## 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. 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**

**2. Prime Numbers:7x**

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

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

**5. Prime Numbers:1x**

**6. v216 =**

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

**8. v5**

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

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

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

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

**13. v2**

**14. Prime Numbers:2x**

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

**16. v225=**

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

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

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

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

**21. v3**

**22. Positive integers with more than two factors are ____.**

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

**24. 3n + 3n + 3n = _____ = ______**

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

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

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

**28. Prime Numbers:0x**

**29. 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**

**30. v625=**

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

**33. 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**

**34. v169=**

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

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

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

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

**39. Prime Numbers:5x**

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

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

**42. Prime Numbers:8x**

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

**44. Prime Numbers:6x**

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

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

**47. v196=**

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

**49. v256=**

**50. Prime Numbers:4x**