Sansue = Japanese Math for Kids 「英語で算数」: NADA

Showing posts with label NADA. Show all posts

Math Exam.L3 : NADA-2009-Day1

Time : 60 minutes

Passing mark : 70%

Answer : End of the problem

Problem 1

Find X.

1/2009 + 1/392 = 1/X

Problem 2

When 180 pencils were distributed to all students of A class per four pencils per person, several remained.

When another 200 pencils are distributed to all students of B class per six pencils per person, several fall short.

Then, when five pencils per person were distributed in B class, several remained.

Moreover, all remaining pencils in both classes could be exactly distributed to all students of A and B class per one pencil per person and no pencil remained.

Find the number of the student of A class.

Problem 3

There is a hexagon ABCDEF as shown in a figure.
How many ways of method of the division which divides this hexagon into three parts by two diagonal lines is there in all?

Problem 4

There is a straight road connecting A point and B point.

Taro walks from A point to B point and Jiro walks from B point to A point with a fixed speed respectively.

Both of them started at the same time and passed on the way.

25 minutes after passing, Taro arrived at B point and Jiro arrived at A point the 24 minutes after Taro’s arrival.

Find the least integer ratio of the speed of Taro and Jiro.

Problem 5

There is a disk as shown in a figure and three needles which continue rotating with a fixed speed clockwise respectively around the center O of the disk.
The time concerning a needle rotating one time is 5 minutes, 8 minutes, and 14 minutes sequentially from a long needle.
All of three needles overlapped at a certain time.
Find the time concerning all of three needles overlapping next.

Problem 6

(1) Find the number of an integer more than or equal to 1 and less than or equal to 999 which are not a multiple of 9 and do not contain 9 in the number of each digit.

(2) For the integer applicable to (1), find the 999th number counting from the least one in all integers.

Problem 7

The following operation is repeated for a certain integer repeatedly.
<Operation>
It doubles.
However,
When the doubled number is 150 or more, 100 is subtracted from this doubled number.
When the doubled numbers is 101 or more and 149 or less, 50 is subtracted from this doubled number.
When the doubled number is 100 or less, it leaves in this doubled number.

For example, when this operation is repeated 4 times starting with 36, the integer acquired is 72, 94, 88, and 76 at order.

(1) When you repeat this operation 4 times, find the number of integers that the result becomes 60.

(2) When you repeat this operation 101 times, find the least number among the integers that the result becomes 60.

Problem 8

There is a parallelogram ABCD as shown in a figure.
The points E and F are points of dividing the side BC into three equally.
The point G is a point of the middle of the side CD.
Find the area ratio of the area of a shadow area and the area of parallelogram ABCD.

Problem 9

As shown in a figure, the circle A centering on the point A with a radius of 3 cm and the circle B centering on the point B with a radius of 2 cm have touched.
The points C and D are points on the circumference of the circle B.
The points E and F are points on the circumference of the circle A.
Three point A, E and C are on a straight line and three point A, F and D are also on a straight line.
Find the area ratio of a quadrangle ACBD and the triangle AEF.

Problem 10

Fig. 1 shows the figure which put two disks 1 cm in radius together at the point A.
Place this figure into the frame of the right triangle of Fig. 2 and when you move this figure so as not to protrude from the frame, find the area of the range where the point A can move.

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Problem 11

The straight line L of the figure divides the shadow area into three parts with an equal area.

Find the length of AB.

Problem 12

As shown in Fig.1, there are three point A, B and P on the even ground.
There are ABCD of a 3m-high rectangular wall and PQ of a 9m-high pillar standing on the ground straight.
Fig.2 shows the picture looked at these from right above.
Wall ABCD is illuminated by the electric light in the position at the tip Q of the pillar.
Find the area of the shadow of the wall made into the ground.
Neither the size of an electric light nor the thickness of a wall shall be considered.

Problem 13

As for quadrangular pyramid O-ABCD in a figure, the bottom is a square and all the length of OA, OB, OC and OD is equal. K, L, M, N, P, Q, R, and S are the middle points of each side.
This quadrangular pyramid is cut by three planes of the plane which passes along P, K, N, R and the plane which passes along P, L, M, R and the plane which passes along S, K, L, Q and divides into some solids.
Find the ratio of the volume of a solid including the vertex O and the volume of the quadrangular pyramid O-ABCD.

Answer / Continue »

Math Exam.L3 : NADA-2007-Day1

Time : 50 minutes

Passing mark : 70%

Answer : End of the problem

Problem 1

Find X.

7/200 × (1/2 + 1/3 + 1/7 - 1/X) = (1/4 + 1/5 + 1/6) / (19 - 1/2)

Problem 2

Three clocks, A, B and C were set at noon of one day.

When it was 6:00 p.m. by A, it was 5:50 p.m. by B In the same day.

When it was 7:00 p.m. by B, it was 7:20 p.m. by C.

When it is 11:00 p.m. by C of the day, find the time of A and B.

Problem 3

Integers of which top is 2, end is 7 and all interval numbers are 0 such as 207, 2007, 20007, ‥ ‥ ‥, are divided by 27 and 81.

Find the smallest number among such numbers which is divisible by 27 and indivisible by 81.

Problem 4

Ten students roll three dice respectively and consider a number of sums which come out as the person's score.
The sum total of the ten persons' score was 100.
Moreover, after dividing total score of each student by 3 and omitting below the decimal point, ten students’ sum total was 30.
After dividing total score of each student by 3 and rounding off the number of 1st decimal digit, ten students’ sum total was 34.
In these ten students, find the number of students whose score is the number when it is divided by three, one remains.

Problem 5

40 g of salt solutions are in both of two beakers A and B each.
The ratio of the concentration of salt solution of A and B is 3 : 2.
I add 60 g of water to B and mixed it well and transferred some of salt solutions in B to A.
Furthermore, I add some water in both of A and B to become 100 g of salt solutions.
The ratio of the concentration of salt solution of A and B was to be 7 : 3.
Find the weight of the salt solution I transferred from B to A.

Problem 6

The figure below is a graphic made by arranging 36 equilateral triangles in order whose length of one side is 1 cm.

The point P moves for 4 seconds with the speed of 1 cm in one second along the side of the figure.

How many ways of movement returning to A first 4 seconds after leaving Point A?

P moves straight on between the two vertex.

P may pass along the same side 2 times or more.

Problem 7

As for the integer of 6 figures made using six numbers, 1, 2, 3, 4, 5, 6 and the integer is a multiple of 64, the smallest integer is 123456.

Then find the largest integer.

Problem 8

A dray moves at the speed of 30 m/m to B point 6000 m away from A point.
When a dray moves 900 m, Taro in A point start to pursue the dray with a ball.
If he catches up with the dray, he put the ball in the dray and he will return toward A point immediately.
He receives a ball at A point and start to pursue the dray again.
Taro repeats this motion until the dray arrives at B point.
The speed of Taro is 90 m/m.
Find the time until he finally puts a ball in the dray since he begins to move at first.

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Problem 9

There are two points of P and Q.

Point P is a starting point and balls are put at point Q.

There is a game repeat carrying balls from Q to P after starting P and competing for the number of balls carried up to point P from point Q.

In this game, robots A and B competed each other.

A carries 3 balls at a time and it takes 15 seconds for going back and forth.

B carries 5 balls at a time and it takes 25 seconds for going back and forth.

Although B began to move immediately after the game started, it took 10 seconds for A to begin to move.

Find the time while A leads among 420 seconds from the start.

Moreover, find the time while B leads.

Problem 10

As shown in a figure, there are two squares and there is a circle in a small square.
Find the area of a shadow area.

Pi is assumed to be 3.14.

Problem 11

The quadrangle ABCD in a figure is a square with 5 cm one-side.
All the length of AE, BF, CG, and DH is 2 cm.
Find the area of a shadow area.

Problem 12

ABCD-EFGH in a figure is a box of rectangular prism 60cm in length, 80cm in width and 40cm in height and there is no lid.
There is a 40cm high pillar is straightly erected on the intersection M of a diagonal line of the bottom.
The vertex O of the pillar and chalk are tied up with string 50cm in length.
The length of MG is 50cm.
Pi is assumed to be 3.14.

(1) Find the area of the part painted with chalk in the outside of the box.

(2) Find the area of the part painted with chalk in the inside of the box.

Problem 13

There is a square mat board one side 5cm as shown in the figure and it is partitioned into grid square 25.
I pile up cubes of one side 1cm on the square by the number written in the each square.
In faces of the cube, attach a red square seal of one side 1cm on each surface visible from the outside.
I do not attach the seal on other surfaces (the surface in contact with the mat board or cubes , etc.).

(1) Find the number of seal attached.

(2) Find the number of cubes just three seals attached .

Answer / Continue »

Math Exam.L3 : NADA-2006-Day1

Time : 50 minutes

Passing mark : 70%

Answer : The end of the problem

Problem 1

Find X.

1/17 - X/2006 = (2/17 + 17/59) × 1/22

Problem 2

Three different numbers are selected and put in order from four different numbers 1, 3, X, and 9 so that the integer of triple figures is made.

The number of triple figures is 24 pieces and the average is 555.

Find X.

Problem 3

The distance between A point and B point is 10 km.
Taro walks from A point at 4 km/h to B point.

He walks for 30 minutes and take a rest for 5 minutes and he repeat this time cycle.

Jiro goes to A point from B point at 12 km/h by a bicycle without taking a rest and return to B point.
Taro and Jiro left at the same time.
Find the time (time after they left) for Jiro to pass Taro.
Moreover, find the distance from A point to the point Jiro passed.

Problem 4

The questionnaire survey was conducted on 40 sixth graders in an elementary school.
The questionnaire was as for three subjects, language, mathematics (Sansue) and science, if they like it, mark ○, if they do not like it, mark ×.
The grand total of ○ was 100 and that of × was 20.
There was no pupil who marked × to all three subjects.
There are 35 pupils who marked ○ to mathematics.
Among these, there are two pupils who marked ○ only to mathematics and four students who marked × to mathematics and ○ to science.
Answer the following questions.

(1) Find the number of the pupil who marked ○ only to language.

(2) Find the number of pupil at most who marked ○ to all three subjects.

Problem 5

There is an integer of 5 figures which is a multiple of 36.

In addition, the integer contains 2, 3 and 5 in either digit.

For example, it is 53928 etc.

Find the smallest number in such integers.

Problem 6

When 100 is divided by 35, a quotient is 2 and remainder is 30.

When 100 is divided by 40, a quotient is 2 and remainder is 20.

Find the number of three digits integer including 100 which a quotient becomes the same, when it is divided by 35 and 40.

And also find the largest integer among them.

Problem 7

As for the admission ticket of a certain theater, the advance tickets and the day tickets are available at a rate of 7 : 3.

The advance tickets are on sale three weeks before to the previous day and the day tickets are on sale 2 hours before opening of the performance.

The day ticket audience of one day began to stand in a line 3 hours before opening and joined the sequence four persons per one minute.

The day tickets were sold at a sales window of the theater to six persons per one minute.

Answer the following questions.

(1) How many day tickets audience had stood in a line 10 minutes before opening of the performance?

(2) How many minutes did the person take to enter the theater who is the day tickets visitor and was in the 120th from the beginning of the line?
(Find the time this person was in the line.)

(3) Before opening of the performance, ten percent of scheduled number of the advance tickets remained unsold and 80 percent of schedule number of of the day tickets were sold.
Find the total number of audience this day.

Problem 8

In trapezoid ABCD as shown in a figure, the point O is an intersection of a diagonal line.

The area of △ AOB is 10 cm² and △ BOC is 25 cm².

Find the area of trapezoid ABCD.

Problem 9

Fig. 1 and Fig. 2 are development views of the cube in which the numbers from 1 to 6 were written to each face.
It is considered that the sum of numbers written to three faces gathering in the one vertex of each cube.
As for Fig.1, the greatest sum of numbers is 15.
In the case of Fig. 2, find the greatest sum of numbers.

Problem 10

As shown in a figure, there are the right hexagon ABCDEF and a right heptagon ABGHIJK.

Find the angle of X and Y.

Problem 11

As shown in the figure, five pieces equilateral triangle of the same size are put in order without a gap.
Among quarters point of BC, point D is the point closest to the B.
The length of AE is 9 cm.
Find the length of AD.

Problem 12

Triangle ABC is a right triangle of AB = 18 cm, AC = 24 cm and BC = 30 cm.
The points P and Q are points on the bisectors of angle B and angle C, respectively.
PQ is parallel to BC. PH and AB, QK and AC are vertical respectively.
The area of pentagon AHPQK is half of the area of triangle ABC.
Find the length of PH and the length of PQ.

Problem 13

The shadow portion in the figure is made of cutting off four isosceles triangles 2cm in height from the square which is 8 cm one side.

Find the volume of the quadrangular pyramid made by assembling this development.

Answer / Continue »

Math Exam.L3 : NADA-2003-Day2

Time : 60 minutes
Passing marks : 70%

Answer : End of the problem

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Problem 1

I divide integers more than 6 by 6 and add a remainder to a quotient.

I express this calculation in → and continue it until it becomes 5 or less.

12 / 6 = 2 remainder 0, then 2 + 0 = 2.

When begin with 12, it is expressed as 12 → 2.

50 / 6 = 8 remainder 2, then 8 + 2 = 10, 10 / 6 = 1 remainder 4, then 1 + 4 = 5.

When begin with 50, it is expressed as 50 → 10 → 5.

Answer the following questions.

(1) When I begin this calculation with 2003, express the result by using →.

(2) Find the number of integers more than 6 to be suitable for A when it is expressed in one arrow as A → B.

(3) Find the smallest integer in integers more than 6 to be suitable for A when it is expressed in two arrows as A → B → C.

In addition, find the biggest integer.

(4) Find the smallest integer in integers more than 6 to be suitable for A when it is expressed in four arrows as A → B → C → D → E.

In addition, find the biggest integer.

Problem 2

A rectangle departs from the position in a figure and is moving in the direction of an arrow at 2 cm/s.

(1) Find the time when the rectangle is completely inside of the triangle.

(2) Find the area of the portion of the rectangle out of a triangle 12 seconds after leaving.

(3) Find the time when the area of the portion of the rectangle which is contained in the triangle is 30 cm² or more.

Problem 3

The figure shows a cube whose length of one side is 6cm.

Two points of P,Q moves on the side of the cube with a speed of 2cm per second, 3cm per second respectively.

P,Q leave A at the same time.

P moves in order of A → E → H → G → C → B → A and repeats this cycle.

Q moves in order of A → D → C → G → F → E → A and repeats this cycle.

Answer the following questions.

(1) Find the time when P and Q meet for the first time after leaving A.

(2) Find the time when P and Q meet for the fifth time after leaving A.

Problem 4

There is a flower clock in a certain town and the long hand advances one round in one hour with a fixed speed.
The hour hand stands still first 59 seconds in every minute and advances 1 of 720 round with a fixed speed in last one second.
The long hand and the hour hand have overlapped exactly at 0:00 a.m.
Answer to the following questions.

(1) Find the time when the long hand and the hour hand become right-angled during 0:00 a.m. and 1:00 a.m.

(2) Find the time when the long hand and the hour hand become right-angled during 8:00 a.m. and 9:00 a.m. except exactly at 9:00 a.m.

Problem 5

There are some parallelograms whose length of two sides is 2 cm and 1 cm, and one inside angle is 60 degrees.
These are connected at the vertex so that all of the 2 cm sides are parallel as shown in Fig.1 and Fig.2.

(1) A and B were connected as shown in Fig.1.
Find the area ratio of the sum of the area of two triangles painted black and the area of one parallelogram.

(2) C and D were connected as shown in Fig.2.
Find the area ratio of the sum of the area of four triangles painted black and the area of one parallelogram.

Answer / Continue »

Math Exam.L3 : NADA-2005-Day1

Time : 60 minutes

Passing mark : 70%

Answer : End of the problem

Problem 1

Find X.

2005 × 1/17 = X × 1/119 + 48 × 17/7

Problem 2

A singer performed concert 3 times and sang ten songs in each concert.
Out of ten songs in each concert he sang five songs which he did not sing in other two concerts.
In case the same song sung even twice or more is counted as one song, how many songs the most did this singer sing in three concerts ?

Problem 3

There are four integers of two digit.

The sum and difference of two numbers of these four numbers were all investigated.

The largest number in sum is 187 and the smallest number is 137.

The largest number in difference is 40 and the smallest number is 10.

Find the 2nd smallest number among four numbers.

Problem 4

There are three cars A, B, and C.

These cars can run 10 km, 15 km, and 20 km with the gasoline of 1L, respectively.

A, B, and C ran total of 100 km consuming the gasoline of 8L in total.

C ran 3 times as much distance as A.

Find the distance where B ran.

Problem 5

There is a track and total weight of cargo must be set 2000 kg or less and total volume of cargo must be set 24 m3 or less.

The weight of one piece of the product A is 100 kg and the volume is 0.8 m³.

The weight of one piece of the product B is 50 kg and the volume is 3 m³.

When you load A and B in this track, find the maximum number of pieces of A and B in total to be loaded.

Problem 6

There are three different integers and the product of the three integers is larger than the sum of the three integers by four.
There are two sets of group of such three integers.
Largest integer is 4 in one group.
Find the each product of two groups.

Problem 7

A certain product are sold at A store, B store, and C store.

Total of 6867 pieces sold in three stores this month and the number of product increased more than the previous month was same in each store.

It means that in this month total sales of this product was increased by 15% in A store, 10% in B store and 6% in C store.

Find the sum total number of the sales of three stores in the previous month.

Problem 8

There are eight color cards with number, three blue cards blue1, blue1, blue1 and red cards red1, red1, red2, red2, red3.
I arrange them in a line.
Answer the following questions about the way of arrangement that there are just four places where the card of different color adjoins each other like red2-blue1-blue2-red1-red1-red3-blue1-red2 for example.

(1) When distinguishing the color of a card and not distinguishing a number, how many ways of arrangement is there?

(2) When distinguishing both the color of a card and a number, how many ways of arrangement is there?

Problem 9

The quadrangle ABCD in a figure is a parallelogram. QS and BC are parallel and RT and CD are also parallel.
The point P which is an intersection of QS and RT is on the diagonal line BD.
(The length of BP) : (length of PD) = 2 : 1.
Find the area ratio between the sum of the area of the triangle AQT and CSR and the area of parallelogram ABCD.

Problem 10

Both triangle ABC and ADE in a figure are a right-angled isosceles triangle.
(length of BD) : (length of DC) = 1 : 3.
Find the area ratio of triangle DCE and triangle ABC.

Problem 11

In a figure below, the length of AC is 10 cm and that of AF is 6 cm.

The ratio of the length of AD to BD is 3 : 2.

The ratio of the length of BE to EC is 5 : 2.

Find the angle of X.

Problem 12

Make a large cube of 5cm one side by piling up 125 dices of 1cm one side without a gap.
This large cube is cut by the plane passing through the three vertex of the cube as shown in a figure.

As for the portion of the triangular pyramid below the cutting plane, find the following each number.

(1)The number of the dices which is not cut.

(2)The number of a solid with the volume larger than 0.5 cm³ in the solid made by cutting a dice.

(3)The number of a solid with the volume smaller than 0.5 cm³ in the solid made by cutting a dice.

Problem 13

Find the volume of the solid which is made by assembling the development view of the figure.
Each triangular face is an equilateral triangle.
Each face of a hexagon is a made figure where one side cuts out two right-angled isosceles triangles whose equal lengths of two sides are 1 cm from the square which is 2 cm one side.

Answer / Continue »

Math Exam.L3 : NADA-2004-Day1

Time : 50 minutes

Passing mark : 70%

Answer : End of the problem

Problem 1

Find X

5/7 × (X × 119/15 + 1/4) / 11/8 = 16/11

Problem 2

There are 3 kind coins of A, B, and C.

Each weight of combination of A 6 sheets, B 1 sheet, C 1 sheet and A 1 sheet, B 4 sheets, C 1 sheet and A 1 sheet, B 1 sheet, C 3 sheets is 61g.

Find the weight of 1 sheet of C.

Problem 3

The memorial day of the 100th anniversary of the foundation of A junior high school is October 24, 2027.

When the years are a multiple of 4 when the years of A.D. cannot be divided by 100, it is a leap year.

January 31, 2004 is Saturday.

When February 1, 2004 is set to the 1st day, what number is October 24, 2027? and what day of the week is it?

Problem 4

When salt solution Xg with 8% concentration, salt solution Yg with 12% concentration and the salt 10g are mixed and stirred well, salt solution 800g with 10% concentration will be made.

Find X and Y, respectively.

Problem 5

When the integer A was divided by the integer B, the quotient was 32 and remainder was 10.
Furthermore, when division process was continued to the 3rd decimal digit, it was 32.322 and it was not divisible yet.

Find the integers A and B.

Problem 6

Taro was born in May, Jiro was born in July and Hanako was born in September, respectively.

In March, 1992, Taro was 14 years old and Hanako was 23 years old.

At a certain date in several years after March, 1992, Taro was 23 years old and the sum total of the age of Taro, Jiro and Hanako was 1.4 times of the sum total in the time of March, 1992.

Find the age of Jiro at a certain date in several years after March, 1992.

Problem 7

Taro reads a book of 151 pages, Jiro reads a book of 216 pages and Hanako reads a book of 294 pages.

For example, if everyone reads 4 pages a day, as for the number of pages read on the day which each finishes reading, it is 3 pages for Taro, 4 pages for Jiro and 2 pages for Hanako.

How many pages should be read a day in order to become the same number of pages which three persons read on the day which each finishes reading?

Moreover, find the number of pages read on the day which each finishes reading.

Noted that the number of pages read on the last day of reading is less than the number of pages read every day.

Problem 8

There was water full in the tank. I scheduled to drain away the water in the tank at the rate of 6m³ per minute.
After started draining, the volume of water in the tank became 3/4 of the full and it was rescheduled.
After the change, I drained at the ratio of 7m³ per minute until the volume of the water in the tank becomes half of the drainage started.
I stopped draining afterwards for seven minutes.
Next, I drained at the ratio of 14m³ per minute afterwards. After rescheduled, the time of the tank emptied was earlier by two minutes than first plan.
Find the capacity of this tank.

Problem 9

The paper of the square whose length of a diagonal line is 20 cm is placed on the desk.

This paper is rotated on the desk by 45 degrees centering on the one vertex.

Find the area of the portion which this paper passes.

Pi is assumed to be 3.14.

Problem 10

A figure is a rectangular prism and AB = 5cm, AD = 6cm, and AE = 8cm.

Moreover, BF = 4 cm, AG = 2cm.

A rectangular prism is divided into two solids by the plane which passes along three point C, F, and G.

Find the ratio of the volume of a large solid to the volume of a small solid.

Problem 11

Fig.1 and Fig.2 show development views of solids.

The development view of Fig.1 consists of one rectangle, two equilateral triangles, and two trapezoids.

The developed view of Fig.2 consists of four equilateral triangles.

Find the volume ratio of the solid made by assembling Fig.1 and the solid made by assembling Fig.2.

Problem 12

3 sets of sides of the hexagon in the figure faced each other are parallel.

As for each of 3 sets, the ratio of the length of a short side and a long side is 1 : 3.

Find the area ratio of the area of a shadow area, and the area of a hexagon.

Problem 13

In a figure, AB and CD are vertical.

AE = 24 cm, BE = 6 cm, CE = 18 cm, DE = 8 cm.

The area of a circle is 785 cm².

Find the sum of the area of a shadow area.

Problem 14

In a figure, AG is vertical to BC.

The points D and E are the middle points of AG and AC, respectively.

The point F is an intersection of BE and CD.

The length of DE is 2 cm.

The area of triangle ABC is 36 cm².

The area of the triangle CEF is 2 cm².

Find the length of AG.

Problem 15

There is a right-angled isosceles triangle ABC.

There is another right triangle DBE width is shorter than ABC by 3 cm and length is longer than ABC by 6 cm.

The figure shows two triangles overlap.

The point F is an intersection of AC and DE.

The ratio of the area of triangle CEF to ADF is 3 : 8.

Find the area of triangle ABC.

Answer / Continue »

Math Exam.L3 : NADA-2003-Day1

Time : 50 minutes, Passing mark : 70%

Answer : Please click "Answer >>" at the end of the problem.

Problem 1
Find X.
(2003 + X ) × 1/4 × 1/5 × 1/6 × 1/8 + 7/10 = 17/6

Problem 2
There are some one-yen coins.
When I change these into five-yen coins as many as possible, the total number of coins is decreased by 60 pieces.
Furthermore, when I changes those coins into ten-coins as many as possible, the total number of coins becomes ten pieces.
Find the number of one-yen coins first.

Problem 3

The ratio of the amount of the money that Taro and Jiro had was 7 : 4.
When Taro gave 150 yen to Jiro, the ratio of the money that Taro and Jiro had became 8 : 5.
Find the amount of the money Taro had first.

Problem 4
As for a price of an apple, a persimmon, and an orange, the price of apple is highest and that of orange is cheapest.

When I purchase five pieces in all including at least one of each fruit, the total amount differs in six kinds of 580 yen, 600 yen, 620 yen, 640 yen, 660 yen, and 700 yen depending on the combination of five pieces.

Find the sum total when I purchase one apple, one persimmon, and one orange.

Moreover, find the price of one persimmon.

Problem 5
I plan to distribute notes in a certain class.

Supposing I distribute four notes to to every boy and six to every girl, seven notes will remain.

Supposing I distribute six to every boy and four to every girl, nine notes fall short.

Supposing I distribute five to every boy and seven to every girl, 33 notes fall short.

Find the number of boys in this class.

Moreover, find the number of notes.

Problem 6
Yesterday I could exchange some amount of Japanese yen I had into 100 US dollars.
Today the Japanese yen of the same amount as yesterday can be exchanged for 1.02 times as many dollars, but I exchanged 12750 yen into 100 US dollars.
Find the amount of money of the Japanese yen which it had yesterday.

Problem 7
When integer of 6 digits 5ABC15 becomes a multiple of 999, find the integer ABC of 3 digits.

Problem 8

When doing some shopping, the consumption tax is 5% of sales price and less than 1 yen is omitted.
For example, if sales price is 219 yen, 10 yen consumption tax will be cost and 229 yen will be paid.
When sales price is 220 yen, 231 yen will be paid.
Therefore, 230 yen does not emerge with the amount of money including the consumption tax.
Find an amount of money nearest to 1000 yen among those which do not emerge with the amount of money of including consumption tax.

Problem 9
I arrange four number of 1,2,3,4 to one line.
For example, I arrange it as "2,4,1,3".
Considering a set of two numbers, there are three cases that big number is on the left side than small number which is "2 and 1", "4 and 1", and "4 and 3".
This case is called that “the number of inverse order of “2,4,1,3” is 3.”

The table shows the number of inverse order and arrangement ways of each number of inverse order about all 24 ways of arrangement of 1,2,3,4.

When I arrange five numbers of 1,2,3,4,5 to one line, I think about the number of inverse order in the same way as a case of the number of four.
Answer the following questions.

(1) What is the number of inverse order when I arrange it as "5,2,4,1,3"?

(2) In reference to an upper table, considering 120 arrangement ways of 1,2,3,4,5, how many ways are there the number of inverse order is 5?

Problem 10
In a figure, a quadrangle ABCD is a parallelogram.
(length of AE) : (length of ED) = 2 : 3.
The area of the triangle ABE is 80 cm².
Find the area of triangle CDF.

Problem 11
I make a large equilateral triangle by arranging small equilateral triangle 1cm of the length of one side side by side with no gap nor overlapping.
How many small equilateral triangles do I need to make a large equilateral triangle of 20cm of one side?

Problem 12
There is a paper of rectangle as shown in a figure.
The length of vertical side, horizontal side and diagonal line are 15 cm, 20 cm and 25 cm respectively.
This paper is folded so that A and C may overlap.
Find the sum total of a triangular area with which paper has not overlapped in this case.

Problem 13
The shadow area of a figure is a figure which is a combination of three equilateral triangles with 6 cm one side cm and three sectors 6 cm in radius.
When a circle 1 cm in radius takes one round touching the circumference of this figure, find the area of the portion along which this circle passes.
Pi is assumed to be 3.14.

Problem 14
There is a big wall which stands vertically to the ground.
The bottom of the square pillar of Fig.2 is a trapezoid as shown in Fig.1.

The height is 30 cm.
It is placed as the side CD is parallel to the wall and the distance to the wall is 10 cm.
The angle to look up at the sun from the ground is 45 degrees.
The shadow area of Fig.2 expresses the shadow made on the ground of this quadratic prism.
Find the area of the whole shadow made to the wall by this quadratic prism.

Problem 15
Solid O-ABCD in a figure is a right quadrangular pyramid.
The bottom is a square and all the length of OA, OB, OC and OD is equal.
Moreover, E and F divide OB and OD into the ratio of 3 : 1, respectively.
The intersection of the plane which passes along three point A, E, F and the side OC is set to G.
Find OG : GC.
Moreover, in two portions of the right quadrangular pyramid divided by this plane, find the volume ratio of the volume of a portion containing O and the volume of the right quadrangular pyramid.

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