Day1

Answer&Solution

P1 Operation with fraction (distribution)

Find the number in X.

X/4 - X/7 = 3

P2 Magic square 3 × 3

As shown in the figure, five numbers are put in nine grids.

Other numbers are put into the remaining grids and it is arranged that products of three numbers in any vertical or horizontal row become same.

Find the number in A at this time.

P3 The volume when water freezes

When water freezes, suppose that the volume increases by one-eleventh.

Inversely, when ice is melted to become water, how much does the volume decrease?

P4 Work done by two persons

To finish a certain work, it will take 12 days by Taro and 15 days by Jiro.

Taro and Jiro jointly started to finish the work but Jiro rested a number of days.

It took 8 days to finish the work.

How many days did Jiro rest ?

P5 100 m dash

Taro raced with Jiro 100m dash.

Jiro was 10m this side to the goal when Taro made a goal.

If Taro starts from 10m back from a start point, who will win ?

P6 Average speed

I went to Point B from point A at 3 km/h and returned to A from B at 6 km/h.

Find the speed of the average.

P7 Buy apple and orange

I planed to buy 20 apples and oranges in total. one apple costs 70 yen and one orange costs 40 yen.

However, because I bought the number of apples and oranges adversely, 120 yen remained.

Find the amount of money planned?

P8 Repack oranges in the bag

There are ten oranges per bag in several bags.

When this was repacked to fifteen oranges per bag, four bags remained.

How many bags are there?

P9 Fraction can not be reduced

How many fractions are there which cannot be reduced to its lowest numbers among 1/45, 2/45, 3/45 -- 44/45 ?

P10 Divided by 4 and 5

Among the numbers which will remain 2 when it is divided by 4, and will remain 3 when it is divided by 5, what is the largest number of two-digit numbers?

P11 Three digits number out of four cards

When creating the number of three digits by choosing and putting three sheets in order out of four cards, 1, 2, 4, and 7, how many kinds of multiples of 2 are made?

P12 Four children between parents

How many ways of forming line that four children stand in one line of side among parents are there?

Parents stand at the both ends of the line.

P13 Time going up by elevator

There is a building of 25 stories and it took 5 seconds to go up from the first(base) floor to the fifth floor in an elevator.

How many seconds does going up by the same speed from the first floor to the 25th floor take?

P14 Trees planted along the road

Trees are planted from end to end along a road.

When planting every 6 m, ten trees are needed more than the case where it plants every 8 m.

Find the length of this road.

P15 Area of trapezoid

Find the area of trapezoid of the figure.

P16 Overlapped two triangles

△DBE and △ABC are overlapped as shown in the figure below.

AB : DB = 7 : 3 and BC : BE = 8 : 5.

The area of △DBE is 15 cm2.

Find the area of △ABC.

P17 Development view is square

Find the volume of the solid that can be assembled by the deployment view as shown below.

P18 Cutting a cylinder

The figure below is a solid obtained by cutting the cylinder on a slant.

Find its volume.

Pi is assumed to be 3.

P19 How many liars in four ?

Four persons, A, B, C, and D, said as follows :

A said "B is a liar."

B said "C is a liar."

C said "D is a liar."

D said "A is a liar."

How many liars are there among these four persons ?

P20 Move half distance of before

In order to go to a certain place 10 km from here, I'm going to move forward as follows :

First time, I move 5 km.

Second time I move 2.5 km of the half of 5 km.

Third time I move 1.25 km of half of 2.5 km. --------

When I move forward like above, how many times does it it take to reach the goal ?