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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
{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}
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
324
= the square root of 9 = 3

2. √ 2
32
225
= the square root of 9 = 3
1.41

3. 1/8
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
...yields a negative result (-1)^57 = -1
81
12.50%

4. 11^2
64
(a+b)(a^2-ab+b^2)
121
27

5. 14^2
196
...yields a positive result (-1)^2 = 1
(a-b)(a^2+ab+b^2)
16.67%

6. 2^2
4
...yields a smaller result (1/2)^2 = 1/4
25
512

7. 1/6
A^2 + 2ab + b^2
A^2 - 2ab + b^2
16.66%
(A+B)(A-B)

8. 1/6
27
16.67%
169
7776

9. 13^2
{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}
169
8
125

10. 2^5
625
1024
13
32

11. to multiple powers (or raise a power to a power)
Multiply the exponents 7^2(^3) = 7^6
83.33%
(A+B)(A-B)
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

12. √ 625
81
25
...yields a negative result (-1)^57 = -1
2.23

13. what happens when an exponent is negative?
1.41
= the square root of 9 = 3
2
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4

14. 17^2
289
A^2 - 2ab + b^2
128
256

15. a^3+b^3
27
(a+b)(a^2-ab+b^2)
1296
289

16. 4^5
= the cube root of 8 = 2
{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}
1024
...yields a positive result (-1)^2 = 1

17. √ 4
289
3125
25%
2

18. to multiple powers with the same base...
196
16
Add the exponents and keep the base 7^3 x 7^5 = 7^8
3125

19. 2/5
144
40%
27
75%

20. 2^9
144
You cannot simplify this one
512
27

21. raising a fraction between zero and 1 to a power...
32
512
...yields a smaller result (1/2)^2 = 1/4
64

22. 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}
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
1.41
125

23. 2^3
8
= the cube root of 8 = 2
243
= the square root of 9 = 3

24. 6^4
83.33%
1296
...yields a negative result (-1)^57 = -1
Multiply the exponents 7^2(^3) = 7^6

25. 2^6
Multiply the exponents 7^2(^3) = 7^6
64
2.449
256

26. 1/20
1.41
4
(a-b)(a^2+ab+b^2)
5%

27. 3^5
25
243
1.73
= the square root of 9 = 3

28. 16^2
...yields a negative result (-1)^57 = -1
75%
256
2

29. 2^7
Multiply the exponents 7^2(^3) = 7^6
87.50%
128
= the cube root of 8 = 2

30. 4^3
64
512
256
75%

31. 6^5
1024
7776
16.66%
1296

32. 5^3
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
243
125
256

33. 2^4
20%
87.50%
16
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3

34. 1/12
16.67%
8.33%
512
121

35. 5^4
25
625
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120
2.23

36. 6^3
216
2
7776
225

37. a negative number raised to an odd power...
A^2 - 2ab + b^2
2
...yields a negative result (-1)^57 = -1
20%

38. (a-b)^2 =
Add the exponents and keep the base 7^3 x 7^5 = 7^8
8
A^2 - 2ab + b^2
4

39. 3^4
13
81
256
625

40. √25+16 = √41
3125
You cannot simplify this one
144
A^2 + 2ab + b^2

41. Express 8^1/3 as a radical
87.50%
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120
= the cube root of 8 = 2
16.67%

42. √ 6
2.449
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
64
256

43. to divide powers with the same base...
64
169
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
2.449

44. 5/6
512
83.33%
64
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4

45. √ 5
...yields a positive result (-1)^2 = 1
2.23
289
4

46. 1/4
2
A^2 - 2ab + b^2
25%
16.66%

47. 1/2
324
1.73
50%
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120

48. 19^2
5%
121
(a+b)(a^2-ab+b^2)
361

49. √ 169
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120
75%
13
7776

50. 3^3
87.50%
27
1024
81