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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. ? 4
50%
2
1.73
225

2. ? 169
87.50%
7776
Add the exponents and keep the base 7^3 x 7^5 = 7^8
13

3. 1/6
625
12.50%
16.67%
7776

4. ? 2
1.41
7776
81
...yields a smaller result (1/2)^2 = 1/4

5. (a-b)^2 =
A^2 + 2ab + b^2
A^2 - 2ab + b^2
40%
...yields a smaller result (1/2)^2 = 1/4

6. 5^5
3125
144
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
625

7. 4^3
216
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
64
12.50%

8. 2^2
256
20%
...yields a negative result (-1)^57 = -1
4

9. ? 6
2.449
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
= the square root of 9 = 3
225

10. 1/6
16.66%
243
256
...yields a smaller result (1/2)^2 = 1/4

11. 2^6
64
{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}
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120
289

12. 12^2
64
1296
16
144

13. 1/12
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
87.50%
1.41
8.33%

14. 6^4
12.50%
87.50%
13
1296

15. 18^2
32
?25.16 = ?25 . ?16 = 5.4 - ?50 . ?18 = ?50.18 = ?900 = 30 - ?144:16 = ?144 : ?16 = 12/4 = 3
324
75%

16. 3^5
289
83.33%
243
121

17. 2^7
128
121
144
3125

18. (a+b)^2 =
169
5%
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
A^2 + 2ab + b^2

19. 13^2
256
128
32
169

20. Multiples of 8
You cannot simplify this one
196
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120

21. Multiples of 12
32
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120
144
20%

22. 2^3
8
27
361
64

23. a negative number raised to an even power...
144
A^2 + 2ab + b^2
5%
...yields a positive result (-1)^2 = 1

24. Simplifying a root
(a+b)(a^2-ab+b^2)
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
169
361

25. 2^4
?25.16 = ?25 . ?16 = 5.4 - ?50 . ?18 = ?50.18 = ?900 = 30 - ?144:16 = ?144 : ?16 = 12/4 = 3
40%
16
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

26. 3^3
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
1296
27
?25.16 = ?25 . ?16 = 5.4 - ?50 . ?18 = ?50.18 = ?900 = 30 - ?144:16 = ?144 : ?16 = 12/4 = 3

27. to multiple powers (or raise a power to a power)
Multiply the exponents 7^2(^3) = 7^6
144
(a-b)(a^2+ab+b^2)
3125

28. 16^2
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120
12.50%
256
20%

29. 19^2
A^2 - 2ab + b^2
361
64
50%

30. ? 3
128
20%
...yields a negative result (-1)^57 = -1
1.73

31. 11^2
121
125
13
(A+B)(A-B)

32. 5^4
20%
625
243
...yields a positive result (-1)^2 = 1

33. 2^9
2
216
512
121

34. A^2-B^2
(A+B)(A-B)
256
16.66%
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120

35. Examples of roots simplification
7776
...yields a positive result (-1)^2 = 1
?25.16 = ?25 . ?16 = 5.4 - ?50 . ?18 = ?50.18 = ?900 = 30 - ?144:16 = ?144 : ?16 = 12/4 = 3
243

36. a negative number raised to an odd power...
128
...yields a negative result (-1)^57 = -1
289
256

37. 1/5
243
8
20%
16.67%

38. Express 8^1/3 as a radical
125
7776
144
= the cube root of 8 = 2

39. a^3-b^3
144
1.41
(a-b)(a^2+ab+b^2)
64

40. 3/4
75%
(a+b)(a^2-ab+b^2)
You cannot simplify this one
{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}

41. to multiple powers with the same base...
169
Add the exponents and keep the base 7^3 x 7^5 = 7^8
= the cube root of 8 = 2
...yields a positive result (-1)^2 = 1

42. 2/5
{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}
64
40%
216

43. ? 625
3125
25
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
20%

44. 2^8
12.50%
(A+B)(A-B)
256
3125

45. 4^5
196
64
2.449
1024

46. a^3+b^3
81
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
(a+b)(a^2-ab+b^2)
256

47. 3^4
?25.16 = ?25 . ?16 = 5.4 - ?50 . ?18 = ?50.18 = ?900 = 30 - ?144:16 = ?144 : ?16 = 12/4 = 3
12.50%
81
20%

48. 6^3
216
169
512
You cannot simplify this one

49. 1/2
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
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
50%
40%

50. 14^2
256
125
16
196

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