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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. Simplifying a root
2.23
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
Add the exponents and keep the base 7^3 x 7^5 = 7^8
...yields a positive result (-1)^2 = 1

2. A^2-B^2
(A+B)(A-B)
= the cube root of 8 = 2
40%
A^2 - 2ab + b^2

3. Express 8^1/3 as a radical
256
= the cube root of 8 = 2
12.50%
You cannot simplify this one

4. 3^3
27
40%
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
20%

5. Express 9^1/2 as a radical
1296
27
= the square root of 9 = 3
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120

6. √ 6
2.449
169
361
13

7. 6^4
27
1296
361
256

8. 7/8
12.50%
243
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
87.50%

9. a^3+b^3
(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
{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}
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

10. 17^2
5%
289
1296
8

11. 4^4
125
25%
256
243

12. 3/4
225
...yields a negative result (-1)^57 = -1
75%
3125

13. 12^2
(a+b)(a^2-ab+b^2)
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
144
1.41

14. 3^4
83.33%
Multiply the exponents 7^2(^3) = 7^6
87.50%
81

15. 2^8
...yields a negative result (-1)^57 = -1
256
...yields a positive result (-1)^2 = 1
...yields a smaller result (1/2)^2 = 1/4

16. 6^3
{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}
= the square root of 9 = 3
216
A^2 - 2ab + b^2

17. raising a fraction between zero and 1 to a power...
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3
8
{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 smaller result (1/2)^2 = 1/4

18. 4^3
225
16.67%
83.33%
64

19. 2^5
32
121
75%
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3

20. 1/6
50%
121
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
16.66%

21. 5^3
125
64
1024
1.41

22. Multiples of 15
2
12.50%
...yields a negative result (-1)^57 = -1
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120

23. 11^2
8.33%
1.73
121
625

24. 19^2
(a-b)(a^2+ab+b^2)
20%
361
...yields a smaller result (1/2)^2 = 1/4

25. 1/2
= the square root of 9 = 3
{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}
8
50%

26. 1/8
1296
87.50%
...yields a positive result (-1)^2 = 1
12.50%

27. 2^7
50%
128
83.33%
256

28. 14^2
{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}
625
196
64

29. 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
...yields a smaller result (1/2)^2 = 1/4
256

30. a^3-b^3
16
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120
1024
(a-b)(a^2+ab+b^2)

31. √ 4
121
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
2
1.41

32. 2^3
256
4
2.449
8

33. √25+16 = √41
A^2 + 2ab + b^2
1.41
You cannot simplify this one
243

34. 2^2
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
8
4
...yields a positive result (-1)^2 = 1

35. Multiples of 8
1.73
1296
83.33%
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120

36. to divide powers with the same base...
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
1024
256
16.67%

37. 1/5
243
20%
...yields a positive result (-1)^2 = 1
216

38. √ 3
289
1.73
64
(a-b)(a^2+ab+b^2)

39. 1/6
87.50%
16.67%
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}

40. 1/4
{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}
A^2 - 2ab + b^2
2.449
25%

41. 2^6
64
= the square root of 9 = 3
2
25%

42. 5^5
4
(a-b)(a^2+ab+b^2)
3125
= the square root of 9 = 3

43. a negative number raised to an even power...
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
128
...yields a positive result (-1)^2 = 1
16

44. 2^9
32
64
1.73
512

45. (a-b)^2 =
A^2 - 2ab + b^2
1.41
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
169

46. Examples of roots simplification
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3
144
16.66%
A^2 - 2ab + b^2

47. 5^4
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120
625
87.50%
256

48. √ 625
= the square root of 9 = 3
25
169
(A+B)(A-B)

49. 3^5
256
16.67%
Add the exponents and keep the base 7^3 x 7^5 = 7^8
243

50. 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
A^2 - 2ab + b^2
87.50%
2