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GMAT Number Properties

Subjects : gmat, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • Match each statement with the correct term.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. Positive integers with more than two factors are ____.






2. The prime factorization of a perfect square contains only ______ powers of primes.






3. In an evenly spaced set - the average can be found by finding ________.






4. Prime Numbers:2x






5. The average of an EVEN number of consecutive integers will ________ be an integer.






6. In an evenly spaced set - the ____ and the ____ are equal.






7. Let N be an integer. If you add two non-multiples of N - the result could be _______.






8. Positive integers with only two factors must be ___.






9. v5






10. v625=






11. v3






12. The prime factorization of __________ contains only EVEN powers of primes.






13. Prime Numbers:0x






14. v2






15. Any integer with an ODD number of total factors must be _______.






16. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.






17. v169=






18. All perfect squares have a(n) _________ number of total factors.






19. 3n + 3n + 3n = _____ = ______






20. For ODD ROOTS - the root has ______.






21. Prime Numbers:9x






22. Any integer with an EVEN number of total factors cannot be ______.






23. N! is _____ of all integers from 1 to N.






24. v256=






25. If 2 cannot be one of the primes in the sum - the sum must be _____.






26. How to find the sum of consecutive integers:






27. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.






28. The formula for finding the number of consecutive multiples in a set is _______.






29. Prime Numbers:1x






30. If N is a divisor of x and y - then _______.






31. How to solve: If p is the product of the integers from 1 to 30 - inclusive - what is the greatest integer n for which 3n is a factor of p?






32. If estimating a root with a coefficient - _____ .






33. Prime Numbers:6x






34. Prime Numbers:4x






35. The sum of any two primes will be ____ - unless ______.






36. v225=






37. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.






38. How to test for sufficiency: If p is an integer - is p/n an integer? (1) k1p/n is an integer(2) k2p/n is an integer






39. Prime Numbers:5x






40. In an evenly spaced set - the sum of the terms is equal to ____.






41. How to solve: For any positive integer n - the sum of the 1st n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 301? (A) 10 -100 (B) 20 -200 (C) 22 -650 (D) 40 -200 (E) 45 -150






42. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15






43. How to solve: If k - m - and t are positive integers and k/6 + m/4 = t/12 - do t and 12 have a common factor greater than 1? 1. k is a multiple of 3 2. m is a multiple of 3






44. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.






45. Prime Numbers:3x






46. Prime factors of _____ must come in pairs of three.






47. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.






48. Prime Numbers:8x






49. The PRODUCT of n consecutive integers is divisible by ____.






50. If the problem states/assumes that a number is an integer - check to see if you can use _______.