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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. to multiple powers with the same base...
64
Add the exponents and keep the base 7^3 x 7^5 = 7^8
4
= the cube root of 8 = 2

2. 17^2
289
A^2 - 2ab + b^2
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120
256

3. √ 625
196
You cannot simplify this one
25
16

4. 4^3
16
128
625
64

5. a^3+b^3
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120
64
81
(a+b)(a^2-ab+b^2)

6. 5^3
1296
125
83.33%
...yields a positive result (-1)^2 = 1

7. Multiples of 15
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
512
225
7776

8. Simplifying a root
You cannot simplify this one
216
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
3125

9. to divide powers with the same base...
216
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
(a+b)(a^2-ab+b^2)
50%

10. 19^2
Add the exponents and keep the base 7^3 x 7^5 = 7^8
8
20%
361

11. 1/6
2.23
16.67%
8.33%
1024

12. 3/4
1296
169
64
75%

13. 6^4
1296
50%
(a-b)(a^2+ab+b^2)
16.67%

14. 7/8
7776
16.67%
83.33%
87.50%

15. 6^5
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3
169
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
7776

16. 1/20
5%
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120
81
216

17. 5^5
125
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
3125
16.67%

18. √ 5
243
16.67%
2.23
A^2 - 2ab + b^2

19. 12^2
= the square root of 9 = 3
144
7776
25

20. 1/5
= the square root of 9 = 3
20%
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120
64

21. √ 4
8.33%
2
256
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120

22. 11^2
(A+B)(A-B)
1.41
25
121

23. raising a fraction between zero and 1 to a power...
2
256
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
...yields a smaller result (1/2)^2 = 1/4

24. what happens when an exponent is negative?
A^2 + 2ab + b^2
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
(A+B)(A-B)
A^2 - 2ab + b^2

25. 14^2
512
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
196
121

26. 15^2
1024
(A+B)(A-B)
225
(a+b)(a^2-ab+b^2)

27. Prime Numbers between 1 - 100 (total of 25)
225
87.50%
{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}
27

28. 2/5
16
40%
25
256

29. Express 8^1/3 as a radical
= the cube root of 8 = 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
512
256

30. 13^2
25
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
2

31. Examples of roots simplification
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
169
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3

32. √ 2
32
1.41
7776
75%

33. A^2-B^2
...yields a positive result (-1)^2 = 1
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
2.23
(A+B)(A-B)

34. Multiples of 8
256
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
125

35. a negative number raised to an even power...
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120
216
...yields a positive result (-1)^2 = 1
20%

36. 1/2
40%
50%
8.33%
75%

37. 2^9
196
20%
...yields a positive result (-1)^2 = 1
512

38. Multiples of 12
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
75%
196

39. 2^3
8
...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
1024

40. 2^5
128
20%
64
32

41. to multiple powers (or raise a power to a power)
Add the exponents and keep the base 7^3 x 7^5 = 7^8
Multiply the exponents 7^2(^3) = 7^6
625
144

42. 1/4
40%
3125
25%
Add the exponents and keep the base 7^3 x 7^5 = 7^8

43. 6^3
1024
216
225
...yields a smaller result (1/2)^2 = 1/4

44. 2^4
625
83.33%
16
361

45. 5/6
83.33%
2
7776
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4

46. 18^2
...yields a negative result (-1)^57 = -1
324
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3
13

47. √ 6
64
Add the exponents and keep the base 7^3 x 7^5 = 7^8
2.449
You cannot simplify this one

48. 2^2
256
128
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}

49. Express 9^1/2 as a radical
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3
= the square root of 9 = 3
40%
A^2 - 2ab + b^2

50. 2^7
216
128
289
16.66%