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190207
$$n^{3}$$ is a four-digit number whose unit digit is 3. What is the unit digit of the sum of the four digits of $$n^{3}$$ ?
190302
The area of a circle is $$\frac{9π^{2}}{4}$$. What is the diameter of the circle?
200301
There is a rectangular box, with a length of 4, a width of 4, and a height of
1
. At present, there are two kinds of small packages: spherical packaging boxes and cylindrical packaging boxes. (
1
) 16 identical spherical packaging boxes with a diameter of
1
can be contained in this rectangular box. (2) 16 identical cylindrical packaging boxes with a bottom-circle diameter of
1
and a height of
1
can be contained in this rectangular box. Assume that the space ratio of 16 small spherical boxes in this rectangular box is S, and the space ratio of 16 small cylindrical boxes in this rectangular box is C. Which of the following can correctly represent the relationship between S and C?
During a volcanic eruption the particles of dust precipitate at the rate of $${2}\cdot\frac{
1
}{4}$$ inches every three hours. If a volcano erupted for the first time for 2 hours and erupted again on the next day from 11:00 to 20:00, what was the total fall-out of particles in inches?
OG19-数学分册
How many integers between
1
and 16, inclusive, have, exactly 3 different positive integer factors? (Note: 6 is NOT such an integer because 6 has 4 different positive integer factors:
1
, 2, 3, and 6.)
Ready4
If
is an integer greater than zero, then
is
Magoosh
Lisa and Phillip are in a group of J employees. From this group of J employees, K will be selected, at random, to sit in a line of K chairs. There are absolutely no restrictions in either the selection process or the order of seating—both are entirely random. What is the probability that the employee Lisa is seated exactly next to employee Phillip?
Statement #
1
: K = 15
Statement #2
: K = J
Magoosh
If line k in the xy-coordinate plane has the equation Ax + By = C, what is the slope of line k ?(
1
) A = 2B(2) C = 4B
Magoosh
Right now, a barrel of water is exactly 40% full of water. What is the volume of the barrel?
Statement #
1
: If the water in the barrel right now were increased by 25%, then the barrel would be exactly half full.
Statement #2
: If a volume of water equal to half of what is in the barrel right now were added to the barrel, the empty space left in the barrel then would equal the volume of the water now.
Magoosh
Is quadrilateral ABCD a square?Statement #
1
: angle A = angle C = 90ºStatement #2: AB = AD
Magoosh
What is the value of $$9x^2$$ – 30xy +$$ 25y^2$$ ?
Statement #
1
: 3x – 5y = 20
Statement #2
: x + y = 12
Magoosh
If wxyz $$\neq$$ 0, does the ratio of w to x equal the ratio of y to z?(
1
)$$\frac {w}{y}$$ = $$\frac {x}{z}$$(2) wy = xz
Magoosh
Mark has fewer than 9 coins. Each coin is either a quarter (worth $0.25) or a dime (worth $0.10). How many dimes does Mark have?(
1
) The total value of Mark's coins is $1.70(2) Mark has three times as many quarters as he has dimes.
Magoosh
If line k is in the xy–coordinate plane, what is the slope of k?(
1
) The x–intercept of k is 3.(2) The y–intercept of k is -2.
Magoosh
If w, x and y are different positive integers, and wxy = 24, is xy divisible by 6?(
1
) wy is not divisible by 6.(2) x is even.
Magoosh
Andrew and Georgia are in a group of M employees. From this group of M employees, N will be selected, at random, to sit in a line of N chairs. There are absolutely no restrictions in either the selection process or the order of seating—both are entirely random. What is the probability that the employee Andrew is seated somewhere to the right of employee Georgia?Statement #
1
: N = 15Statement #2: N = M
Magoosh
A certain hospital has 400 patients, who are classified in one of two categories: intensive care (IC) and regular care (RC). What percent of the hospital's patients are in IC?
Statement #
1
: 60% of the patients are male, and the rest are female
Statement #2
: 25% of the male patients are in IC, and 80% of the female patients are in the RC.
Magoosh
How many shirts does Phil own?(
1
) 12 of Phil's shirts are dress shirts.(2) 85 percent of Phil's shirts are not dress shirts.
Magoosh
In a certain company, 25% of the women and 17% of the men participate in the voluntary equity program. Let M be the number of male employees. If there are 600 employees total, what is the value of M?
Statement #
1
: M > 100
Statement #2
: more than 130 employees participate in the voluntary equity program
Magoosh
A class contains boys and girls. What is the probability of selecting a boy from the class?
Statement #
1
: there are 35 students in the class
Statement #2
: the ratio of boys to girls is 3:4
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