Math New Drill (Level 1) : Number sense and theory Three fractions multiplied by a same fraction

Three fractions 28/3, 35/6, and 77/8 are multiplied by the same fraction and each product becomes to be integer. 

Find the fraction more than 10 and the nearest to 10 among such fractions. 

Math New Drill (Level 1) : Number sense and theory Find a fraction

Find such a fraction when 5 is subtracted from a denominator, it will be 1/9 and when 5 is added to a numerator, it will be 1/4.

Math New Drill (Level 1) : Number sense and theory Problem 6 TOYOEIWA-2008

There are ten cards. 

One of odd numbers from 1 to 19 is written on each card. 

When taking out two cards in order four times, each sum was 16, 18, 24, and 34 in order. 

Find the numbers of the 2nd set and the 3rd set, respectively.

Math New Drill (level 1) : Number sense and theory Problem 2(2) TOYOEIWA-2008

Find the number of figures to be divisible by 3 or 5 in integers from 1 to 200.

Math New Drill (Level 2) : Number sense and theory SNJ00-0705-L2 Pieces of figure 1 from 1 to 8000

In the numbers from 1 to 8000, how many pieces of 1 are used altogether?

Math New Drill (Level 2) : Number sense and theory SNJ00-0704-L2 Three integers with 5 of GCD and 450 of LCM

There are three different integers. 

Each of these integers is less than 90 more than 35. 

The Greatest Common Divisor of these three integers is 5 and the Least Common Multiple is 450. 

Find all the groups of these three integers.

Math New Drill (Level 2) : Number sense and theory SNJ00-0705-L2 Sum total of consecutive integers

In two or more consecutive set of integers, how many sets of integers are there when all integers are added in the set, the sum total becomes 2009?

Math New Drill (Level 1) : Number sense and theory SNJ00-0702-L1 Integers with three divisors

Find integers with three divisors between 50 and 300.

Math New Drill (Level 2) : Number sense and theory SNJ00-0703-L2 Find the capacity of the train

There is a train that just 32.5 % of the capacity can sit. 

When 40 people get on this train, all of them can sit. 

When 60 people get on this train, some cannot sit. 

Find the capacity of this train.

Math New Drill (Level 1) : Number sense and theory SNJ00-0705-L1 Sum of consecutive integers

When the sum of seven consecutive integers is 140, find the first number.

Math New Drill (Level 1) : Number sense and theory SNJ00-0703-L1 Multiple of 12 and 17

When 12 is added to a certain numbers, it'll be a multiple of 17, and when 17 is added, it is a multiple of 12. 

Among such numbers find the second smallest number.

Math New Drill (Level 2) : Number sense and theory SNJ00-0704-L2 Find denominators of two fractions

The least common multiple of the two integers X and Y (X< Y) is 96 and 1/X + 1/Y = 19/96. 

Find X and Y. 

Math New Drill (Level 1) : Number sense and theory SNJ00-0703-L1 Find multiple of 13

In 4 -digit integer 8xx1, how many pieces of number which is multiple of 13 are there?

Math New Drill (Level 2) : Number sense and theory Problem4 NAKANO ATTACHED TO MEIJI UNV.-2014

Sign [x] is assumed as a sign to calculate the product of each digit of a certain number x like Example.

Example: [46] = 24,   [88] = 64 

Answer the following questions. 

(1) Find all integers x of two digits that become "[54] + [35] = [x]".

(2) Find all integers x of two digits that become "[[x] + 21] = 36." 

Math New Drill (Level 2) : Number sense and theory SNJ00-0705-L3 Multiple each digit of numbers

(1) There are 2 digits of numbers of 10, 11, 12, 13, .... 99.

Multiple each tens digit and ones digit number of each number and make 90 pieces of numbers.

Find the sum total of 90 numbers.

(2) There are 4 digits of numbers of 1000, 1001, 1002, 1003, .... 2013.

Multiple each of thousands, hundreds, tens and ones digit number of each number and make 1014 pieces of numbers.

Find the sum total of 1014 numbers.

(3) Among 2014 pieces of numbers made in (2), find the pieces of figures whose ones digit is 7.

Math New Drill (Level 2) : SNS00-0705-L2 The total of each digit of either number is divided by 7

Among two consecutive natural number, find the least two numbers that the total of each digit of either number can be divided by seven.

Math New Drill (Level 3) : Remainder when the 100th power of 123 is divided by 11

Find the remainder when the number of the 100th power of 123 is divided by 11.

Noted 

Math New Drill (Level 2) : Number sense and theory : Integers not including 7

In integers from 1 to 3000, find the number of figures that do not use number 7.

New Math Drill (Level 1) : Number sense and theory Problem 1(4) OTSUMA-2014

Among fractions that are larger than 7/9 and smaller than 6/7, find the fraction whose numerator is 13.

Math New Drill (Level 2) : Number sense and theory Problem 7 TOHO-2014

There is a bar of length 180cm. 

I mark points on the bar where it is divided M equally and N equally respectively. 

M and N are integers and M is bigger than 2 and is smaller than N. 

For example when M is 4 and N is 6, it is marked respectively. 

As the mark at one point is overlapped as shown in the lower figure, number of point becomes seven. 

Answer the following questions. 

(1) In case M is 5 and N is 6, find the number of point. 

Find the shortest length of interval between two points. 

(2) In case M is 8 and N is 12, find the number of point. 

 Find the shortest length of interval between two points. 

(3) There are two cases of combination of M and N which make the number of point eight. 

Answer these combinations of M and N. 

(4) Answer all combinations of M and N that the shortest length becomes 12cm among the length of the interval between points.