Difference between revisions of "1997 PMWC"

m (Problem T3)
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== Problem I1 ==
 
Evaluate 29 27/28 x 27 14/15
 
  
[[1997 PMWC Problems/Problem I1|Solution]]
 
 
== Problem I2 ==
 
 
[[1997 PMWC Problems/Problem I2|Solution]]
 
 
== Problem I3 ==
 
Peter is ill. He has to take medicine A every 8 hours,
 
medicine B every 5 hours and medicine C every 10 hours.
 
If he took all three medicines at 7 a.m. on Tuesday, when will he take them altogether again?
 
 
[[1997 PMWC Problems/Problem I3|Solution]]
 
 
== Problem I4 ==
 
 
[[1997 PMWC Problems/Problem I4|Solution]]
 
 
== Problem I5 ==
 
 
[[1997 PMWC Problems/Problem I5|Solution]]
 
 
== Problem I6 ==
 
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?
 
 
[[1997 PMWC Problems/Problem I6|Solution]]
 
 
== Problem I7 ==
 
40% of girls and 50% of boys in a class got an 'A'. If there
 
are only 12 students in the class who got 'A's and the ratio of
 
boys and girls in the class is 45, how many students are
 
there in the class?
 
 
[[1997 PMWC Problems/Problem I7|Solution]]
 
 
== Problem I8 ==
 
<math>997-996-995+994+993-992+991-990-989+988+989-986+\cdots+7-6-5+4+3-2+1=?</math>
 
 
[[1997 PMWC Problems/Problem I8|Solution]]
 
 
== Problem I9 ==
 
A chemist mixed an acid of 48% concentration with the
 
same acid of 80% concentration, and then added 2 litres of
 
distilled water to the mixed acid. As a result, he got 10
 
litres of the acid of 40% concentration. How many
 
millilitre of the acid of 48% concentration that the chemist
 
had used? (1 litre = 1000 millilitres)
 
 
[[1997 PMWC Problems/Problem I9|Solution]]
 
 
== Problem I10 ==
 
Mary took 24 chickens to the market. In the morning she
 
sold the chickens at <math>\</math>7 each and she only sold out less than
 
half of them. In the afternoon she discounted the price of
 
each chicken but the price was still an integral number in
 
dollar. In the afternoon she could sell all the chickens, and
 
she got totally <math>\</math>132 for the whole day. How many
 
chickens were sold in the morning?
 
 
[[1997 PMWC Problems/Problem I10|Solution]]
 
 
== Problem I11 ==
 
A rectangle ABCD is made up of five small congruent rectangles as shown in the given figure. Find the perimeter, in cm, of ABCD if its area is <math>6750 cm^2</math>.
 
[[Image:ABCD.gif]]
 
 
[[1997 PMWC Problems/Problem I11|Solution]]
 
 
== Problem I12 ==
 
In a die, 1 and 6,2 and 5,3 and 4 appear on opposite faces.
 
When 2 dice are thrown, product of numbers appearing on
 
the top and bottom faces of the 2 dice are formed as follows:
 
  number on top face of 1 st die x number on top face of 2nd die
 
  number on top face of 1st die x number on bottom face of 2nd die
 
  number on bottom face of 1st die x number on top face of 2nd die
 
  number on bottom face of 1st die x number on bottom face of 2nd die
 
What is the sum of these 4 products ?
 
 
[[1997 PMWC Problems/Problem I12|Solution]]
 
 
== Problem I13 ==
 
A truck moved from A to B at a speed of 50 km/h and
 
returns from B to A at 70 km/h. It traveled 3 rounds within
 
18 hours. What is the distance between A and B?
 
 
[[1997 PMWC Problems/Problem I13|Solution]]
 
 
== Problem I14 ==
 
If we make five two-digit numbers using the digits 0, 1, 2,...9 exactly once, and the product of the five numbers is maximized, find the greatest number among them.
 
 
[[1997 PMWC Problems/Problem I14|Solution]]
 
 
== Problem I15 ==
 
How many paths from A to B consist of exactly six line
 
segments (vertical, horizontal or inclined)?
 
[[Image:1997_PMWC-I15.png]]
 
 
[[1997 PMWC Problems/Problem I15|Solution]]
 
 
== Problem T1 ==
 
 
[[1997 PMWC Problems/Problem T1|Solution]]
 
 
== Problem T2 ==
 
Evaluate
 
 
<math>1(\dfrac{1}{1}+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10})</math>
 
 
<math>+3(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10})</math>
 
 
<math>+5(\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10})</math>
 
 
<math>+7(\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10})</math>
 
 
<math>+9(\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10})+11(\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10})</math>
 
 
<math>+13(\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10})+15(\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10})</math>
 
 
<math>+17(\dfrac{1}{9}+\dfrac{1}{10})+19(\dfrac{1}{10})</math>
 
 
 
[[1997 PMWC Problems/Problem T2|Solution]]
 
 
== Problem T3 ==
 
To type all the integers from 1 to 1997 using a typewriter on a piece of paper, how many times is the key '9' needed to be pressed?
 
 
 
[[1997 PMWC Problems/Problem T3|Solution]]
 
 
== Problem T4 ==
 
 
[[1997 PMWC Problems/Problem T4|Solution]]
 
 
== Problem T5 ==
 
 
[[1997 PMWC Problems/Problem T5|Solution]]
 
 
== Problem T6 ==
 
 
 
[[1997 PMWC Problems/Problem T6|Solution]]
 
 
== Problem T7 ==
 
 
[[1997 PMWC Problems/Problem T7|Solution]]
 
 
== Problem T8 ==
 
 
[[1997 PMWC Problems/Problem T8|Solution]]
 
 
== Problem T9 ==
 
 
[[1997 PMWC Problems/Problem T9|Solution]]
 
 
== Problem T10 ==
 
 
[[1997 PMWC Problems/Problem T10|Solution]]
 

Revision as of 15:57, 9 January 2008