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Test your basic knowledge 
GMAT Quick Math And Formulas
Start Test
Study First
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 reenforces your understanding as you take the test each time.
1. to multiple powers (or raise a power to a power)
16
243
1.73
Multiply the exponents 7^2(^3) = 7^6
2. 4^3
...yields a negative result (1)^57 = 1
64
625
256
3. 3^3
361
27
Take the reciprocal of the base and change the sign of the exponent (2)^2 = 1^2/2^2 = 1/4
216
4. 5^3
Multiply the exponents 7^2(^3) = 7^6
2.23
144
125
5. a negative number raised to an even power...
...yields a positive result (1)^2 = 1
A^2  2ab + b^2
12  24  36  48  60  72  84  96  108  120
361
6. 2^4
16
87.50%
256
83.33%
7. 12^2
256
√25.16 = √25 . √16 = 5.4  √50 . √18 = √50.18 = √900 = 30  √144:16 = √144 : √16 = 12/4 = 3
512
144
8. A^2B^2
1296
(A+B)(AB)
2.23
√25.16 = √25 . √16 = 5.4  √50 . √18 = √50.18 = √900 = 30  √144:16 = √144 : √16 = 12/4 = 3
9. √ 5
Add the exponents and keep the base 7^3 x 7^5 = 7^8
12.50%
2.23
256
10. 2^7
2.23
128
121
256
11. 7/8
1.41
87.50%
243
81
12. 6^3
32
216
512
169
13. 2^9
512
125
50%
= the cube root of 8 = 2
14. 5^4
625
...yields a positive result (1)^2 = 1
1024
20%
15. a^3b^3
(A+B)(AB)
75%
(ab)(a^2+ab+b^2)
1.41
16. 2^5
32
7776
40%
64
17. √ 3
8.33%
1.73
...yields a positive result (1)^2 = 1
(a+b)(a^2ab+b^2)
18. 5/6
196
...yields a positive result (1)^2 = 1
83.33%
16.66%
19. 16^2
256
12  24  36  48  60  72  84  96  108  120
16.67%
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. 1/6
Multiply the exponents 7^2(^3) = 7^6
(ab)(a^2+ab+b^2)
√25.16 = √25 . √16 = 5.4  √50 . √18 = √50.18 = √900 = 30  √144:16 = √144 : √16 = 12/4 = 3
16.66%
21. 6^5
216
You cannot simplify this one
Take the reciprocal of the base and change the sign of the exponent (2)^2 = 1^2/2^2 = 1/4
7776
22. to divide powers with the same base...
324
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
27
You cannot simplify this one
23. 14^2
196
13
16.66%
1296
24. 4^5
...yields a negative result (1)^57 = 1
225
1024
75%
25. a negative number raised to an odd power...
16
Add the exponents and keep the base 7^3 x 7^5 = 7^8
128
...yields a negative result (1)^57 = 1
26. Prime Numbers between 1  100 (total of 25)
16.66%
{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}
2.449
324
27. √ 4
324
1.41
2
= the square root of 9 = 3
28. Examples of roots simplification
256
361
√25.16 = √25 . √16 = 5.4  √50 . √18 = √50.18 = √900 = 30  √144:16 = √144 : √16 = 12/4 = 3
20%
29. 1/5
324
64
20%
2.449
30. 1/2
128
...yields a positive result (1)^2 = 1
20%
50%
31. √ 6
(A+B)(AB)
2.449
27
83.33%
32. Simplifying a root
12  24  36  48  60  72  84  96  108  120
243
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
33. 2^2
2.449
16.67%
4
√25.16 = √25 . √16 = 5.4  √50 . √18 = √50.18 = √900 = 30  √144:16 = √144 : √16 = 12/4 = 3
34. 11^2
(a+b)(a^2ab+b^2)
121
16.67%
7776
35. (ab)^2 =
2.23
289
(a+b)(a^2ab+b^2)
A^2  2ab + b^2
36. √25+16 = √41
You cannot simplify this one
8  16  24  32  40  48  56  64  72  80  88  96  104  112  120
512
8
37. to multiple powers with the same base...
512
1296
Add the exponents and keep the base 7^3 x 7^5 = 7^8
A^2 + 2ab + b^2
38. 19^2
15  30  45  60  75  90  105  120
256
361
16.67%
39. √ 169
1024
8
16.67%
13
40. raising a fraction between zero and 1 to a power...
...yields a smaller result (1/2)^2 = 1/4
169
12  24  36  48  60  72  84  96  108  120
121
41. Multiples of 8
75%
225
8  16  24  32  40  48  56  64  72  80  88  96  104  112  120
...yields a smaller result (1/2)^2 = 1/4
42. 3^4
√25.16 = √25 . √16 = 5.4  √50 . √18 = √50.18 = √900 = 30  √144:16 = √144 : √16 = 12/4 = 3
16.66%
(A+B)(AB)
81
43. 3/4
81
75%
2.449
169
44. 1/4
...yields a positive result (1)^2 = 1
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
25%
75%
45. √ 625
12.50%
Multiply the exponents 7^2(^3) = 7^6
25
81
46. √ 2
50%
128
1.41
1.73
47. Express 8^1/3 as a radical
1296
25
...yields a negative result (1)^57 = 1
= the cube root of 8 = 2
48. what happens when an exponent is negative?
13
32
Take the reciprocal of the base and change the sign of the exponent (2)^2 = 1^2/2^2 = 1/4
256
49. 2^8
256
81
50%
√25.16 = √25 . √16 = 5.4  √50 . √18 = √50.18 = √900 = 30  √144:16 = √144 : √16 = 12/4 = 3
50. 2^3
7776
...yields a smaller result (1/2)^2 = 1/4
87.50%
8