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OG数学09/25
| 4.if x and y are nonzero integers, is x/y an integer?1).x is the product of 2 and some other intefer 2).There is only one pair of positive
integers whose product equals y.
my answer, E, because we can define the exact integers of x and y
5.is x^2-y^2 a positive number? 1>, x-y is a positive number. 2>. x +y is a positive number
my answer C, i think here we can get the answer as follows: x^2-y^2= (x+y)*(x-y)
6. If y =/ 0 and y=/ -1, which is greater, x/y or x/(y+1)? 1>. x=/ 0 2>. x>y
my answer E
7. S is a set of integers such that i) if a is in S, then -a is in S, and ii) if each of a and b is in S, then ab is in S. Is -4 in S?
1>. 1 is in S 2>. 2 is in S
dont know how to calculate
8. if Ruth began a job and worked continuously until she finished, at what time of day did she finish the job?
1>. She started the job at 8:15 a.m. and at noon of the same day she had worked exactly half of the time that it took her to do the
whole job. 2>. She was finished exactly 7*1/2 hours after she had started.
my answer A
9. Is x and even integer? 1>. x is the square of an integer. 2>. x is the cube of an integer
my answer E, for from two terms here, we can get 0,1
10.Before play-offs, a cerain team had won 80 percent of its games. Agter play-offs, what percent of all its games had the team won?
1>. The team competed in 4 play-off games. 2>. The team won all of its play-off games.
my answer E, cause we dont know the number of games before play-offs.
11. If x and y are integers, is xy+1 divisible by 3? 1>. when x is divided by 3, the remainder is 1 2>. When y is divided by 9, the
remainder is 8
my answer C, we know from the two terms, the unit digit of xy+1 is the multible of 3, such as 4*7+1
12. If x=/ 0, is |x| <1? 1>. x^2<1 2>. |x|< 1/x
my answer A, cause we can get the result of x from term 1, -1. Before the exchange, bowl x contained 2 black jelly beans. 2>. After the exchange, bowl y contained 1 jelly bean of each color.
my answer E, cause we dont know wether bowl y contains two red jelly beans
14. If ( ) represents a digit in the 7-digit number 3,62( ),215, what is the value of ( )? 1>. The sum of the 7 digits is equal to 4 times an
integer. 2>. The missing digit is different from any of the other digits in the number.
my answer C, the missing digits are 4,7,8,9, however, accord to the term 1, 19+x=4*y, only digit is 7
15. Is x less than y? 1>. x-y+1<0 2>. x-y-1<0
my answer C, according to the rules of inequality, we can plus 1 and 2, then we get x<0
16. The (x,y) pair (-1,1) satisfies which of teh following equations? I. 2x^3 - y^2 =-3 II. 2x^2 - y^3 = 1 III. x^2 - 2y^3 = -1
A. I only B. I and II only C. II and III only D. I, II, and III
dont know how to do
17. A milliner bought a job lot of hats, 1/4 of which were brown. The milliner sold 2/3 of the hats including 4/5 of the brown hats. What
fraction of the unsold hats were brown? A. 1/60 B. 2/15 C. 3/20 D. 3/5 E. 3/4
my method (1/4*4/5)/1/3, my answer D
18. How many integers n greater than 10 and less than 100 are there such that, if the digits of n are reversed, the resulting integer is
n+9? A. 5 B 6 C7 D 8 E 9
my method: 10a + b +9 = 10b + a---> a +1=b, so , there are 12,23,34,45,56,67,78,89 according to the condition here
my answer 8
19. Over the last three years a scientist had an average (arithmetic mean) yearly income of $45,000. The scientist cearned 1(1/2) times
as much the second year as the first year and 2*1/2 times as much the third year as the first year. What was the scientist's income the
second year? A.$9,000 B. $13,500 C $27,000 D.$40,500 E. $45,000
my method: b=3/2a, c=5/2a, my answer D
20. How many two-digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?
A. None B. one, C. two D. three E. four
my method, according to the given conditions, the number should be the multible of 30 +1, so there are 31,61,91
my answer D.
21. What is the 1st term in sequence S? 1>. The 3rd term in S is 2 2>. The 2nd term in S is twice the 1st, and the 3rd is three times
the 2nd
my answer C, the sequence S is 1/3,2/3,2 |
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