Math New Drill (Level 2) : Ratios and Proportions Problem5 NAKANO ATTACHED TO MEIJI UNV.-2014

Cows are pastured at some grassland. 

When 6 cows are pastured, grasses are eaten up in 30 days. 

When 10 cows are pastured, grasses are eaten up in 12 days. 

At this time, answer the next questions. 

Noted that grasses grow at a fixed rate every day in this grassland. 

In addition the amount of the grass each cow eats per day is same. 

(1) Find the number of cow to be pastured without the grass of the grassland being eaten up. 

(2) How many cows at least should be pastured in order to eat all the grass of the grassland within six days?

Math New Drill (Level 2) : Number sense and theory Problem4 NAKANO ATTACHED TO MEIJI UNV.-2014

Sign [x] is assumed as a sign to calculate the product of each digit of a certain number x like Example.

Example: [46] = 24,   [88] = 64 

Answer the following questions. 

(1) Find all integers x of two digits that become "[54] + [35] = [x]".

(2) Find all integers x of two digits that become "[[x] + 21] = 36." 

New Math Drill (Level 2) : Geometry (Plane figure) Problem3(2) NAKANO ATTACHED TO MEIJI UNV.-2014

As shown in the figure below, there is a trapezoid ABCD, and AD and BC are parallel, and AD = 2cm, BC = 3cm. 

P and Q are points on the side AB, DC and AP : PB = DQ : QC = 2 : 1. 

R is an intersection of PQ and AC. 　

S is an intersection of CD and the extended line of BR. 

T is an intersection of the extended lines of BR and AD. 

In this case, find DS : SQ : QC by the ratio of the simplest integer.

New Math Drill (Level 1) : Geometry(Solid figure) Problem3(1) NAKANO ATTACHED TO MEIJI UNV.-2014

There is a container whose all corners are the right angle as shown in the Fig.1 below. 

Water is put in 2/3 of the container. 

And the container is put on with the shaded face being placed in the bottom as shown in Fig.2. 

In this case, find the height of the water.

Math New Drill (Level 1) : Ratios and Proportions Problem2(6) NAKANO ATTACHED TO MEIJI UNV.-2014

A salt solution of 400g is in each container A, B, and C and density in A, B , and C is 16%, 8%, and 4% respectively. 

When total of 100g salt solution was taken out of container A and B and it added to container C, the density of container C became 5%. 

Find the weight of the salt solution taken out of container A.

Math New Drill (Level 1) : Geometry (Plane figure) Problem2(5) NAKANO ATTACHED TO MEIJI UNV.-2014

In the figure below, the area of triangle ADF, triangle DEF, triangle CEF, and triangle BCE is equal. 

Find the length of segment AD.

Math New Drill (Level 1) : Geometry (Plane figure) Problem2(4) NAKANO ATTACHED TO MEIJI UNV.-2014

As shown in the figure below, eight circles with radius 4cm each are lined in touch with the next circle. 

When the center of each circle is connected by the line, find the area of ​​the shaded area. 

Pi is assumed to be 3.14.

Math New Drill (Level 1) : Geometry(Solid figure) Problem2(3) NAKANO ATTACHED TO MEIJI UNV.-2014

10 pieces of dice are piled up on the desk so that the direction of each face might become same as shown in the figure below. 

Find the total of the number of dice spots not to be seen from anywhere.

Math New Drill (Level 1) : Ratios and Proportions Problem2(2) NAKANO ATTACHED TO MEIJI UNV.-2014

The number of students of girls in a certain junior high school is 95% of the number of students of boys.

The number of absentees on a certain day were four and all of them were girls. 

The ratio of the number of girls' attendant in this day became 11/12 of the boy. 

Find the number of all students of this junior high school.

Math New Drill (Level 1) : Ratios and Proportions Problem2(1) NAKANO ATTACHED TO MEIJI UNV.-2014

In a certain shop, it stocked 90 pieces of cup at 7200 yen. 

They sold at the list price of 150 yen per one piece, but some remained unsold. 

The profit was 3000 yen. 

Find the number of the cut remained unsold.

Math New Drill (Level 1) : Patterns and Regularity Problem1(4) NAKANO ATTACHED TO MEIJI UNV.-2014

When 5/7 is represented in decimal, find the number of the 2014th decimal place.