NADA-2005-Day1

Time : 60 minutes

Passing mark : 70%

Answer

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.