1991 state countdown round
TRANSCRIPT
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MATHCOUNTS
1990-1991
State Countdown Round
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How many of the even counting
numbers less than 100 areprime?
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nswer! 1
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"he probability of rain on anygiven day in tlanta is #0$%
fter how many days would youe&pect it to have rained on '0
days?
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nswer! 1(0 )days*
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"wo fair tetrahedral )four-sided*dice are thrown% +f the faces of
each are numbered ', (, , and 9,what is the probability that the sumof the numbers on the bottom faces
is a prime?
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nswer! 0
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.hat is the shortest distance that canbe traveled if you start at any point, , /,
C, or and visit the other three pointsonce?
( ' /
2 (
C
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nswer! 1'
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How many positive integer pairs
)&, y* satisfy 3 & 4 y,'when 3 #?
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nswer! ( )pairs*
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+f the digit is placed to the rightof a three-digit number, forming
a four-digit number, the value ofthe original number increases by,000% .hat was the originalnumber?
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nswer!
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5ifty cards numbered 1 to (0 areplaced in a bo&% +f a card isselected at random, what is the
probability that the card is aprime number and a multiple of
seven? 6&press your answer asa common fraction%
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1(0
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.hat is the last digit in the
product of all natural numbersbetween 1 and 100?
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nswer! 0
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+f (7 is e&pressed as the product
of its prime factors in e&ponentialform, what is the sum of itse&ponents?
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nswer! (
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"his table shows the distribution of scores of 8r%Sampsons 10-point :ui;% .hat is the median score?
Test Scores Frequency10 I
9 II
8 III7 IIII
6 IIII
5
4 I
3
2 II
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nswer!
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certain type of < => by 11 paperhas a thic@ness of 0%0# cm% +f
1(,000 sheets of paper are stac@edon top of each other, what is the
height, in meters, of the stac@?
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nswer! ' )meters*
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Aoints , /, C, and are located on /such that / 3 ' 3 /C% +f a point is
selected at random, what is theprobability that it is between C and ?6&press your answer as a common
fraction%
C /
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1#
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"hree identical s:uares are
placed side by side to form arectangle with a perimeter of
102 inches% .hat is the area, ins:uare inches, of each s:uare?
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nswer! 19 )s:uare inches*
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/rad is less than '0 years old%
His age is a multiple of (% Be&tyear his age will be a multiple of% How old is /rad now?
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nswer! #0 )years old*
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How many different triangles are
in the figure?
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nswer! 1' )triangles*
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How many even numbers arebetween #01 and 20(?
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nswer! 101
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.hat is the positive s:uare rootof 1&1?
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nswer! 2&<
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.hen n is divided by (, the
remainder is 1% .hat is theremainder when 'n is divided by(?
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nswer! '
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6&press 10$ of '0$ of (0 as adecimal%
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nswer! 1%(
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3 1, #, ', 2, (, , , <, 9, DE%
.hat fractional part of the numbersin set are not divisible by '?
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#'
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Si& softball teams are to play
each other once% How manygames are needed?
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nswer! 1( )games*
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"wo ropes, 1< meters in lengthand #2 meters in length, need to
be cut into pieces which are allthe same length% .hat is thegreatest possible length of eachpiece?
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nswer! )meters*
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.hat value of n ma@es thissentence true?
n 3 n 4 1
9
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nswer! #
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+f f)&* 3 '& 4 # and g)&* 3 )& F 1*#
,what is f)g)-#**?
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nswer! #9
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+f 8arch 1 is a 8onday, what day ofthe wee@ will it be #0 days later?
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nswer! 5riday
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Given & 3 ' and y 3 #, simplify!
#&' F 'y#
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nswer!
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Simplify! 727'7
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nswer! '(
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+n how many different orders
can a group of si& people beseated around a round table?
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nswer! 1#0 )ways*
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How many different
arrangements are there usingthe letters in the wordAR6?
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nswer! ''0 )arrangements*
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.hat is I#00 to the nearest tenth?
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nswer! 12%1
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.hat is the positive geometricmean of < and 1<?
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nswer! 1#
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5ind the midpoint of the line
segment with endpoints )(, -(* and) -(, (*%
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nswer! )0, 0*
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Give the decimal e&pression for :$ of:%
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nswer! 0%01:#
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Solve for &! #& 4 # 3 1#<
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nswer! (
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"he area of a triangle is 00 s:uare
feet% 5ind the altitude, in feet, ofthe triangle if the length of the baseis '0 feet%
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nswer! 20 )feet*
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"he longest side of a right triangle
is ( feet and the shortest side is 'feet% .hat is the area of thetriangle in s:uare meters?
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nswer! )s:uare meters*
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+f each side of a s:uare is
increased by (0$, what is thepercent of increase in the area ofthe s:uare?
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nswer! 1#( )percent*
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5our lines are drawn in a plane%
.hat is the ma&imum number ofdistinct regions in which thelines could divide the plane?
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nswer! 11
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Simplify! 0%D 4 0%'''D0%999D
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nswer! 1
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.hat percent of <0$ of a
number will lave the numberunchanged?
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nswer! 1#( )percent*
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5ind the number of s:uare units inthe area of the shaded region%
)0, '0* )#0, '0* )'0, '0*
)'0, #0* )0, 10*
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nswer! (00 )s:% units*
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+f y 3 - 4 I)( F &*, find & when y 3'%
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nswer! -9(
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+n :uadrilateral /C, angle /and angle C are trisected asshown% .hat is the degree
measure of angle 5? / C
5
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nswer! <0 )degrees*
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5ind the number of s:uare units inthe area of the triangle%
)-#, *
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nswer! '# )s:uare units*
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.hat is the smallest integer thatsatisfies K#& F 'KL <?
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nswer! -#
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How many two-digit wholenumbers are divisible by 12?
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nswer!
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.hat percent of the whole
numbers less than 100 have noremainders when divided by (?
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nswer! #0 )percent*
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.hat is the 100
th
even wholenumber?
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nswer! 19<
/C is a s:uare 2 inches on a side,
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and each of the inside s:uares is
formed by Moining the midpoints of theouter s:uares sides% .hat is the areaof the shaded region?
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nswer! 2 )s:uare inches*
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+f all multiples of ' and allmultiples of 2 are removed from
the list of numbers 1 through100, how many whole numbers
are left?
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nswer! (0 )whole numbers*
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FINALS
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ivide 2abc by #a#b 'd#
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cd#
a
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.hat is the simplest radicalform of 'I2 ÷ I#?
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nswer! I#
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"wo fair cubical dice are tossed%.hat is the probability,
e&pressed as a commonfraction, that the sum of thenumbers showing on the dice
will be four?
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11#
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+f a N b is defined as a 4 b,
#what is the value of N )' N (*?
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nswer! (
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+f & and y are positive integers
such that &y 3 10<, what is theleast possible value of & 4 y?
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nswer! #1
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5ind II#(,000%
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nswer! 20
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6&press the value of1 of 10$ of 0%001 in scientific notation%
100
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nswer! 1 or)1%0* J 10-
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5ind the sum of all solutions to
this e:uation!&# 4 # 3 10#
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nswer! 0
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.hat is the sum of the lengths, incentimeters, of the two legs of a
'0-0-90 right triangle, if the lengthof the hypotenuse is #I cm?
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nswer! I 4 'I#
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How many diagonals can bedrawn for a he&agon?
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nswer! 9 )diagonals*
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