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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. 1/4
25%
256
8
243

2. 1/5
4
20%
You cannot simplify this one
121

3. √ 169
361
13
216
243

4. 1/8
40%
12.50%
144
3125

5. 2^10
3125
75%
256
1024

6. 1/6
(a+b)(a^2-ab+b^2)
2.23
16.67%
13

7. Express 9^1/2 as a radical
= the square root of 9 = 3
...yields a negative result (-1)^57 = -1
256
169

8. 4^4
256
40%
1024
...yields a positive result (-1)^2 = 1

9. 16^2
16.66%
256
128
7776

10. 5^4
(A+B)(A-B)
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
625
512

11. a negative number raised to an odd power...
{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}
...yields a negative result (-1)^57 = -1
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
16

12. √ 4
2
25
Multiply the exponents 7^2(^3) = 7^6
125

13. 12^2
144
125
= the square root of 9 = 3
256

14. to multiple powers (or raise a power to a power)
64
Multiply the exponents 7^2(^3) = 7^6
(A+B)(A-B)
{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. 1/12
32
25
8.33%
75%

16. 1/6
289
8.33%
You cannot simplify this one
16.66%

17. 2^8
75%
...yields a negative result (-1)^57 = -1
16.66%
256

18. 3/4
1.41
75%
1024
40%

19. 5/6
2
83.33%
32
256

20. Prime Numbers between 1 - 100 (total of 25)
5%
144
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}

21. 15^2
225
361
2.449
5%

22. Multiples of 12
256
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120
1.41
...yields a smaller result (1/2)^2 = 1/4

23. √ 5
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
2.23
1024
361

24. 2^3
12.50%
8
20%
256

25. 3^4
2.23
81
75%
256

26. 6^3
...yields a positive result (-1)^2 = 1
256
13
216

27. 3^5
243
216
83.33%
13

28. 13^2
20%
125
169
256

29. Examples of roots simplification
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3
121
83.33%
1296

30. 1/20
5%
144
...yields a smaller result (1/2)^2 = 1/4
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3

31. 1/2
50%
= the square root of 9 = 3
You cannot simplify this one
87.50%

32. (a-b)^2 =
A^2 - 2ab + b^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}
324
75%

33. a^3-b^3
125
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3
(a-b)(a^2+ab+b^2)
1024

34. Simplifying a root
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120
75%
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
8.33%

35. 11^2
1.41
64
512
121

36. (a+b)^2 =
169
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120
A^2 + 2ab + b^2
8.33%

37. 14^2
83.33%
196
64
...yields a smaller result (1/2)^2 = 1/4

38. 2^6
2.23
64
A^2 + 2ab + b^2
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3

39. a^3+b^3
(a+b)(a^2-ab+b^2)
256
121
32

40. 19^2
5%
361
25
2.23

41. 17^2
20%
324
64
289

42. 6^4
2
1024
1296
225

43. 5^3
1.41
196
125
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120

44. √ 6
(A+B)(A-B)
2.449
1.41
13

45. Multiples of 8
8
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120
64
(a-b)(a^2+ab+b^2)

46. to divide powers with the same base...
Add the exponents and keep the base 7^3 x 7^5 = 7^8
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
225
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120

47. 18^2
256
625
(a-b)(a^2+ab+b^2)
324

48. 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}
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
Multiply the exponents 7^2(^3) = 7^6
40%

49. to multiple powers with the same base...
Add the exponents and keep the base 7^3 x 7^5 = 7^8
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3
A^2 - 2ab + b^2
= the cube root of 8 = 2

50. Express 8^1/3 as a radical
216
= the cube root of 8 = 2
512
81