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OG19-数学分册 A positive integer is divisible by 9 if and only if the sum of its digits is divisible by 9. If n is a positive integer, for which of the following values of k is $$25 \times 10^{n} + k \times 10^{2n}$$ divisible by 9?
The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 16, and k < m < r < s < t. If t is 40, what is the greatest possible value of the median of the 5 integers?
Magoosh Which data set has the greater standard deviation, data set K or data set L?(1) Every element in data set K is a multiple of 3.(2) Every element in data set L is a multiple of 9.
Ready4

For the positive integers and , represents the number of zeros between the decimal point and the first nonzero digit to the right of the decimal point in the reciprocal of the product of and , when that reciprocal is expressed as a terminating decimal. What is the value of ?
If S is the infinite sequence $${S}_{1}={9}$$, $${S}_{2}={99}$$, $${s}_{3}={999}$$ . . ., $${S}_{k}={10}^{k}-{1}$$, . . ., is every term in S divisble by the prime number p ?(1)p is greater than 2.(2)At least one term in sequence S is divisble by p.
PREP07 Test 2 If machine J, working alone at its constant rate, takes 2 minutes to wrap 60 pieces of candy, how many minutes does it take machine K, working alone at its constant rate, to wrap 120 pieces of candy? (1) Machine K, working alone at its constant rate, takes more than 5 minutes to wrap 60 pieces of candy. (2) Machines J and K, working together at their respective constant rates, take 1 minute and 30 seconds to wrap 60 pieces of candy.
Ready4

What is the value of k in the equation 25− 100 8 +k=m?

  1. m= 100 8
  2. k m =0
Ready4

If k, n, and m are positive integers, is kn even?

  1. k= m 3
  2. n= ( m−1 ) 3
191222 Each of the three machines works at the same constant rate. It takes k hours for two machines to produce goods. It takes 2 hours less for three machines than for two machines to produce same amount of goods. What is the value of k?
Ready4 If n is a positive integer and <font color='#FE8080'>k</font> + 2 = 3^{n}, which of the following could NOT be a value of k?
OG16 OG17 OG18 OG19 OG20 OG2022 A certain truck uses $$\frac{1}{12}$$ + $${k}{v}^{2}$$ gallons of fuel per mile when its speed is v miles per hour, where k is a constant. At what speed should the truck travel so that it uses $$\frac{5}{12}$$ gallon of fuel per mile?(1) The value of k is $$\frac{1}{10800}$$(2) When the truck travels at 30 miles per hour, it uses $$\frac{1}{6}$$ gallon of fuel per mile.
OG12 OG15 The inflation index for the year 1989 relative to the year 1970 was 3.56, indicating that, on the average, for each dollar spent in 1970 for goods, $3.56 had to be spent for the same goods in 1989. If the price of a Model K mixer increased precisely according to the inflation index, what was the price of the mixer in 1970 ?(1)The price of the Model K mixer was $102.40 more in 1989 than in 1970.(2)The price of the Model K mixer was $142.40 in 1989.
Magoosh The numbers a, b, c, and d are all positive, and J = $$\frac{a}{b}$$ and K = $$\frac{c}{d}$$. Is J greater than K?Statement #1: a < b, c < d, and c > aStatement #2: a + 7 = c and b + 4 = d
Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on shelf K. What is the median weight of the 89 boxes on these shelves?(1) The heaviest box on shelf J weighs 15 pounds.(2) The lightest box on shelf K weighs 20 pounds.
The three-digit integer kss is the sum of the two-digit integers ks and rs, where k, r, and s are the digits of the integers. Which of the following must be true?I. k = 2II. r = 9III. s = 5
PREP07 Test 1 $$a_1,a_2,a_3,. . .,a_{15}$$In the sequence shown,$$a_n = a_{n - 1} + k$$, where 2 $$\le n \le 15$$ and k is a nonzero constant. How many of the terms in the sequence are greater than 10 ?(1) $$a_1 = 24$$(2) $$a_8 = 10$$
If all of the employees of Company K who worked there last January are still there, how many employees does Company K have now?(1)Last January the ratio of the number of male employees to the number of female employees was 2 to 3.(2)Since last January, Company K has employed 400 new male employees and no new female employees, raising the ratio of the number of male employees to the number of female employees to 3 to 4.
190321 p=10k+1. k is a positive integer. What's the unit digit of $$(p^2)^100$$?
Magoosh If 20 percent of 3k is 6, what is 40 percent of k?
OG12 OG15 OG16 OG17 Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?(1)Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes.(2)Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes.