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数论
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Is three digit integer n divisible by 12?(1) n is divisible by 4.(2) The hundreds digit and the units digit of n are divisible by 3.
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排列组合
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There are 8 books on a shelf, of which 2 are paperbacks and 6 are hardbacks. How many possible selections of 4 books from this self include at least one paperback?
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The sequence $$a_1$$, $$a_2$$, $$a_3$$.....$$a_n$$...is such that $$a_n=\frac{a_{n-1}+a_{n-2}}{2}$$ for all $${n}\ge{3}$$. If $${a}_{3}$$=4 and $${a}_{5}$$ = 20, what is the value of $${a}_{6}$$ ?
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What is the value of$${1} \over{x^{2}-y^{2}} $$*$${-1}\over{x^{2}+2xy+y^{2}}$$?1.$$2y=x^{2}-y^{2}$$2.x+y=4
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OG19-定量推理
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If N is a positive odd integer, is N prime?
(1) $$N = 2^{k} + 1$$ for some positive integer k.
(2) $$N + 2$$ and $$N + 4$$ are both prime.
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OG19-定量推理
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If a, b, and c are consecutive integers and 0 < a < b < c, is the product abc a multiple of 8 ?
(1) The product ac is even.
(2) The product be is a multiple of 4.
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OG19-定量推理
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The sequence $$a_{1}$$, $$a_{2}$$, $$a_{3}$$, $$a_{4}$$,$$a_{5}$$ is such that
$$a_{n}=a_{n-1}+5$$ for $$2\leq n\leq 5$$. If$$ a_{5} = 31$$, what is
the value of $$a_{1}$$ ?
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OG19-定量推理
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There are 10 books on a shelf, of which 4 are paperbacks and 6 are hardbacks. How many possible selections of 5 books from the shelf contain at least one paperback and at least one hardback?
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OG19-定量推理
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If x is to be chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7}, what is the probability that xy will be even?
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OG12 PREP07 Test 2
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If n is a positive integer, is $$n^3 - n$$ divisible by 4 ?(1)$$n = 2k + 1$$, where k is an integer.(2)$$n^2 + n$$ is divisible by 6.
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OG12
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In the xy-plane, the line with equation ax + by + c = 0, where $$abc \neq 0$$, has slope$$\frac{2}{3}$$. What is the value of b?(1) a = 4(2) c = −6
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OG12 OG15 OG16 OG17 OG18
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A student`s average (arithmetic mean) test score on 4 tests is 78. What must be the student`s score on a 5th test for the student`s average score on the 5 tests to be 80?
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OG12 OG15
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Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce In 4 minutes?
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OG19-文本逻辑 OG20-文本逻辑
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The passage suggests that, in the early 1990s, Michaels would have been most likely to agree with which of the following statements about the disparity mentioned in the lines 3-4?
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OG12 OG15 OG16 OG17
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What is the tenths digit in the decimal representation of a certain number?(1)The number is less than $$\frac1 3$$(2)The number is greater than $$\frac1 4$$
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OG12
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Is the integer P odd?(1)The sum of P, P + 4, and P+ 11 is even.(2)The sum of P - 3, P, and P + 11 is odd.
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OG17 OG18 OG19 OG20 OG2022
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If the range of the six numbers 4, 3, 14, 7, 10, and x is 12, what is the difference between the greatest possible value of x and least possible value of x ?
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OG18 OG19 OG20 OG2022
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Clarissa will create her summer reading list by randomly choosing 4 books from the 10 books approved for summer reading. She will list the books in the order in which they are chosen. How many different lists are possible?
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OG19 OG20 OG2022
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Ron is 4 inches taller than Amy ,and Barbara is 1 inch taller than Ron .If Barbara`s height is 65 inches ,what is the median height ,in inches ,of these three people ?
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OG20 OG2022
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If m and n are integers, what is the value of m + n ?
1.$$(x + m)(x + n) = x^{2} + 5x + mn\ and\ x ≠ 0.$$
2.$$mn = 4$$
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