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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. √ 5
2.23
Add the exponents and keep the base 7^3 x 7^5 = 7^8
256
A^2 + 2ab + b^2

2. 19^2
(a-b)(a^2+ab+b^2)
75%
361
256

3. 2^5
289
125
16
32

4. 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
20%
64
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4

5. √ 625
{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}
25
3125
20%

6. Express 9^1/2 as a radical
= the square root of 9 = 3
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

7. 2^4
125
16
(a-b)(a^2+ab+b^2)
1024

8. 1/20
...yields a smaller result (1/2)^2 = 1/4
20%
7776
5%

9. 1/5
{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}
128
20%
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120

10. 13^2
243
169
...yields a positive result (-1)^2 = 1
216

11. 2^7
7776
20%
128
(a-b)(a^2+ab+b^2)

12. 12^2
87.50%
144
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120
1.41

13. √ 2
289
32
1.41
625

14. √ 3
1.73
12.50%
Multiply the exponents 7^2(^3) = 7^6
128

15. to divide powers with the same base...
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
2
16.67%
75%

16. Multiples of 12
12 - 24 - 36 - 48 - 60 - 72 - 84 - 96 - 108 - 120
(a+b)(a^2-ab+b^2)
1.73
1.41

17. 1/6
13
289
16.67%
2

18. 2^9
...yields a negative result (-1)^57 = -1
512
144
256

19. 14^2
196
{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}
1296
361

20. 6^5
= the cube root of 8 = 2
7776
81
2

21. 1/8
...yields a negative result (-1)^57 = -1
12.50%
13
= the square root of 9 = 3

22. 6^3
1296
216
125
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3

23. 7/8
87.50%
A^2 - 2ab + b^2
1.41
3125

24. 1/2
50%
64
7776
256

25. Prime Numbers between 1 - 100 (total of 25)
361
256
196
{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}

26. √25+16 = √41
You cannot simplify this one
128
256
64

27. 5^5
512
1024
3125
243

28. raising a fraction between zero and 1 to a power...
...yields a smaller result (1/2)^2 = 1/4
...yields a negative result (-1)^57 = -1
324
169

29. 1/12
8.33%
1024
16
2

30. 3/4
A^2 + 2ab + b^2
(a+b)(a^2-ab+b^2)
75%
128

31. 2/5
40%
...yields a smaller result (1/2)^2 = 1/4
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
225

32. 3^4
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
= the square root of 9 = 3
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120
81

33. 2^3
A^2 + 2ab + b^2
125
2.23
8

34. 6^4
196
1296
512
50%

35. what happens when an exponent is negative?
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}
= the cube root of 8 = 2
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4

36. 3^3
13
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
27

37. to multiple powers (or raise a power to a power)
512
(A+B)(A-B)
Multiply the exponents 7^2(^3) = 7^6
7776

38. 18^2
3125
324
256
16.66%

39. √ 4
(a+b)(a^2-ab+b^2)
A^2 - 2ab + b^2
5%
2

40. Multiples of 15
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
16
A^2 - 2ab + b^2
5%

41. a negative number raised to an odd power...
81
...yields a negative result (-1)^57 = -1
169
2

42. 2^8
You cannot simplify this one
2
256
121

43. to multiple powers with the same base...
Add the exponents and keep the base 7^3 x 7^5 = 7^8
...yields a smaller result (1/2)^2 = 1/4
15 - 30 - 45 - 60 - 75 - 90 - 105 - 120
8 - 16 - 24 - 32 - 40 - 48 - 56 - 64 - 72 - 80 - 88 - 96 - 104 - 112 - 120

44. 5^4
128
625
16
Multiply the exponents 7^2(^3) = 7^6

45. √ 169
13
2.23
2.449
A^2 + 2ab + b^2

46. a^3-b^3
361
(a-b)(a^2+ab+b^2)
= the cube root of 8 = 2
√25.16 = √25 . √16 = 5.4 - √50 . √18 = √50.18 = √900 = 30 - √144:16 = √144 : √16 = 12/4 = 3

47. 11^2
= the cube root of 8 = 2
2
Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
121

48. 1/6
Add the exponents and keep the base 7^3 x 7^5 = 7^8
16.66%
16.67%
81

49. (a-b)^2 =
20%
243
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}

50. 2^10
12.50%
A^2 + 2ab + b^2
2.23
1024