from: category_eng
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1. | |
2. E |
Understanding |
There are several even number and multiple of 3. Why is the 36 a multiple of 3? | |
(1) Even numbers: 36, 38, 42 (2) Multiple of 3 : 33, 36,39,42 Even though we take both, we can't answer for the question. |
3. B |
Understanding |
LCM problem | |
x: a number of students in the class. It's multiple of 8 and 12. x=8p=12q. 2*2*2p 2*2*3q |
4. D |
Understanding |
5. e |
Understanding |
81=3*3*3*3 | |
x should be a factor of 81. (1) x can be 3*3, 3*3*3, 3*3*3*3 to make it integer. (2) X should be a multiple of 3 |
6. C | |
7. C | |
How many 3s in 30!? at least 10.. In addition to, think about multiple of 9 and multiple of 27 | |
8. D | |
7150=2*5*5*(11*13) | |
9. A |
Understanding |
Divisible by 1 through 7 ? Multiple of 1 through 7? | |
The number should have 1 through 7 as a factor. so.. 2*3*2*5*7*p so.. What is the smallest number then? |
10. A | |
Pick a number | |
11. E |
Mathematical Writing |
d is divisible by 25 d= 25k | |
(1) d=25p =5*5p (2) d= 40q=2*2*2*5q If we take both conditions, d is a multiple of 2*2*2*5*5. so.. |
12. B | |
13. E | |
12, 30, 21.. (1)and (2) are equivalent | |
14. E |
Understanding |
Two consecutive number is divisible by 2 Three consecutive number is divisible by 3. | |
15. A | |
16. E | |
We can express the three consecutive integers as n, n+1, n+2 | |
17. D |
Understanding |
147000=3*7*7*2^3*5^3 what's your target to find? |
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This is the same question of finding #of factor 7. 147000=3*7*7*2^3*5^3 so.. There are two 7's. Discussion) How about 147000000?
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18. A | |
96=3*2^5 | |
19. E | |
Factorize 3150 | |
20. A | |
(10x+y)+(10y+x)=11(x+y) | |
21. A | |
15x+29y=440. 29y=5(88-3x) y should be multiple of 5. but less than 20. | |
22. B |
Understanding |
n=m*k? (1)3n=m*p (2)13n=m*q, m is less than 13 so that it can't be a multiple of 13, which means that q is a multiple of 13. Therefore, n is a multiple of m. |