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A square countertop has a square tile inlay in the center, leaving an untiled strip of uniform width around the tile. If the ratio of the tiled area to the untiled are is 25 to 39, which of the following could be the width, in inches, of the strip? I. 1 II. 2 III. 4 (A) I only (B) II only (C) I and ...
A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?
According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12-ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?
The sequence a1, a2, a3......an of n integers is such that ak = - a (k-1) if k is even. Is the sum of the terms in the sequence positive?
(1) n is odd
(2) a(n ) is positive
When a certain tree was first planted, it was 4 feet tall, and the height of th etree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each y...
At least 100 students at a certain high school study Japanese. If 4% of the students at teh school who study French also study Japanese, do more students at teh school study French than Japanese? (1) 16 students at teh school study both French & Japanese. (2) 10% of the students at the school who st...
If r and s are positive integers, is r/s an integer?
(1) Every factor of s is also a factor of r
(2) Every prime factor of s is also a prime factor of r
The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical B present. If the concentration of checmical B is increased by 100%, which of the following is closest to the percent change in the concentration of the checmical A required to keep the re...
If n and y are positive integers and 450y = n^3, which of the following must be an integer?
I. y/3 * 2^2 * 5
II. y/ 3^2 * 2 * 5
III. y/3* 2 * 5^2
I, II, and III
can someone also please explain their reasoning
billzhao wrote:990=11*10*9, so n should be at least 11relaxin99 wrote:If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 990, what is the least value of n?
Hi, thanks for the explanation. why would 11 be the least value of n and not 9?
For which of the following functions is f(x) = f(1-x) for all x?
f(x) = 1-x
f(x) = 1-x^2
f(x) = x^2 - (1-x^2)
f(x) = x^2(1-x)^2
f(x) = x/1-x
If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 990, what is the least value of n?
For every positive even integer n, the function h(n) is defined to be the product of all even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is
between 2 and 10
between 10 and 20
between 20 and 30
between 30 and 40
greater than 40
2^5 + 2^5 + 3^5 + 3^5 + 3^5
2^6 + 3^6
2^7 + 3^8
4^5 + 9^5
I always get exponents wrong, can someone please guide me to where i can find a basics on exponents on this forum, thank you