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1. Question 1: If both 11² and 3³ are factors of the number a * 4³ * 6² * 13¹¹, then what is the smallest possible value of a?
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2. Question 2: How many different positive integers exist between 10⁶ and 10⁷, the sum of whose digits is equal to 2?
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3. Question 3: A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
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4. Question 4: How many keystrokes are needed to type numbers from 1 to 1000?
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5. Question 5: When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4. What is the value of the divisor?
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6. Question 6: How many integral divisors does the number 120 have?
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7. Question 7: How many trailing zeros will be there after the rightmost non-zero digit in the value of 25!?
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8. Question 8: What is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33?
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9. Question 9: Data Sufficiency : Is x³ > x² ?
   (1)    x > 0
   (2)    x < 1
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10. Question 10: Data Sufficiency : Is a terminating decimal?
    (1)    x is a multiple of 2
    (2)    y is a multiple of 3
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11. Question 11: Data Sufficiency : Is the positive integer X divisible by 21?
    (1)    When X is divided by 14, the remainder is 4
    (2)    When X is divided by 15, the remainder is 5
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12. Question 12: Data Sufficiency : If x and y are positive integers, is y odd?
    (1)    x is odd.
    (2)    xy is odd.
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13. Question 13: Data Sufficiency : Is xy < 0?
    (1)    5|x| + |y| = 0
    (2)    |x| + 5|y| = 0
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14. Question 14: Data Sufficiency : When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?
    (1)    When 2x is divided by d, the remainder is 23.
    (2)    When 3x is divided by d, the remainder is 22.
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15. Question 15: Data Sufficiency : How many of the numbers x, y, and z are positive if each of these numbers is less than 10?
    (1)    x + y + z = 20
    (2)    x + y = 14
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