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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. 1/8
12.50%
(ab)(a^2+ab+b^2)
A^2  2ab + b^2
169
2. 18^2
27
75%
8
324
3. √25+16 = √41
You cannot simplify this one
361
2
√25.16 = √25 . √16 = 5.4  √50 . √18 = √50.18 = √900 = 30  √144:16 = √144 : √16 = 12/4 = 3
4. Express 9^1/2 as a radical
1024
27
15  30  45  60  75  90  105  120
= the square root of 9 = 3
5. 2/5
Take the reciprocal of the base and change the sign of the exponent (2)^2 = 1^2/2^2 = 1/4
128
You cannot simplify this one
40%
6. (a+b)^2 =
625
A^2 + 2ab + b^2
(A+B)(AB)
{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}
7. 1/6
...yields a smaller result (1/2)^2 = 1/4
225
1024
16.66%
8. 11^2
A^2  2ab + b^2
225
121
83.33%
9. 2^9
83.33%
512
7776
121
10. 3^5
243
A^2 + 2ab + b^2
289
27
11. 17^2
64
289
25%
2.449
12. 15^2
27
225
32
256
13. √ 2
1.41
1024
64
256
14. √ 6
50%
Multiply the exponents 7^2(^3) = 7^6
625
2.449
15. Examples of roots simplification
40%
(ab)(a^2+ab+b^2)
87.50%
√25.16 = √25 . √16 = 5.4  √50 . √18 = √50.18 = √900 = 30  √144:16 = √144 : √16 = 12/4 = 3
16. to multiple powers (or raise a power to a power)
(a+b)(a^2ab+b^2)
169
Multiply the exponents 7^2(^3) = 7^6
3125
17. 6^4
75%
{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
4
18. 1/4
243
25%
= the cube root of 8 = 2
40%
19. 5^4
Multiply the exponents 7^2(^3) = 7^6
144
625
225
20. 5^5
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
3125
= the cube root of 8 = 2
15  30  45  60  75  90  105  120
21. a negative number raised to an odd power...
...yields a negative result (1)^57 = 1
64
8  16  24  32  40  48  56  64  72  80  88  96  104  112  120
75%
22. Simplifying a root
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
121
= the cube root of 8 = 2
23. 4^3
64
...yields a negative result (1)^57 = 1
3125
1.73
24. 6^5
7776
64
144
256
25. 1/12
8
8.33%
13
{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. 2^6
64
16
(a+b)(a^2ab+b^2)
83.33%
27. √ 4
2
216
3125
(ab)(a^2+ab+b^2)
28. 1/20
361
324
5%
32
29. 4^5
625
50%
1024
Add the exponents and keep the base 7^3 x 7^5 = 7^8
30. 1/2
8  16  24  32  40  48  56  64  72  80  88  96  104  112  120
50%
83.33%
2
31. A^2B^2
256
3125
15  30  45  60  75  90  105  120
(A+B)(AB)
32. 4^4
256
2.23
512
225
33. Prime Numbers between 1  100 (total of 25)
15  30  45  60  75  90  105  120
(ab)(a^2+ab+b^2)
512
{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}
34. (ab)^2 =
20%
8
√25.16 = √25 . √16 = 5.4  √50 . √18 = √50.18 = √900 = 30  √144:16 = √144 : √16 = 12/4 = 3
A^2  2ab + b^2
35. 2^7
128
64
1.41
(ab)(a^2+ab+b^2)
36. 2^8
12.50%
...yields a smaller result (1/2)^2 = 1/4
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
37. to divide powers with the same base...
Subtract the exponents and keep the base the same 4^5/4^2 = 4^3
256
√25.16 = √25 . √16 = 5.4  √50 . √18 = √50.18 = √900 = 30  √144:16 = √144 : √16 = 12/4 = 3
7776
38. 3/4
243
...yields a negative result (1)^57 = 1
75%
27
39. 2^3
{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
1024
256
40. Multiples of 15
...yields a smaller result (1/2)^2 = 1/4
15  30  45  60  75  90  105  120
83.33%
1.41
41. Express 8^1/3 as a radical
= the cube root of 8 = 2
Add the exponents and keep the base 7^3 x 7^5 = 7^8
12.50%
27
42. 19^2
= the cube root of 8 = 2
361
20%
√25.16 = √25 . √16 = 5.4  √50 . √18 = √50.18 = √900 = 30  √144:16 = √144 : √16 = 12/4 = 3
43. 5/6
83.33%
2.23
(A+B)(AB)
13
44. √ 169
...yields a smaller result (1/2)^2 = 1/4
625
13
3125
45. a negative number raised to an even power...
225
...yields a positive result (1)^2 = 1
361
16.66%
46. 6^3
216
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
{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}
47. 2^2
Take the reciprocal of the base and change the sign of the exponent (2)^2 = 1^2/2^2 = 1/4
4
2
324
48. √ 625
243
289
25
256
49. 1/6
361
16.67%
= the cube root of 8 = 2
256
50. Multiples of 8
144
40%
8  16  24  32  40  48  56  64  72  80  88  96  104  112  120
324