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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. 2^8
256
...yields a smaller result (1/2)^2 = 1/4
64
12.50%

2. 1/5
13
1296
20%
25%

3. a negative number raised to an odd power...
12.50%
1296
...yields a negative result (-1)^57 = -1
3125

4. 1/2
A^2 + 2ab + b^2
1296
50%
512

5. Multiples of 8
75%
256
20%
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120

6. 12^2
361
144
2
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120

7. 5^4
625
1.73
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
83.33%

8. 3/4
75%
625
A^2 + 2ab + b^2
40%

9. 2^9
256
512
2.23
324

10. Multiples of 15
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
20%
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
8.33%

11. 5/6
83.33%
125
You cannot simplify this one
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. 7/8
16.66%
2.23
2
87.50%

13. (a-b)^2 =
A^2 - 2ab + b^2
128
144
196

14. 3^5
243
16.67%
81
625

15. √25+16 = √41
1024
You cannot simplify this one
2.449
32

16. 1/20
5%
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120
40%
20%

17. 18^2
= the square root of 9 = 3
324
40%
Multiply the exponents 7^2(^3) = 7^6

18. 1/12
75%
Add the exponents and keep the base 7^3 x 7^5 = 7^8
8.33%
324

19. to divide powers with the same base...
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
144
12.50%
512

20. Examples of roots simplification
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3
289
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
2.449

21. to multiple powers (or raise a power to a power)
1.73
81
(a-b)(a^2+ab+b^2)
Multiply the exponents 7^2(^3) = 7^6

22. 6^3
64
You cannot simplify this one
216
...yields a smaller result (1/2)^2 = 1/4

23. 1/6
64
16.67%
512
1024

24. 5^3
8.33%
625
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
125

25. 3^3
27
169
81
2.23

26. Express 9^1/2 as a radical
...yields a negative result (-1)^57 = -1
128
87.50%
= the square root of 9 = 3

27. 1/8
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
75%
12.50%
256

28. 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}
3125
1024
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

29. what happens when an exponent is negative?
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
216
16
196

30. A^2-B^2
(A+B)(A-B)
169
25
225

31. 2^10
1.73
16.66%
1024
289

32. 13^2
7776
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
256
169

33. a^3-b^3
(a-b)(a^2+ab+b^2)
(a+b)(a^2-ab+b^2)
64
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

34. 2/5
= the square root of 9 = 3
12.50%
361
40%

35. Express 8^1/3 as a radical
= the cube root of 8 = 2
75%
3125
144

36. raising a fraction between zero and 1 to a power...
...yields a smaller result (1/2)^2 = 1/4
324
216
64

37. 5^5
16
(a-b)(a^2+ab+b^2)
3125
A^2 - 2ab + b^2

38. a^3+b^3
81
512
(a+b)(a^2-ab+b^2)
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3

39. √ 169
87.50%
13
81
{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}

40. a negative number raised to an even power...
A^2 + 2ab + b^2
1.73
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
...yields a positive result (-1)^2 = 1

41. √ 6
1296
289
25
2.449

42. to multiple powers with the same base...
A^2 - 2ab + b^2
Add the exponents and keep the base 7^3 x 7^5 = 7^8
16
361

43. 17^2
2.449
289
50%
...yields a negative result (-1)^57 = -1

44. 3^4
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120
289
A^2 + 2ab + b^2
81

45. 16^2
1296
144
(a-b)(a^2+ab+b^2)
256

46. 2^5
2.23
83.33%
32
50%

47. √ 2
8.33%
1.41
1024
5%

48. 11^2
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3
1.41
121
2

49. Simplifying a root
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 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
125

50. √ 5
256
...yields a smaller result (1/2)^2 = 1/4
2.23
27