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Ready4	If $k$ is a positive integer, then $k(k+1)(k+3)$ is
Ready4	If $a$ and $b$ are two consecutive even integers such that $a > b$ and $3a < 2b$ , then which of the following describes the range of possible values for $b$ ?
300难题	When opened and lying flat, a birthday card is in the shape of a regular hexagon. The card must be folded in half along 1 of its diagonals before being placed in an envelope for mailing. Assuming that the thickness of the folded card will not be an issue, will the birthday card fit inside a rectangular envelope that is 4 inches by 9 inches? 1.Each side of the regular hexagon is 4 inches long. 2.The area of the top surface (which is the same as the area of the bottom surface) of the folded birthday card is less than 36 square inches.
Ready4	Today, Anne is three times as old as Bobbi and Bobbi is 4 years younger than Charles. If Anne, Bobbi and Charles are all alive 3 years from today, which of the following must be true on that day? I. Charles is 4 years older than Bobbi. II. Anne is three times as old as Bobbi. III. Charles is younger than Anne.
Ready4	The average distance between the Earth and the moon is approximately $3.8 \times 10^{5}$ kilometers. Which of the following is the closest to the average distance in feet? (1 kilometer is approximately $3.2 \times 10^{4}$ feet.) $10^{4}$
	Are there exactly 4 distinct keys that are working on the old typewriter?1. An old typewriter is defective in such a way that its blank key is not functioning, and the typewriter allows only 4 letters per word by forcing a space character to be inserted after each four-letter word. A monkey sitting at the typewriter is aware of this peculiarity and presses only distinct keys for each four-letter sequence. Some keys of this typewriter are not functioning.2. A monkey is able to create only 24 distinct four-letter words.
OG19-定量推理	A total of 20 amounts are entered on a spreadsheet that has 5 rows and 4 columns; each of the 20 positions in the spreadsheet contains one amount. The average (arithmetic mean) of the amounts in row i is $$R_i$$ ($$1 \leq i \leq 5$$). The average of the amounts in column j is $$C_j$$ ($$ 1\leq j \leq 4$$). What is the average of all 20 amounts on the spreadsheet? (1) $$R_1 + R_2 + R_3 + R_4 + R_5 = 550$$ (2) $$C_1 + C_2 +.C_3 + C_4 = 440$$
Ready4	A town has a public relations committee and an events committee. If each of the $48$ members is on at least one of these committees, how many are on the events committee only? (1) $\frac{3}{<font color='#FE8080'>4</font>}$ of the members are on the public relations committee. (2) $\frac{1}{3}$ of the members are on both committees.
Ready4	Is $k$ between $-2$ and $1$ on the number line? (1) $k$ is to the right of $-<font color='#FE8080'>4</font>$ on the number line. (2) $k$ is to the left of $-3$ on the number line.
Ready4	Machine $N$ folds boxes at a constant rate and can fold 300 boxes in 4 hours. Machine $P$ also folds boxes at a constant rate. How much less time would it take both machines running simultaneously to fold 300 boxes? (1) Yesterday Machine $N$ folded 400 boxes and Machine $P$ folded 200 boxes. (2) Machine $P$ folds boxes at a rate of 150 boxes in 4 hours.
Ready4	Of the students in a certain class, each student is either left-handed or right-handed and each student either has brown eyes or blue eyes. Of these students, $\frac{3}{<font color='#FE8080'>4</font>}$ are right-handed; and of those who are right-handed, $\frac{2}{3}$ have brown eyes. How many of the students are right-handed and have blue eyes? (1) 8 students have blue eyes. (2) 24 students are in the class.
Ready4	If $n$ is an integer and $<font color='#FE8080'>4</font><n<10$ , what is the value of $n$ ? (1) $n$ is a factor of $32$ . (2) $n$ is a factor of $24$ .
Ready4	A square patch from a quilt has a square interior surrounded by a border of uniform width. If the ratio of the area of the interior of the patch to the area of its border is 100 to 44, which of the following could be the width, in centimeters, of the border? I. $2$ II. $<font color='#FE8080'>4</font>$ III. $11$
Ready4	A square table has a square glass inlay in the center, and a wooden strip of uniform width surrounding the glass. If the ratio of the glass inlay to the wooden strip is 4 to 5, which of the following could be the width, in feet, of the wooden strip? I. $\tfrac{1}{<font color='#FE8080'>4</font>}$ II. $\tfrac{1}{2}$ III. 1
Ready4	If $2 < \frac{5-x}{<font color='#FE8080'>4</font>}$ , which of the following must be true? I. $-(x+3)$ is positive. II. $\left \| x-2 \right \| < 5$ III. $3 < x$
Ready4	If $3 < \frac{8-x}{5}$ , which of the following must be true? I. $\|x+<font color='#FE8080'>4</font>\| > 3$ II. $7 < x$ III. $-(x+7)$ is positive.
Ready4	If $<font color='#FE8080'>4</font> < \frac{7 - x}{3}$ , which of the following must be true? I. $5 < x$ II. $\|x + 3\| > 2$ III. $-(x + 5)$ is positive
Ready4	If the numbers $\frac{1}{<font color='#FE8080'>4</font>}$ , $\frac{3}{8}$ , $\frac{3}{16}$ , $\frac{5}{12}$ , and $\frac{5}{16}$ were ordered from greatest to least, the difference between the greatest and least numbers of the resulting sequence would be
Ready4	If $a$ and $b$ are positive, is $\tfrac{b}{a}<\tfrac{a}{b}$ ? (1) $\tfrac{b}{9a}=\tfrac{<font color='#FE8080'>4</font>}{5}$ (2) $b=a+6$
Ready4	If Chris saved $400 of his earnings last month, how much did Chris earn last month? (1) Chris spent $\tfrac{1}{3}$ of his earnings last month on rent and saved $\tfrac{1}{<font color='#FE8080'>4</font>}$ of the remainder. (2) Last month, Chris paid three times as much in loan payments as he saved.