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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. Express 9^1/2 as a radical
= the square root of 9 = 3
64
243
...yields a smaller result (1/2)^2 = 1/4

2. 5/6
(a+b)(a^2-ab+b^2)
169
512
83.33%

3. (a+b)^2 =
121
3125
A^2 + 2ab + b^2
8.33%

4. 3^5
243
25%
Multiply the exponents 7^2(^3) = 7^6
64

5. 2^2
4
{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}
1296
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120

6. 11^2
225
40%
216
121

7. 2/5
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120
40%
Add the exponents and keep the base 7^3 x 7^5 = 7^8
...yields a smaller result (1/2)^2 = 1/4

8. 2^3
8
2
2.449
256

9. 14^2
1.73
...yields a negative result (-1)^57 = -1
81
196

10. a negative number raised to an odd power...
75%
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120
...yields a negative result (-1)^57 = -1
50%

11. a^3+b^3
...yields a positive result (-1)^2 = 1
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
25
(a+b)(a^2-ab+b^2)

12. 4^3
16.66%
625
64
256

13. 4^5
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120
256
75%
1024

14. 1/12
64
A^2 + 2ab + b^2
8.33%
Multiply the exponents 7^2(^3) = 7^6

15. Multiples of 15
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
81
2.23
(a+b)(a^2-ab+b^2)

16. 1/8
13
256
You cannot simplify this one
12.50%

17. √ 169
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
324
512
13

18. (a-b)^2 =
A^2 - 2ab + b^2
7776
8
25

19. 5^5
...yields a positive result (-1)^2 = 1
A^2 - 2ab + b^2
1024
3125

20. 3^4
A^2 - 2ab + b^2
81
64
87.50%

21. 1/4
81
(A+B)(A-B)
25%
125

22. Express 8^1/3 as a radical
1.73
83.33%
= the cube root of 8 = 2
81

23. √25+16 = √41
A^2 - 2ab + b^2
You cannot simplify this one
1.73
...yields a smaller result (1/2)^2 = 1/4

24. 17^2
1024
256
83.33%
289

25. 2^4
7776
2
16
3125

26. A^2-B^2
144
25%
87.50%
(A+B)(A-B)

27. raising a fraction between zero and 1 to a power...
2.449
...yields a smaller result (1/2)^2 = 1/4
256
289

28. √ 6
8.33%
3125
2.449
256

29. 2^8
256
1024
{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}
225

30. 1/20
1024
= the square root of 9 = 3
...yields a positive result (-1)^2 = 1
5%

31. 3/4
75%
2.23
5%
20%

32. to multiple powers (or raise a power to a power)
7776
75%
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3
Multiply the exponents 7^2(^3) = 7^6

33. 18^2
324
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
3125
You cannot simplify this one

34. √ 5
2.23
50%
64
169

35. a^3-b^3
(a-b)(a^2+ab+b^2)
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120
40%
{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}

36. 13^2
...yields a smaller result (1/2)^2 = 1/4
1024
64
169

37. 2^5
32
Add the exponents and keep the base 7^3 x 7^5 = 7^8
8
16.66%

38. to multiple powers with the same base...
1.41
50%
144
Add the exponents and keep the base 7^3 x 7^5 = 7^8

39. 7/8
289
4
87.50%
...yields a negative result (-1)^57 = -1

40. 2^7
7776
128
256
16

41. Examples of roots simplification
361
75%
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3
2.449

42. 2^9
83.33%
32
289
512

43. 5^3
125
32
Multiply the exponents 7^2(^3) = 7^6
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120

44. to divide powers with the same base...
256
A^2 - 2ab + 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
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3

45. √ 3
A^2 - 2ab + b^2
1.73
225
12.50%

46. 19^2
8.33%
361
27
= the cube root of 8 = 2

47. 1/6
16.66%
4
1024
64

48. 4^4
5%
128
13
256

49. √ 4
2
289
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120

50. Prime Numbers between 1 - 100 (total of 25)
{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
A^2 + 2ab + b^2
2