Daily Practice - MugenPrep

Filter by topic or difficulty. 5 random problems per session.

AMC8 2019 #8 © MAA

Gilda has a bag of marbles. She gives

20%

of them to her friend Pedro. Then Gilda gives

10%

of what is left to another friend, Ebony. Finally, Gilda gives

25%

of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself?

Solution

After Gilda gives

20

% of the marbles to Pedro, she has

80

% of the marbles left. If she then gives

10

% of what's left to Ebony, she has

(0.8*0.9)

72

% of what she had at the beginning. Finally, she gives

25

% of what's left to her brother, so she has

(0.75*0.72)

boxed{textbf{(E)} 54}

of what she had in the beginning left.

AMC8 2015 #18 © MAA

An arithmetic sequence is a sequence in which each term after the first is obtained by adding a constant to the previous term. For example, $2,5,8,11,14$ is an arithmetic sequence with five terms, in which the first term is $2$ and the constant added is $3$ . Each row and each column in this $5times5$ array is an arithmetic sequence with five terms. The square in the center is labelled $X$ as shown. What is the value of $X$ ?

AMC8 2012 #5 © MAA

In the diagram, all angles are right angles and the lengths of the sides are given in centimeters. Note the diagram is not drawn to scale. What is ,

X

in centimeters?

[figure]

Solution

File:2012amc85.png

1 + 1 + 1 + 2 + X = 1 + 2 + 1 + 6\
5 + X = 10\
X = 5

Thus, the answer is

boxed{textbf{(E)} 5}

AMC8 2014 #24 © MAA

One day the Beverage Barn sold 252 cans of soda to 100 customers, and every customer bought at least one can of soda. What is the maximum possible median number of cans of soda bought per customer on that day?

Solution

In order to maximize the median, we need to make the first half of the numbers as small as possible. Since there are

100

people, the median will be the average of the

50text{th}

and

51text{st}

largest amount of cans per person. To minimize the first

49

, they would each have one can. Subtracting these

49

cans from the

252

cans gives us

203

cans left to divide among

51

people. Taking

frac{203}{51}

gives us

3

and a remainder of

50

. Seeing this, the largest number of cans the

50

th person could have is

3

, which leaves

4

to the rest of the people. The average of

3

and

4

3.5

. Thus our answer is

boxed{text{(C) }3.5}

There are $81$ grid points (uniformly spaced) in the square shown in the diagram below, including the points on the edges. Point $P$ is in the center of the square. Given that point $Q$ is randomly chosen among the other $80$ points, what is the probability that the line $PQ$ is a line of symmetry for the square?

[figure]

Solution

[figure] Lines of symmetry go through point

P

, and there are

8

directions the lines could go, and there are

4

dots at each direction.

frac{4times8}{80}=boxed{textbf{(C)} frac{2}{5}}

. == Solution 2 == Divide the grid into 4 4x5 quadrants. Each row of 5 points has 1 point on a horizontal/vertical line of symmetry + 1 point on a diagonal line of symmetry:

boxed{textbf{(C)} frac{2}{5}}

. ==Video Solution by Math-X (First fully understand the problem!!!)== https://youtu.be/IgpayYB48C4?si=AdzSEy4Ocrte4gEU&t=1650 ~Math-X ==Video Solution (HOW TO THINK CREATIVELY!!!)== https://youtu.be/PizqK-oBLqk ~Education, the Study of Everything == Video Solution 3== The Learning Royal : https://youtu.be/8njQzoztDGc == Video Solution 4 == Solution detailing how to solve the problem: https://www.youtube.com/watch?v=4L95z9DwlhI&list=PLbhMrFqoXXwmwbk2CWeYOYPRbGtmdPUhL&index=7 ==Video Solution 5== https://youtu.be/TAKmC11vitM ~savannahsolver ==Video Solution by The Power of Logic(1 to 25 Full Solution)== https://youtu.be/Xm4ZGND9WoY ~Hayabusa1

🔀 Next Problems