NADA-2007-Day1

Time : 50 minutes

Passing mark : 70%

Answer

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.

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.