representation, the sum of the digits of N is
- (A) 7
- (B) 14
- (C) 21
- (D) 28
- (E) 35
3. What is the sum of the digits of the decimal form of the product 21999 ∙ 52001?
- (A) 2
- (B) 4
- (C) 5
- (D) 7
- (E) 10
4. The value of (256)0.16(256)0.09 is
- (A) 4
- (B) 16
- (C) 64
- (D) 256.25
- (E) –16
5. Let w, x, y, and z, be whole numbers. If 2w ∙ 3x ∙ 5y ∙ 7z = 588 then what does 2w + 3x + 5y + 7z equal?
- (A) 21
- (B)25
- (C) 27
- (D) 35
- (E) 56
6. If x and y are positive integers for which 2x3y = 1296, what is the value of x + y?
- (A) 8
- (B) 9
- (C) 10
- (D) 11
- (E) 12
7. An integer x is chosen so that 3x + 1 is an even integer. Which of the following must be an odd integer?
- (A) x + 3
- (B) 2x
- (C) x ⎼ 3
- (D) 7x + 4
- (E) 5x + 3
8. A three-digit number XYZ is formed of three different non-zero digits X, Y and Z. A new number is formed by rearranging the same three digits. What is the greatest possible difference between the two numbers? (For example, 345 could be rearranged into 435, for a difference of 435 – 345 = 90.)
- (A) 792
- (B) 293
- (C) 564
- (D) 984
- (E) 297
9. How many three-digit positive integers, with digits x, y and z in the hundred’s, ten’s and unit’s place respectively exist such that x < y, z < y, x ≠ y, and x ≠ 0?
- (A) 245
- (B) 285
- (C) 240
- (D) 320
- (D) 328
10. Avirupa gives half of her 24 pages to a friend. How many pages does she give away?
- (A) 2
- (B) 4
- (C) 6
- (D) 12
- (E) 48