NADA-2004-Day1

Time : 50 minutes

Passing mark : 70%

Answer

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.