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GMAT Quick Math And Formulas

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. ? 5
(A+B)(A-B)
13
2.23
87.50%

2. ? 4
1024
83.33%
16
2

3. 2^9
25
121
512
16.67%

4. Prime Numbers between 1 - 100 (total of 25)
You cannot simplify this one
Add the exponents and keep the base 7^3 x 7^5 = 7^8
8.33%
{2 -3 -5 -7 -11 -13 -17 -19 -23 -29 -31 -37 -41 -43 -47 -53 -59 -61 -67 -71 -73 -79 -83 -89 -97}

5. 16^2
(a+b)(a^2-ab+b^2)
16
40%
256

6. Simplifying a root
GMAT very often tries to trick you by giving a root linked by addition where it is tempting to simplify the terms - for example: ?(25 + 16). It is tempting to think that this will result into 5 + 4 - but you can only simplify roots when the terms ins
...yields a negative result (-1)^57 = -1
8.33%
4

7. Express 9^1/2 as a radical
7776
A^2 + 2ab + b^2
= the square root of 9 = 3
83.33%

8. 2/5
2
40%
A^2 - 2ab + b^2
32

9. 6^3
2
216
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
= the square root of 9 = 3

10. 1/8
243
27
8.33%
12.50%

11. 2^4
1024
16
216
16.66%

12. a^3+b^3
(a+b)(a^2-ab+b^2)
Add the exponents and keep the base 7^3 x 7^5 = 7^8
216
125

13. 4^3
5%
64
87.50%
...yields a smaller result (1/2)^2 = 1/4

14. to multiple powers with the same base...
144
Add the exponents and keep the base 7^3 x 7^5 = 7^8
27
4

15. Examples of roots simplification
?25.16 = ?25 . ?16 = 5.4 - ?50 . ?18 = ?50.18 = ?900 = 30 - ?144:16 = ?144 : ?16 = 12/4 = 3
361
512
A^2 + 2ab + b^2

16. 5^5
3125
?25.16 = ?25 . ?16 = 5.4 - ?50 . ?18 = ?50.18 = ?900 = 30 - ?144:16 = ?144 : ?16 = 12/4 = 3
...yields a negative result (-1)^57 = -1
1296

17. 2^2
3125
25%
20%
4

18. 1/20
225
1024
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
5%

19. 2^7
...yields a positive result (-1)^2 = 1
83.33%
2.23
128

20. 7/8
75%
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
87.50%

21. 5^4
64
3125
256
625

22. to multiple powers (or raise a power to a power)
16
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
289
Multiply the exponents 7^2(^3) = 7^6

23. to divide powers with the same base...
(A+B)(A-B)
216
144
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3

24. 2^10
4
1024
12.50%
512

25. Multiples of 15
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
8
40%
...yields a negative result (-1)^57 = -1

26. a^3-b^3
243
16.66%
(a-b)(a^2+ab+b^2)
...yields a positive result (-1)^2 = 1

27. 1/4
144
25%
12.50%
169

28. Multiples of 8
You cannot simplify this one
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120
289
361

29. 5/6
144
324
= the cube root of 8 = 2
83.33%

30. 3^5
64
243
13
169

31. ? 169
12.50%
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120
13
121

32. a negative number raised to an odd power...
20%
...yields a negative result (-1)^57 = -1
87.50%
8

33. ? 6
8
361
2.449
75%

34. 5^3
125
256
64
Multiply the exponents 7^2(^3) = 7^6

35. 3^3
Multiply the exponents 7^2(^3) = 7^6
27
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120

36. ? 2
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
64
1.41
8

37. 18^2
324
1024
196
16

38. 4^4
256
(a-b)(a^2+ab+b^2)
...yields a negative result (-1)^57 = -1
2.449

39. Express 8^1/3 as a radical
32
216
= the cube root of 8 = 2
83.33%

40. (a-b)^2 =
A^2 - 2ab + b^2
625
81
64

41. 17^2
4
324
289
3125

42. 6^5
7776
324
216
1.41

43. 2^8
27
2
= the cube root of 8 = 2
256

44. 1/2
13
64
64
50%

45. 2^5
3125
32
512
64

46. 12^2
13
?25.16 = ?25 . ?16 = 5.4 - ?50 . ?18 = ?50.18 = ?900 = 30 - ?144:16 = ?144 : ?16 = 12/4 = 3
144
16

47. what happens when an exponent is negative?
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
1024
256
2.449

48. 2^6
8.33%
64
4
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120

49. 1/6
1.41
25
2
16.67%

50. ? 3
1024
1.73
...yields a negative result (-1)^57 = -1
169

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