## Test your basic knowledge |

# GMAT Number Properties

**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 _______.**