# Number Properties & Sequences

GMAT Practice Questions in Number Theory, AP, GP

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You may get five to seven questions from Number systems, number properties and number theory and one or two questions from sequences and series in the GMAT quant section - in both variants viz., problem solving and data sufficiency. The concepts tested include LCM, HCF, perfect squares, prime factorization, number of factors, remainders, factorials, odd and even numbers, and arithmetic and geometric progressions.

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1. If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of a?

1. 121
2. 3267
3. 363
4. 33
5. None of the above
2. How many different positive integers exist between 106 and 107, the sum of whose digits is equal to 2?

1. 6
2. 7
3. 5
4. 8
5. 18
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?

1. 13
2. 59
3. 35
4. 37
5. 12
4. How many keystrokes are needed to type numbers from 1 to 1000??

1. 3001
2. 2893
3. 2704
4. 2890
5. None of these
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. 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?

1. 11
2. 17
3. 13
4. 23
5. None of these
6. How many integral divisors does the number 120 have?

1. 14
2. 16
3. 12
4. 20
5. None of these
7. How many trailing zeros will be there after the rightmost non-zero digit in the value of 25! (factorial 25)?

1. 25
2. 8
3. 6
4. 5
5. 2
8. What is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33?

1. 3
2. 27
3. 30
4. 21
5. 18
9. Data Sufficiency : Is x3 > x2 ?

1. x > 0
2. x < 1
10. Data Sufficiency : Is ${$frac{x}{y}}$ a terminating decimal? 1. x is a multiple of 2 2. y is a multiple of 3 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 12. Data Sufficiency : If x and y are positive integers, is y odd? 1. x is odd. 2. xy is odd. 13. Data Sufficiency : Is xy < 0? 1. 5|x| + |y| = 0 2. |x| + 5|y| = 0 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. 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 16. What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3? 1. 897 2. 164,850 3. 164,749 4. 149,700 5. 156,720 17. How many 3 digit positive integers exist that when divided by 7 leave a remainder of 5? 1. 128 2. 142 3. 143 4. 141 5. 129 18. The average of 5 consecutive integers starting with m as the first integer is n. What is the average of 9 consecutive integers that start with$m + 2)?

1. m + 4
2. n + 6
3. n + 3
4. m + 5
5. n + 4
19. The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 15 terms of the arithmetic progression?

1. 300
2. 120
3. 150
4. 170
5. 270
20. If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 9, what is the common ratio of the G.P?

1. 3
2. $\frac {1} {3}$
3. 2
4. 9
5. $\frac {1} {9}$
21. Set A contains all the even numbers between 2 and 50 inclusive. Set B contains all the even numbers between 102 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?

1. 2500
2. 5050
3. 11325
4. 6275
5. 2550
22. Data Sufficiency : A set S contains the following elements: {7, 11, 15, 19, 23, x}. What is the value of x?

1. The elements are in arithmetic progression.
2. x is prime.
23. In the first 1000 natural numbers, how many integers exist such that they leave a remainder 4 when divided by 7, and a remainder 9 when divided by 11?

1. 11
2. 14
3. 12
4. 13
5. 10
24. Data Sufficiency : What is the 6th term of the Arithmetic sequence?

1. The sum of the 6th to the 12th term of the sequence is 77.
2. The sum of the 2nd to the 10th term of the sequence is 108.
25. Data Sufficiency : What is the value of X, if X and Y are two distinct integers and their product is 30?

1. X is an odd integer.
2. X > Y.

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