## Problem Solving

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OFFICIAL GUIDE QUESTION LIBRARY
by beatthegmat »
Join the discussion as you work through your Official Guide and gain...
2
Last post by gentvenus
Wed Sep 09, 2020 12:49 pm
Remainders
by swerve »
If $$p$$ and $$q$$ are positive integers. If $$p$$ is divided by...
0
Last post by swerve
Sun Mar 03, 2024 9:52 am
Remainders
by swerve »
A number when successively divided by $$3, 5$$ and $$8$$ leaves...
0
Last post by swerve
Sun Mar 03, 2024 9:31 am
Three people each took $$5$$ tests. If the ranges of their scores in the $$5$$ practice tests were $$17, 28,$$ and
by BTGmoderatorLU »
Three people each took $$5$$ tests. If the ranges of their scores in...
0
Last post by BTGmoderatorLU
Sat Mar 02, 2024 7:54 am
Tom's Mom is five times as old as him. In $$6$$ years Tom's Mom will be three times as old as him. How old is Tom now?
by AAPL »
Tom's Mom is five times as old as him. In $$6$$ years, Tom's Mom will...
0
Last post by AAPL
Fri Mar 01, 2024 10:21 am
An investment club has had an average rate of return of $$15\%$$ per year for the past $$6$$ years. If Teresa invests
by BTGmoderatorLU »
An investment club has had an average rate of return of $$15\%$$ per...
0
Last post by BTGmoderatorLU
Sat Feb 24, 2024 10:33 am
A certain dog kennel houses only collies, labs, and golden retrievers. If the ratio of collies to labs is $$5{:}9,$$
by BTGmoderatorLU »
A certain dog kennel houses only collies, labs, and golden...
0
Last post by BTGmoderatorLU
Sat Feb 24, 2024 10:13 am
In the figure above, $$JKLMN$$ is a regular pentagon. Find the measure of $$\angle{KQL}$$
by AAPL »
g1.JPG In the figure above, $$JKLMN$$ is a regular pentagon. Find...
0
Last post by AAPL
Thu Feb 22, 2024 5:46 pm
There is a square filed of $$500\,\text{m}$$ long each. It has a compound wall along its perimeter. At one of its
by AAPL »
There is a square field of side $$500\,\text{m}$$ long each. It has a...
0
Last post by AAPL
Thu Feb 22, 2024 5:26 pm
Distance/Rate Problems, Word Problems
by swerve »
Runners $$X$$ and $$Y$$ started an $$18$$-mile race at the same time....
0
Last post by swerve
Wed Feb 21, 2024 6:05 pm
Distance/Rate Problems
by swerve »
Ramesh and Suresh both ran a $$30$$ mile marathon. Ramesh ran $$10$$...
0
Last post by swerve
Wed Feb 21, 2024 5:42 pm
If a rational number $$r$$ satisfies $$0 < r < 1,$$ which one is the minimum among the following choices?
by AAPL »
If a rational number $$r$$ satisfies $$0 < r < 1,$$ which one...
1
Sun Feb 18, 2024 5:05 pm
$$K$$-numbers are positive integers with only $$2$$'s as their digits. For example, $$2, 22,$$ and $$222$$ are $$K$$
by BTGmoderatorLU »
$$K$$-numbers are positive integers with only $$2$$'s as their...
1
Sun Feb 18, 2024 3:41 pm
A businessman earns $$\27800$$ in December, thus decreasing his average annual (Januaru to December) earnings by
by BTGmoderatorLU »
A businessman earns $$\27800$$ in December, thus decreasing his...
0
Last post by BTGmoderatorLU
Sun Feb 18, 2024 7:32 am
The number line above shows the position of a point that has coordinate $$x.$$ Which of the following statements about
by AAPL »
2017-07-12_1248.png The number line above shows the position of a...
0
Last post by AAPL
Sat Feb 17, 2024 12:45 pm
Two students $$A$$ and $$B$$ participate in Physics and Chemistry exams. Each exam subject has $$6$$ different exam code
by AAPL »
Two students $$A$$ and $$B$$ participate in Physics and Chemistry...
1
Fri Feb 16, 2024 10:23 am
The probability that $$B$$ can shoot a target two out of two times is $$0.25.$$ What is the probability that the target
by AAPL »
The probability that $$B$$ can shoot a target two out of two times is...
1
Fri Feb 16, 2024 9:54 am
From a group of $$6$$ boys and $$6$$ girls a volleyball team of $$6$$ players is to be selected. What is the probability
by AAPL »
From a group of $$6$$ boys and $$6$$ girls a volleyball team of $$6$$...
1
Fri Feb 16, 2024 9:48 am
The enrollment at a middle school increased by $$15$$ percent from the previous year. If the schoolâ€™s present enrollment
by BTGmoderatorLU »
The enrollment at a middle school increased by $$15$$ percent from...
1
Fri Feb 16, 2024 9:36 am
A furniture store reduces the retail price of a sofa from $$\800$$ to $$\600.$$ By what percent is the price of the
by BTGmoderatorLU »
A furniture store reduces the retail price of a sofa from $$\800$$...
1
Fri Feb 16, 2024 9:15 am
Combinations, Coordinate Geometry
by swerve »
A $$16$$-step path is to go from $$(-4,-4)$$ to $$(4,4)$$ with each...
0
Last post by swerve
Thu Feb 15, 2024 7:55 am
Coordinate Geometry, Functions And Custom Characters
by swerve »
2019-04-17_1135.png The graph above shows a parabola that is...
0
Last post by swerve
Thu Feb 15, 2024 7:34 am
A teacher has $$120$$ pens, consisting of $$72$$ black pens and $$48$$ red pens. The teacher wants to put together
by swerve »
A teacher has $$120$$ pens, consisting of $$72$$ black pens and...
0
Last post by swerve
Mon Feb 05, 2024 12:55 pm
Babia has seven more marbles than three times the number of marbles that Joe has. If Babia has $$B$$ marbles and Joe has
by swerve »
Babia has seven more marbles than three times the number of marbles...
0
Last post by swerve
Mon Feb 05, 2024 12:28 pm
Suzanne and Melody can paint home in $$10$$ and $$15$$ days respectively. They started painting but unfortunately,
by BTGmoderatorLU »
Suzanne and Melody can paint home in $$10$$ and $$15$$ days...
0
Last post by BTGmoderatorLU
Sat Feb 03, 2024 1:46 pm
Steve traveled the first $$2$$ hours of his journey at $$40\,\text{mph}$$ and the last $$3$$ hours of his journey at
by AAPL »
Steve traveled the first $$2$$ hours of his journey at...
0
Last post by AAPL
Fri Feb 02, 2024 6:17 am
Tom and Jerry are running on the same road towards each other. If Tom is running at a speed of $$2.5$$ meters per second
by AAPL »
Tom and Jerry are running on the same road towards each other. If Tom...
0
Last post by AAPL
Fri Feb 02, 2024 6:00 am
Arithmetic, Word Problems
by swerve »
Tom's movers charge $$\100$$ per hour for their moving services with...
0
Last post by swerve
Mon Jan 29, 2024 11:51 am
Arithmetic, Number Properties
by swerve »
What is the sum of all even integers between $$30$$ and $$50,$$...
0
Last post by swerve
Mon Jan 29, 2024 11:32 am
A group of people decided to cut $$128$$ trees in a certain number of days. For the first $$4$$ days, they were able to
by BTGmoderatorLU »
A group of people decided to cut $$128$$ trees in a certain number of...
0
Last post by BTGmoderatorLU
Sat Jan 27, 2024 9:32 am
Together it takes three different machines $$5$$ hours to complete a job. The first machine takes $$10$$ hours to
by BTGmoderatorLU »
Together it takes three different machines $$5$$ hours to complete a...
0
Last post by BTGmoderatorLU
Sat Jan 27, 2024 9:04 am
Of a set of $$25$$ consecutive integers beginning with $$4,$$ what is the probability that a number selected at random
by AAPL »
Of a set of $$25$$ consecutive integers beginning with $$4,$$ what is...
0
Last post by AAPL
Fri Jan 26, 2024 10:06 am
An experiment has five possible outcomes. The outcomes are mutually exclusive and have probabilities $$x, \dfrac{x}{2}$$
by AAPL »
An experiment has five possible outcomes. The outcomes are mutually...
0
Last post by AAPL
Fri Jan 26, 2024 9:50 am
The variables $$a$$ and $$b$$ are non-zero integers. If $$a = 2b^3/c,$$ what happens to $$c$$ when $$a$$ is halved and
by BTGmoderatorLU »
The variables $$a$$ and $$b$$ are non-zero integers. If $$a =... 0 Last post by BTGmoderatorLU Sun Jan 21, 2024 2:52 pm The ratio of Milk to Water in Solution \(1$$ is $$4{:}1$$ and ratio of Milk to Water in Solution $$2$$ is $$3{:}1.$$
by AAPL »
The ratio of Milk to Water in Solution $$1$$ is $$4{:}1$$ and ratio...
0
Last post by AAPL
Fri Jan 19, 2024 8:01 am
Coordinate Geometry
by swerve »
image521.jpg The point that bisects the line depicted in the figure...
0
Last post by swerve
Wed Jan 17, 2024 6:13 pm
Coordinate Geometry
by swerve »
In the $$XY$$ coordinate plane, lines $$l_1$$ and $$l_2$$ intersect...
0
Last post by swerve
Wed Jan 17, 2024 5:51 pm
If the average of five numbers is $$-10,$$ and the sum of three of the numbers is $$16,$$ then what is the average of
by BTGmoderatorLU »
If the average of five numbers is $$-10,$$ and the sum of three of...
0
Last post by BTGmoderatorLU
Sun Jan 14, 2024 6:57 am
At an elementary school, the students in third grade, fourth grade, and fifth grade run an average of $$12, 15,$$ and
by BTGmoderatorLU »
0
Last post by BTGmoderatorLU
Sun Jan 14, 2024 6:40 am
On a certain map, Washington, D.C., and Montreal are $$4$$ inches apart. If Washington, D.C., and Montreal are actually
by AAPL »
On a certain map, Washington, D.C., and Montreal are $$4$$ inches...
0
Last post by AAPL
Sat Jan 13, 2024 2:42 pm
In the sum above, if $$X$$ and $$Y$$ each denote one of the digits from $$0$$ to $$9$$, inclusive, then $$X=$$
by AAPL »
$$\begin{array}{c} YX7 \\ +6Y \\ \hline Y7X \end{array}$$ In the sum...
0
Last post by AAPL
Sat Jan 13, 2024 2:18 pm
Combinations
by swerve »
In how many ways can the first and second prize in History be awarded...
0
Last post by swerve
Fri Jan 12, 2024 12:03 pm
Combinations
by swerve »
There are $$12$$ empty seats in a row of a theater. In how many ways...
0
Last post by swerve
Fri Jan 12, 2024 11:48 am
Combinations
by swerve »
How many $$3$$-digit integers can be chosen such that none of the...
0
Last post by swerve
Fri Jan 12, 2024 11:27 am
It takes Joey the postman $$1$$ hours to run a $$3$$ mile long route every day. He delivers packages and then returns to
by BTGmoderatorLU »
It takes Joey the postman $$1$$ hours to run a $$3$$ mile long route...
0
Last post by BTGmoderatorLU
Sun Jan 07, 2024 7:11 am
There are $$3$$ green flags, $$2$$ red flags and $$3$$ yellow flags. If all the flags are arranged in a row, what is
by AAPL »
There are $$3$$ green flags, $$2$$ red flags and $$3$$ yellow flags....
0
Last post by AAPL
Sat Jan 06, 2024 10:39 am
A candy dish contains only chocolates and caramels. There are three times as many chocolates as caramels. The chocolates
by AAPL »
A candy dish contains only chocolates and caramels. There are three...
0
Last post by AAPL
Sat Jan 06, 2024 10:22 am
Percent And Interest Problems
by swerve »
If during a one-day period the $$Q$$ train arrives at the station...
0
Last post by swerve
Thu Jan 04, 2024 4:54 pm
Percent And Interest Problems
by swerve »
Following an increase in prices, the price of a candy box was $$10$$...
0
Last post by swerve
Thu Jan 04, 2024 4:36 pm
Last fall, 40 percent of the students at a certain high school participated in after-school activities. Of those
by BTGmoderatorDC »
Last fall, 40 percent of the students at a certain high school...
2
Last post by AndrewSimmon
Tue Jan 02, 2024 1:31 am