IPM / MTSE / IMO test paper for STD IX ( Answers are provided)
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Saturday, February 21, 2015
Saturday, February 14, 2015
Friday, February 13, 2015
puzzle
Your mother stays in Pune. You want to pay a visit on her birthday, and give her a gift of 2 cakes.
On the way to Pune, you will run into 7 check post for collecting toll. You can pay them in kind. In such a case they will demand 1/2 of all your cakes as the price of entry. As a goodwill gesture they return back 1 cake to you.
How many cakes do you need to carry to be able to give 2 cakes to your mom.
On the way to Pune, you will run into 7 check post for collecting toll. You can pay them in kind. In such a case they will demand 1/2 of all your cakes as the price of entry. As a goodwill gesture they return back 1 cake to you.
How many cakes do you need to carry to be able to give 2 cakes to your mom.
Thursday, February 12, 2015
fun with numbers
Remembering Ramanujam
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 + 10 = 1111111111
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 + 10 = 1111111111
fun with numbers
Remembering Ramanujam
more with numbers
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
more with numbers
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
fun with numbers
Remembering Ramanujam
more on interesting numbers
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
more on interesting numbers
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
numbers
Remembering Ramanujam
Fun with numbers --- note the symmetry
1 x 9 + 2 = 11
12 x 9 + 3 = 121
123 x 9 + 3 = 12321
1234 x 9 + 4 = 1234321
12345 x 9 + 5 = 123454321
123456 x 9 + 6 = 12345654321
1234567 x 9 + 7 = 1234567654321
12345678 x 9 + 8 = 123456787654321
123456789 x 9 + 9 = 12345678987654321
Fun with numbers --- note the symmetry
1 x 9 + 2 = 11
12 x 9 + 3 = 121
123 x 9 + 3 = 12321
1234 x 9 + 4 = 1234321
12345 x 9 + 5 = 123454321
123456 x 9 + 6 = 12345654321
1234567 x 9 + 7 = 1234567654321
12345678 x 9 + 8 = 123456787654321
123456789 x 9 + 9 = 12345678987654321
numbers
10th was the BD of Ramanujam
to remember him here is some interesting symmetry in numbers
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
to remember him here is some interesting symmetry in numbers
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
Wednesday, February 11, 2015
Tuesday, February 10, 2015
numbers
The number 142857 has the remarkable property that multiplying it
by 1, 2, 3, 4, 5, and 6 cyclically permutes the digits.
142857 x 1 = 142857
142857 x 2 = 285714
142857 x 3 = 428571
142857 x 4 = 571428
142857 x 5 = 714285
142857 x 6 = 857142
can you think of any other number?
142857 x 1 = 142857
142857 x 2 = 285714
142857 x 3 = 428571
142857 x 4 = 571428
142857 x 5 = 714285
142857 x 6 = 857142
can you think of any other number?
divisibility
Let x and y be integers. Prove that (2x + 3y) is divisible
by 17 if (9x + 5y) is divisible by 17.
puzzle
Puzzle:
Here is a list showing the month and the number for each month...
January 7110
February 826
March 5313
April 541
May 3513
June 4610
July 4710
August 681
Decipher the logic and find the number for September?
Here is a list showing the month and the number for each month...
January 7110
February 826
March 5313
April 541
May 3513
June 4610
July 4710
August 681
Decipher the logic and find the number for September?
Monday, February 9, 2015
Sunday, February 8, 2015
number series
Solve this logical number series puzzle by replace question mark with the correct number
9090 = 4
1234 = 0
6055 = 2
9081 = 4
8888 = ?
9090 = 4
1234 = 0
6055 = 2
9081 = 4
8888 = ?
Wednesday, February 4, 2015
number puzzle
solve the following:
if
5+3+2 = 151022
9+2+4 = 183652
8+6+3 = 482466
5+4+5 = 202541
then find the value of 7+2+5 =
if
5+3+2 = 151022
9+2+4 = 183652
8+6+3 = 482466
5+4+5 = 202541
then find the value of 7+2+5 =
Saturday, January 24, 2015
HCF and LCM,
Delegates from 5 different schools are coming to Srimati sulochanadevi singhania school. The number of delegates from Kendriya vidyalaya is 42, 60 from Poddars', 210 from Hiranandani, 90 from Jamnalal and 84 from Lodha. They are being put up at Satkar Residency Hotel. What is the minimum number of rooms that would be required to accommodate so that each room has the same number of occupants and occupants are all from the same school?
Tuesday, January 20, 2015
distance and speed
If we exclude stoppages, then the speed of a bus is 45 km/h and if we include stoppages, it is 36 km/h. For how much time does the bus stop per hour?
Monday, January 12, 2015
HCF and LCM
A number p is such that:
p = 5k1 + 4,
p = 6k1 + 5,
p = 7k1 + 6,
p = 8k1 + 7,
p = 9k1 + 8,
Find the smallest number that satisfy this condition
p = 5k1 + 4,
p = 6k1 + 5,
p = 7k1 + 6,
p = 8k1 + 7,
p = 9k1 + 8,
Find the smallest number that satisfy this condition
HCF and LCM
The product of 2 numbers and its HCF is 1080. How many such pair of numbers are possible which satisfy the above condition?
Sunday, January 11, 2015
Saturday, January 10, 2015
Thursday, January 8, 2015
Monday, January 5, 2015
divisibility test
Show that 1000....................001 (containing 200 zeroes) is divisible by 1001.
Tuesday, December 30, 2014
JMO - application of addition, subtraction and multiplication
Your are given that 12345 x 33 = 407385
Use this information, and the concept of addition, subtraction, multiplication and division to arrive at the multiplication of 12345 x 336567.
You cannot multiply directly.
Use this information, and the concept of addition, subtraction, multiplication and division to arrive at the multiplication of 12345 x 336567.
You cannot multiply directly.
Monday, December 29, 2014
inequality, JMO
How many positive integer values can x take that satisfy the inequality
(x - 8) (x - 10) (x - 12).......(x - 50) < 0
(x - 8) (x - 10) (x - 12).......(x - 50) < 0
Tuesday, December 23, 2014
Sunday, December 21, 2014
Tuesday, December 16, 2014
mixtures
Nanu bought two
varieties of rice, costing 50 Rs/kg and 60 Rs/kg each, and mixed them in some
ratio. Then he sold the mixture at 70 Rs/kg, making a profit of 20 percent.
What was the ratio of the mixture?
ratio and proportion
The ratio of
marks obtained by Nanu and Bhanu is 6:5. If the combined average of their
percentage is 68.75 and their sum of the marks is 275, find the total marks for
which exam was conducted.
ratio and proportion
Two alloys A and
B are composed of two basic elements p and q. The ratios of the compositions of
the two basic elements in the two alloys are 5:3 and 1:2, respectively. A new alloy X
is formed by mixing the two alloys A and B in the ratio 4:3. What is the ratio
of the composition of the two basic elements in alloy X?
ratio and proportion, ipm, mtse
A house has dogs,
cats and parrot in the ratio of 3:7:5. If the number of cats was more than the
number of dogs by a multiple of both 9 and 7 then what is the minimum of pets
in the house possible?
Monday, December 15, 2014
Sunday, November 30, 2014
Arithmetic progression
In a Society, the houses are
arranged in one line numbering 1 to 49. What is that value of 'x' for which the
sum of the numbers of the houses preceding the house number 'x' is equal to the
sum of the numbers of the houses following it.
Arithmetic Progression
The sequence p1 ,
p2 ...
and q1 ,
q2 …
are in arithmetic progressions such that
p1
+ q1 = 50 and p11 −
p10 =
q99
−
q100 . Find
the sum of the first 100 terms of the progression,
( p1 + q1 ) , ( p2 + q2 ) …
Saturday, November 29, 2014
average
There are 10 numbers, u1, u2, u3........u10,
having a mean/ average of um. If the absolute value of the
difference of the number and the mean are 5, 3, 10, 15, 12, 8, 6, 9, 2 and 4
respectively then which of the numbers lie on one side of the mean.
Monday, November 24, 2014
divisibility, numbers
Let n be the total number of different 5 digit numbers that are divisible by 4. The digits comprise of 1, 2, 3, 4, 5 and 6. No digit is repeated in a number. What is the value of n?
divisibility
If n is a positive integer and (n + 1)(n + 3) is odd, then show that (n + 2)(n + 4) must be a multiple of 8.
Saturday, November 22, 2014
Thursday, November 20, 2014
Number Puzzle
If A3 = _ _ _ _ 76, where A is an element of
Natural number. Find A and all the missing numbers.
Saturday, November 15, 2014
simple equations
A and B start at noon from two towns 60 km apart, A's rate of walking is twice that of B's. If they walk 5 hours before they meet, find their rate of walking.
answer:
A = 8 km/hr, B = 4 km/hr
answer:
A = 8 km/hr, B = 4 km/hr
simple equation
If P and Q represent two towns 48 kms apart, and if A is walking from P to Q at 7 km/hr while B walks from Q to P at 5 km/hr, both starting at 9:00 am, at what time will they be 12 km apart?
Simple Equation
Of the two boys one was taller than the other by 15 cm; the shorter boy has grown by 9 cm and the taller boy has grown by 5 cm, and at present the difference of their heights is 1/15 the of the height of the taller boy. What were their former heights?
Thursday, November 6, 2014
Sunday, November 2, 2014
indeterminate equation, JMO
Find all the possible combinations in which 1000 can be
divided into two parts so that one may be a multiple of 13 and
the other a multiple of 49.
divided into two parts so that one may be a multiple of 13 and
the other a multiple of 49.
indeterminate equation
The librarian observes that one of the first 9 pages and one
other page of two digit is missing from a book. The sum of all the pages in
the book now is 260. What are the possible combinations of missing pages?
Thursday, October 30, 2014
JMO - miscellaneous examples
1. Nanu was asked to divide a number by 6 and then add
12 to the quotient. She, however added 12 to the number first and then divided
it by 6, getting an answer of 112. What was the correct answer?
2. If Nanu travels at 40 km/hr speed, she reaches
school from home at 9:30 am. If she travels at 50 km/hr speed, she reaches at
9:00 am. What is the distance from home to her school?
3. Solve
the alpha-numbers, given that each alphabet represents a unique digit.
S
E N D
+ M O R E
M
O N E Y
Wednesday, October 29, 2014
Alphamatics, JMO
The alphabets given below represent a unique number between 0 to 9.
find the alphabets
E I N
E I N
E I N
+ E I N
------------------------
V I E R
find the alphabets
E I N
E I N
E I N
+ E I N
------------------------
V I E R
Alphamatics, JMO
Each of the alphabets represent a unique number between 0 to 9.
find them
find them
Z E R O E S + O N E S ----------- B I N A R Y
indeterminate equation, JMO
Can integral multiples of 13 and 68 add up to 2000. if so how many such possibilities are there.
Tuesday, October 28, 2014
alphamatics, JMO
If 9 x HATBOX = 4 x BOXHAT
where every Alphabet is unique and has a value of 0 to 9.
Find each of the digits represented by the alphabet.
where every Alphabet is unique and has a value of 0 to 9.
Find each of the digits represented by the alphabet.
alphamatics
A B C D E F
x 6
---------------
D E F A B C
All alphabets represent a unique digit between 1 to 9.
Find the values of the alphabets A,B,C, D, E, F
x 6
---------------
D E F A B C
All alphabets represent a unique digit between 1 to 9.
Find the values of the alphabets A,B,C, D, E, F
series, JMO
The following number is formed by a special pattern and is the only
one of its kind: 8549176320.
What is the pattern?
Look and say sequence
- The series given below is called the "look - and - say" sequence.
- 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ...
- 1 is to be read as "one 1" or 11.
- 11 is to be read as "two 1s" or 21.
- 21 is to be read as "one 2, then one 1" or 1211.
- 1211 is to be read as "one 1, then one 2, then two 1s" or 111221.
- 111221 is to be read as "three 1s, then two 2s, then one 1" or 312211
Monday, October 27, 2014
indeterminate equation, JMO
Divide 112 into two parts one of which when divided by 3 leaves remainder 2 and the other divided by 8 leaves a remainder 7.
indeterminate equation, JMO
Find the fractions, having 7 and 11 for their denominators, such that their sum is 1(34/77)
indeterminate equation, JMO
Divide 152 into two parts so that one may be a multiple of 7 and the other a multiple of 12.
Alphamatics
For questions on letter numbers (alpha-matics)
http://mathforum.org/library/drmath/sets/select/dm_letter_number.html
reference site for puzzles
For puzzles in Alphametics, you may visit the given website:
http://www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/ALPHAMETIC/
http://www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/ALPHAMETIC/
indeterminate equation, JMO
Is it possible to have the sum of multiples of 29 and 48 to be equal to 500.
i.e 48m + 29n = 500, where m and n are natural numbers.
i.e 48m + 29n = 500, where m and n are natural numbers.
indeterminate equation, JMO
Is it possible to have the sum of multiples of 44 and 18 to be equal to 1000.
i.e 44m + 18n = 1000, where m and n are natural numbers.
i.e 44m + 18n = 1000, where m and n are natural numbers.
Indeterminate equation, JMO
Is it possible to have the sum of multiples of 47 and 19 to be equal to 1000.
i.e 47m + 19n = 1000, where m and n are natural numbers.
i.e 47m + 19n = 1000, where m and n are natural numbers.
JMO STD VI
Sunday, October 26, 2014
Saturday, October 25, 2014
indeterminate equations, JMO
The total age of some 7 years old children and some 5 years old children is 60 years. If a team is to be selected from these children such that their total age is 48 years, then in how many ways can it be done?
indeterminate equation, JMO
Students of a class are made to stand in rows. If 4 students are extra in each
row, there would be 2 less rows. If 4 students are less in each row, there would
be 4 more rows. Find the total number of students which satisfies this condition
if the number of students is less than 100.
row, there would be 2 less rows. If 4 students are less in each row, there would
be 4 more rows. Find the total number of students which satisfies this condition
if the number of students is less than 100.
Wednesday, October 22, 2014
JMO questions STD V / STD VI
1.
You are given that 47658 x 39876 = 1900410408. Without
directly multiplying, use the given information to solve the following
question:
52.342 x 0.60124
2.
Find the value of 19999 x 299999 using the
information 19999 = 20000 – 1 and 299999 = 300000 – 1.
3.
Consider the number
12345.....11121314........566. Find the 500th digit.
information
https://sites.google.com/site/tripuramathematicalsociety/olympiad
This site carries a lot of information on reference books for Olympiad.
This site carries a lot of information on reference books for Olympiad.
Tuesday, October 14, 2014
Wednesday, October 8, 2014
pipes and cistern
A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 24 hours. How many liters does the cistern hold?
pipes and cisterns
Three pipes A, B and C can fill a tank in 6 hours. All the three pipes are kept open for 2 hours, C is then closed and A and B fills the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is ................
pipes and cisterns
A tank is filled in 10 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
pipes and cisterns
Three pipes A, B and C can fill up a tank from empty to full in 10 minutes, 20 minutes, and 30 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution P in the liquid in the tank after 6 minutes?
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