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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
A^2 - 2ab + b^2
144
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

2. 1/5
20%
16.66%
...yields a positive result (-1)^2 = 1
8.33%

3. 2/5
40%
4
225
...yields a negative result (-1)^57 = -1

4. raising a fraction between zero and 1 to a power...
83.33%
...yields a positive result (-1)^2 = 1
...yields a smaller result (1/2)^2 = 1/4
27

5. what happens when an exponent is negative?
...yields a negative result (-1)^57 = -1
50%
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
You cannot simplify this one

6. 2^4
324
1296
...yields a positive result (-1)^2 = 1
16

7. 1/6
(a+b)(a^2-ab+b^2)
8.33%
324
16.66%

8. Express 9^1/2 as a radical
...yields a smaller result (1/2)^2 = 1/4
121
= the square root of 9 = 3
1296

9. 1/20
83.33%
128
5%
(a+b)(a^2-ab+b^2)

10. 13^2
A^2 - 2ab + b^2
144
169
13

11. 1/6
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
16.67%
121

12. √ 2
121
1.41
8.33%
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120

13. 17^2
7776
289
1024
144

14. a^3+b^3
(a+b)(a^2-ab+b^2)
27
125
75%

15. 1/12
2.449
125
A^2 - 2ab + b^2
8.33%

16. √ 3
196
(a+b)(a^2-ab+b^2)
1.73
1.41

17. Multiples of 8
64
625
75%
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120

18. 18^2
216
32
75%
324

19. 3^3
256
1.73
27
87.50%

20. Express 8^1/3 as a radical
You cannot simplify this one
...yields a negative result (-1)^57 = -1
= the cube root of 8 = 2
7776

21. Multiples of 12
2.449
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120
25%
5%

22. 5/6
83.33%
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
256
5%

23. 2^8
13
1024
256
512

24. (a-b)^2 =
625
√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)
A^2 - 2ab + b^2

25. √ 6
...yields a positive result (-1)^2 = 1
1296
2.449
361

26. a negative number raised to an odd power...
8
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 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}
...yields a negative result (-1)^57 = -1

27. to multiple powers (or raise a power to a power)
128
Multiply the exponents 7^2(^3) = 7^6
A^2 - 2ab + b^2
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3

28. 6^3
= the square root of 9 = 3
A^2 + 2ab + b^2
216
289

29. 7/8
225
7776
{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}
87.50%

30. √ 5
Multiply the exponents 7^2(^3) = 7^6
125
2.23
Add the exponents and keep the base 7^3 x 7^5 = 7^8

31. 6^5
7776
256
A^2 - 2ab + b^2
= the square root of 9 = 3

32. Prime Numbers between 1 - 100 (total of 25)
12.50%
2.449
{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}
256

33. 11^2
256
= the square root of 9 = 3
1024
121

34. √ 169
225
1024
You cannot simplify this one
13

35. 1/8
169
12.50%
A^2 + 2ab + b^2
16

36. √ 625
2
25
16.67%
216

37. 2^10
1024
12.50%
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
87.50%

38. 5^4
625
4
20%
5%

39. Examples of roots simplification
1296
144
(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

40. 5^3
125
144
27
625

41. A^2-B^2
75%
289
8
(A+B)(A-B)

42. √ 4
128
83.33%
2
= the cube root of 8 = 2

43. 15^2
= the square root of 9 = 3
2.23
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120
225

44. Multiples of 15
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
87.50%
625

45. 3/4
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3
75%
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
...yields a positive result (-1)^2 = 1

46. 2^9
512
A^2 - 2ab + b^2
64
= the cube root of 8 = 2

47. 3^5
A^2 + 2ab + b^2
243
1.73
...yields a negative result (-1)^57 = -1

48. to divide powers with the same base...
A^2 + 2ab + b^2
8.33%
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
1.41

49. to multiple powers with the same base...
(a-b)(a^2+ab+b^2)
Add the exponents and keep the base 7^3 x 7^5 = 7^8
...yields a negative result (-1)^57 = -1
625

50. 6^4
1296
You cannot simplify this one
16.67%
(a+b)(a^2-ab+b^2)