题库 | 考满分，百万出国党的口碑之选。

序号	题目内容
61	A large flower arrangement contains 3 types of flowers: carnations, lilies, and roses. Of all the flowers in the arrangement, $$\frac{1}{2}$$ are carnations, $$\frac{1}{3}$$ are lilies, and $$\frac{1}{6}$$ are roses. The total price of which of the 3 types of flowers in the arrangement is the greatest? 1.The prices per flower for carnations, lilies, and roses are in the ratio 1:3:4, respectively. 2.The price of one rose is $0.75 more than the price of one carnation, and the price of one rose is $0.25 more than the price of one lily.
62	If x and y are integers between 10 and 99, inclusive,is $$\frac{x - y}{9}$$ an integer? 1. x and y have the same two digits, but in reverse order. 2.The tens' digit of x is 2 more than the units' digit, and the tens' digit of y is 2 less than the units' digit.
63	If x is a positive integer, how many positive integers less than x are divisors of x ? 1. $$x^{2}$$ is divisible by exactly 4 positive integers less than $$x^{2}$$. 2. 2x is divisible by exactly 3 positive integers less than 2x.
64	If x and y are integers, is xy+ 1 divisible by 3 ?[br/[ 1.When x is divided by 3, the remainder is 1. 2.When y is divided by 9, the remainder is 8.
65	The 9 participants in a race were divided into 3 teams with 3 runners on each team. A team was awarded 6 - n points if one of its runners finished in nth place, where $$ 1\leq n \leq 5 $$. If all of the runners finished the race and if there were no ties, was each team awarded at least 1 point? 1.No team was awarded more than a total of 6 points. 2.No pair of teammates finished in consecutive places among the top five places.
66	If ⊛ denotes a mathematical operation, does x⊛ y = y⊛ x for all x and y ? 1.For all x and y, x⊛ y = 2($$x^{2} + y^{2}$$). 2.For all y,0⊛ y = 2$$y^{2}$$
67	The first four digits of the six-digit initial password for a shopper's card at a certain grocery store is the customer's birthday in day-month digit form. For example, 15 August corresponds to 1508 and 5 March corresponds to 0503. The 5th digit of the initial password is the units digit of seven times the sum of the first and third digits, and the 6th digit of the initial password is the units digit of three times the sum of the second and fourth digits. What month, and what day of that month, was a customer born whose initial password ends in 16 ? 1.The customer's initial password begins with 21, and its fourth digit is 1. 2.The sum of the first and third digits of the customer's initial password is 3, and its second digit is 1.
68	n = $$2^{4} • 3^{2} • 5^{2}$$ and positive integer d is a divisor of n. is d > $$\sqrt{n}$$ ? 1.d is divisible by 10. 2.d is divisible by 36.
69	If m and n are positive integers, is n even? 1.m(m + 2)+ 1 = mn 2.m(m + n)is odd.
70	Given a positive number N, when N is rounded by a certain method (for convenience, call it Method Y), the result is $$10^{n}$$ if and only if n is an integer and $$5 10^{n-1} \leq N < 510^{n}$$. In a certain gas sample, there are, when rounded by Method Y, $$10^{21}$$ molecules of $$H_2$$ and also $$10^{21}$$ molecules of $$O_2$$. When rounded by Method Y, what is the combined number of $$H_2$$ and $$O_2$$ molecules in the gas sample ? 1.The number of $$H_2$$ molecules and the number of $$O_2$$ molecules are each less than 3 *$$10^{21}$$. 2.The number of $$H_2$$ molecules is more than mice the number of $$O_2$$ molecules.
71	If n is an integer, is $$\frac{n}{15}$$ an integer? 1. $$\frac{3n}{15}$$ i s an integer. 2. $$\frac{8n}{15}$$ is an integer.
72	If K is a positive integer less than 10 and N = 4,321 十 K, what is the value of K ? 1.N is divisible by 3. 2.N is divisible by 7.
73	Can the positive integer n be written as the sum of two different positive prime numbers? 1.n is greater than 3. 2.n is odd.
74	If x, y,and d are integers and d is odd, are both x and y divisible by d ? 1.x + y is divisible by d. 2.x - y is divisible by d.
75	If b is an integer, is $$\sqrt{a^{2}+b^{2}}$$ an integer? 1.$$a^{2} + b^{2}$$ is an integer. 2.$$a^{2} - 3b^{2}$$ = 0
76	Exactly 3 deposits have been made in a savings account and the amounts of the deposits are 3 consecutive integer multiples of $7. If the sum of the deposits is between $120 and $170, what is the amount of each of the deposits? 1.The amount of one of the deposits is $49. 2.The amount of one of the deposits is $63.
77	If m and n are positive integers, what is the value of $$\frac{3}{m}+\frac{n}{4}$$ ? 1.mn=12 2.$$\frac{3}{m}$$ is in lowest terms and $$\frac{n}{4}$$ is in lowest terms.
78	Is x an integer? 1.$$x^{2}$$ is an integer. 2.$$\frac{x}{2}$$ is not an integer.
79	If x and z are integers: is x + $$z^{2}$$ odd? 1.x is odd and z is even. 2.x -z is odd.
80	If b is the product of three consecutive positive integers c, c + 1, and c + 2, is b a multiple of 24? 1.b is a multiple of 8. 2.c is odd.

序号

题目内容

A large flower arrangement contains 3 types of flowers: carnations, lilies, and roses. Of all the flowers in the arrangement, $$\frac{1}{2}$$ are carnations, $$\frac{1}{3}$$ are lilies, and $$\frac{1}{6}$$ are roses. The total price of which of the 3 types of flowers in the arrangement is the greatest? 1.The prices per flower for carnations, lilies, and roses are in the ratio 1:3:4, respectively. 2.The price of one rose is $0.75 more than the price of one carnation, and the price of one rose is $0.25 more than the price of one lily.

If x and y are integers between 10 and 99, inclusive,is $$\frac{x - y}{9}$$ an integer? 1. x and y have the same two digits, but in reverse order. 2.The tens' digit of x is 2 more than the units' digit, and the tens' digit of y is 2 less than the units' digit.

If x is a positive integer, how many positive integers less than x are divisors of x ? 1. $$x^{2}$$ is divisible by exactly 4 positive integers less than $$x^{2}$$. 2. 2x is divisible by exactly 3 positive integers less than 2x.

If x and y are integers, is xy+ 1 divisible by 3 ?[br/[ 1.When x is divided by 3, the remainder is 1. 2.When y is divided by 9, the remainder is 8.

The 9 participants in a race were divided into 3 teams with 3 runners on each team. A team was awarded 6 - n points if one of its runners finished in nth place, where $$ 1\leq n \leq 5 $$. If all of the runners finished the race and if there were no ties, was each team awarded at least 1 point? 1.No team was awarded more than a total of 6 points. 2.No pair of teammates finished in consecutive places among the top five places.

If ⊛ denotes a mathematical operation, does x⊛ y = y⊛ x for all x and y ? 1.For all x and y, x⊛ y = 2($$x^{2} + y^{2}$$). 2.For all y,0⊛ y = 2$$y^{2}$$

The first four digits of the six-digit initial password for a shopper's card at a certain grocery store is the customer's birthday in day-month digit form. For example, 15 August corresponds to 1508 and 5 March corresponds to 0503. The 5th digit of the initial password is the units digit of seven times the sum of the first and third digits, and the 6th digit of the initial password is the units digit of three times the sum of the second and fourth digits. What month, and what day of that month, was a customer born whose initial password ends in 16 ? 1.The customer's initial password begins with 21, and its fourth digit is 1. 2.The sum of the first and third digits of the customer's initial password is 3, and its second digit is 1.

n = $$2^{4} • 3^{2} • 5^{2}$$ and positive integer d is a divisor of n. is d > $$\sqrt{n}$$ ? 1.d is divisible by 10. 2.d is divisible by 36.

If m and n are positive integers, is n even? 1.m(m + 2)+ 1 = mn 2.m(m + n)is odd.

Given a positive number N, when N is rounded by a certain method (for convenience, call it Method Y), the result is $$10^{n}$$ if and only if n is an integer and $$5 *10^{n-1} \leq N < 5*10^{n}$$. In a certain gas sample, there are, when rounded by Method Y, $$10^{21}$$ molecules of $$H_2$$ and also $$10^{21}$$ molecules of $$O_2$$. When rounded by Method Y, what is the combined number of $$H_2$$ and $$O_2$$ molecules in the gas sample ? 1.The number of $$H_2$$ molecules and the number of $$O_2$$ molecules are each less than 3 *$$10^{21}$$. 2.The number of $$H_2$$ molecules is more than mice the number of $$O_2$$ molecules.