## Search found 415 matches

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

##### 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...

#### $$n$$ is a positive integer, and $$k$$ is the product of all integers from $$1$$ to $$n$$ inclusive. If $$k$$ is a multi

##### 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 ...

#### A college admissions officer predicts that 20 of the students who are accepted willl not attend the college. According

##### 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...

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

##### 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...

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

##### 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]

#### Victor's job requires him to complete a series of identical jobs. If Victor is supervised at work, he finishes each job

##### Re: Victor's job requires him to complete a series of identical jobs. If Victor is supervised at work, he finishes each

This problem seems to be transcribed incorrectly, with the given answer being correct only if 3 "saved" represents hours, not days, as stated

#### Which of the following fractions is closest to $$\dfrac12?$$

##### 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: 476

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

##### 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]

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

##### 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...

#### How many roots does the equation $$\sqrt{x^2+1}+\sqrt{x^2+2}=2$$ have?

##### 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...

by regor60

Wed Feb 23, 2022 5:35 am
Forum: Problem Solving
Topic: How many roots does the equation $$\sqrt{x^2+1}+\sqrt{x^2+2}=2$$ have?
Replies: 1
Views: 366

#### If $$x^{a+3}=y^{b+2},$$ where $$x$$ and $$y$$ are distinct prime numbers, what is the value of $$ab?$$

##### 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

#### If $$3^x+3^x+3^x=1,$$ what is $$x?$$

##### Re: If $$3^x+3^x+3^x=1,$$ what is $$x?$$

If 3 of the same thing add to 1, then each thing must be 1/3, meaning X=-1,A

by regor60

Sun Feb 13, 2022 9:59 am
Forum: Problem Solving
Topic: If $$3^x+3^x+3^x=1,$$ what is $$x?$$
Replies: 1
Views: 539

#### A certain electrolyte solution contains 1 gram of salt for every 8 grams of sugar and every 200 grams of water. If the

##### Re: A certain electrolyte solution contains 1 gram of salt for every 8 grams of sugar and every 200 grams of water. If t

Since the original sugar:water was 8:200, and is now halved, the new sugar:water is: 4:200 and water: sugar 200:4 The original salt:sugar was 1:8. Since it is now tripled, the new salt: sugar is 3:8 and sugar:salt 8:3 The water: salt relationship is: Water:sugar x sugar:salt So: 200:4 x 8:3 = 1600:1...

#### A singing choir of 4 children is to be formed. The selection pool consists of 8 siblings pairs. In how many ways can a

##### Re: A singing choir of 4 children is to be formed. The selection pool consists of 8 siblings pairs. In how many ways can

Because each child has to come from a separate sibling pair, you need to first select which pairs will be represented. Four pairs can be selected from 8: 8!/4!4! = 70 ways Since only one child can be selected from each pair and there are 2 ways to select which child from each pair, there are: 2^4 = ...

#### Eight friends go to watch a movie but only $$5$$ tickets were available. In how many different ways can $$5$$ people sit

##### Re: Eight friends go to watch a movie but only $$5$$ tickets were available. In how many different ways can $$5$$ people

If the question were asked "how many ways can the friends attend the movie ?", then this could be considered a combination problem, in which order doesn't matter, namely 8!/3!5! = 56 But because the question indicates that how they sit is important, this becomes a permutation problem in wh...