Search found 405 matches


Re: Starting with 0, a mathematician labels every non-negative integer as one of five types: alpha, beta, gamma, delta,

The pattern of labeling numbers is a repeating pattern of 5 letters. So we need to determine how many cycles plus any fraction of a cycle are contained within the number. We are free to choose which gamma and which delta. Let's choose the smallest, 2 and 3. So, the number for which a label is desire...


Re: If x < y and y < 10, what is the greatest possible integer value of x + y?

Easy to make the assumption that since the question is seeking an integer value that the individual values must also be integers, but that is not stated as a limitation. So the goal is to maximize both X and Y to maximize their sum. Clearly each can be >9 and every amount below 10 that Y is must be ...


Re: If Enid and Topanga each roll a single ten-sided die (which has sides numbered 1 through 10), what is the probabilit

Don't forget ties.

The odds of a tie are one rolls a number and the other has 1/10 chance of matching, so

1/10 chance of tie

This leaves 9/10 chance to roll different numbers.

Half the time a given person will roll higher than the other, so

1/2*9/10 = [spoiler]9/20, B[/spoiler]


Re: On each of the first three days of the month, Danny ate twice the number of apples he had eaten the day before. The

Let X equal the number of apples eaten on the first day. So the second day he ate 2X apples and the third day 4X. Let the number of apples he ate on the 4th day equal Y. The ratio of the number of apples eaten on the third day to the number eaten on the 4th day is then: 4X/Y = 3/5 Y is then equal to...


Re: \(n\) is a positive integer, and \(k\) is the product of all integers from \(1\) to \(n\) inclusive. If \(k\) is a m

\(n\) is a positive integer, and \(k\) is the product of all integers from \(1\) to \(n\) inclusive. If \(k\) is a multiple of \(1440,\) then the smallest possible value of \(n\) is A. 8 B. 12 C. 16 D. 18 E. 24 Answer: A Source: Magoosh The problem is saying that K=N! The smallest multiple of 1440 ...


Re: A college admissions officer predicts that 20 of the students who are accepted willl not attend the college. Accordi

If 20% of those accepted don't enroll, then 100%-20% = 80% of those accepted actually enroll. Setting A = accepted students and X = enrolled students, the above is: (80/100)* A = X With the goal of enrolling X students, the number of students needing to be accepted is A= X*(100/80) = X * (5/4) = 1.2...


Re: If a six sided die is rolled three times, what is the probability of getting at least one even number and at least o

If a six sided die is rolled three times, what is the probability of getting at least one even number and at least one odd number? A. 1/8 B. 1/4 C. 1/2 D. 3/4 E. 7/8 OA D Source: Princeton Review Satisfying the requirement would mean the following possible outcomes without regard to order: OOE OR E...


Re: Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y.

Set the volumes of the equal jugs = A

So A= X/5 and 2Y/3. So Y= 3X/10

To fill Y from X requires Y-2Y/3 or Y/3 additional water.

Y/3 = (3X/10)/3 = X/10

Water remaining in X after this is poured into Y is then

X/5 - X/10 = [spoiler]X/10, D[/spoiler]


Re: Which of the following fractions is closest to \(\dfrac12?\)

Looking at the answer choices, each of A, B ,C and D are 1/2 point away in the numerator from making the division equal to 1/2. So, A, B and C can be eliminated because with their lower denominators compared to D, the 1/2 point difference in the numerator will render them farther away from 1/2 than ...

by regor60

Sun Feb 27, 2022 6:11 am
Forum: Problem Solving
Topic: Which of the following fractions is closest to \(\dfrac12?\)
Replies: 2
Views: 305

Re: The mean of twenty-five consecutive positive integers numbers is what percent of the total?

Call the sum of the 25 integers S.

So the mean of the integers is:

S/25

The mean is what percent of S ?

(S/25)/S = 1/25 = 4/100 =[spoiler]4%,A[/spoiler]


Re: Taylor is making a bracelet. He Starts with 4 blue knots, 6 red knots, and 2 yellow knots, in that order, and repeat

There are 12 knots in each complete series of knots. So, if the last knot is yellow, the total number of knots could be a multiple of 12. However, the last knot being yellow could also mean that the last series contains 11 knots with 1 yellow, if the total number of available yellow knots is not a m...


Re: How many roots does the equation \(\sqrt{x^2+1}+\sqrt{x^2+2}=2\) have?

The X^2 inside the radicals means the left side is always increasing with increasing X and symmetrical around the Y axis, which also means that the left side -2 is always increasing. If the Y intercept is 0 or greater, then the curve doesn't intercept the X axis since the curve would be entirely abo...


Re: If \(x^{a+3}=y^{b+2},\) where \(x\) and \(y\) are distinct prime numbers, what is the value of \(ab?\)

A prime number raised to a power has only that prime number and powers of that number as factors, except when that power is 0, in which case any prime number raised to that power equals 1.

So X^(a+3)=1=Y^(b+2)

a+3= 0=b+2
a=-3 and b=-2

ab=6,D