## 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. Prime factors of _____ must come in pairs of three.**

**2. The two statements in a data sufficiency problem will _______________.**

**3. v256=**

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

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

**6. For ODD ROOTS - the root has ______.**

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

**8. Prime Numbers:9x**

**9. Prime Numbers:2x**

**10. v3**

**11. Prime Numbers:5x**

**12. v625=**

**13. Prime Numbers:4x**

**14. v216 =**

**15. The prime factorization of __________ contains only EVEN powers of primes.**

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

**17. Prime Numbers:0x**

**18. Prime Numbers:6x**

**19. v169=**

**20. 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**

**21. v2**

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

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

**24. Prime Numbers:3x**

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

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

**27. N! is _____ of all integers from 1 to N.**

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

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

**30. v225=**

**31. The average of an ODD number of consecutive integers will ________ be an integer.**

**32. In an evenly spaced set - the mean and median are equal to the _____ of _________.**

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

**34. 3n + 3n + 3n = _____ = ______**

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

**36. How to find the sum of consecutive integers:**

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

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

**39. v196=**

**40. Positive integers with only two factors must be ___.**

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

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

**43. Prime Numbers:8x**

**44. The PRODUCT of n consecutive integers is divisible by ____.**

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

**46. Prime Numbers:1x**

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

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

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

**50. 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**