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Difference between revisions of "2005 CEMC Gauss (Grade 7) Problems/Problem 11"

(Created page with "== Problem == The temperature range on a given day is the difference between the daily high and the daily low temperatures. On the graph shown, which day has the greatest temper...")
 
(→‎See Also)
 
(One intermediate revision by the same user not shown)
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The temperature range on a given day is the difference between the daily high and the daily low temperatures. On the graph shown, which day has the greatest temperature range?  
 
The temperature range on a given day is the difference between the daily high and the daily low temperatures. On the graph shown, which day has the greatest temperature range?  
  
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<math>\text{(A)}\ Monday \qquad \text{(B)}\ Tuesday \qquad \text{(C)}\ Wednesday \qquad \text{(D)}\ Thursday \qquad \text{(E)}\ Friday</math>
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<math>\text{(A)}\ \text{Monday} \qquad \text{(B)}\ \text{Tuesday} \qquad \text{(C)}\ \text{Wednesday} \qquad \text{(D)}\ \text{Thursday} \qquad \text{(E)}\ \text{Friday}</math>
  
 
<asy>
 
<asy>
 
size(300);
 
size(300);
 
draw((0,-10)--(0,10),EndArrow);
 
draw((0,-10)--(0,10),EndArrow);
−
draw((0,0)--(16,0),EndArrow);
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// Comments this line out for reading purposes
 +
//draw((0,0)--(16,0),EndArrow);
 +
draw((0,0)--(16,0),arrow=Arrow(TeXHead));//smaller arrowhead
 
picture temp;
 
picture temp;
 
label(temp,"Temperature ($^\circ$C)");
 
label(temp,"Temperature ($^\circ$C)");
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label(Thurs,"Thurs.");
 
label(Thurs,"Thurs.");
 
add(rotate(90)*Thurs,(8,5.4));
 
add(rotate(90)*Thurs,(8,5.4));
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picture Fri;
+
 
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label(Fri,"Fri.");
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//picture Fri;
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add(rotate(90)*Fri,(10,9));
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//label(Fri,"Fri.");
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//add(rotate(90)*Fri,(10,9));
 +
MP(90,"\textup{ Fri.}",(10,8),N);//MarkPoint(Rotation,Label,Coordinates) textup(upright no-italics)
 
draw((-0.3,-8)--(0.3,-8));
 
draw((-0.3,-8)--(0.3,-8));
 
draw((-0.3,-6)--(0.3,-6));
 
draw((-0.3,-6)--(0.3,-6));
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draw((-0.3,2)--(0.3,2));
 
draw((-0.3,2)--(0.3,2));
 
draw((-0.3,4)--(0.3,4));
 
draw((-0.3,4)--(0.3,4));
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draw((-0.3,6)--(0.3,6));
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//draw((-0.3,6)--(0.3,6));
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draw((-0.3,8)--(0.3,8));
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//draw((-0.3,8)--(0.3,8));
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path Tick=((-.3,0)--(.3,0));draw(shift(0,6)*Tick);draw(shift(0,8)*Tick);
 
dot((2,6));
 
dot((2,6));
 
dot((4,3));
 
dot((4,3));
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draw((5.8,-1.8)--(6.2,-1.8)--(6.2,-2.2)--(5.8,-2.2)--cycle);
 
draw((5.8,-1.8)--(6.2,-1.8)--(6.2,-2.2)--(5.8,-2.2)--cycle);
 
draw((7.8,-4.8)--(8.2,-4.8)--(8.2,-5.2)--(7.8,-5.2)--cycle);
 
draw((7.8,-4.8)--(8.2,-4.8)--(8.2,-5.2)--(7.8,-5.2)--cycle);
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draw((9.8,0.2)--(10.2,0.2)--(10.2,-0.2)--(9.8,-0.2)--cycle);
+
//draw((9.8,0.2)--(10.2,0.2)--(10.2,-0.2)--(9.8,-0.2)--cycle);
 +
path Square=((-.2,-.2)--(-.2,.2)--(.2,.2)--(.2,-.2)--cycle);
 +
filldraw(shift(10,0)*Square,white);// this hides the x-axis behind white filling -- try green
 
label("-8",(-0.3,-8),W);
 
label("-8",(-0.3,-8),W);
 
label("-6",(-0.3,-6),W);
 
label("-6",(-0.3,-6),W);
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==See Also==
 
==See Also==
  
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{{Gauss (Grade 7) box|year=2005|num-b=10|num-a=12}}
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{{CEMC box|year=2005|competition=Gauss (Grade 7)|num-b=10|num-a=12}}

Latest revision as of 00:47, 23 October 2014

Problem

The temperature range on a given day is the difference between the daily high and the daily low temperatures. On the graph shown, which day has the greatest temperature range?

$\text{(A)}\ \text{Monday} \qquad \text{(B)}\ \text{Tuesday} \qquad \text{(C)}\ \text{Wednesday} \qquad \text{(D)}\ \text{Thursday} \qquad \text{(E)}\ \text{Friday}$

[asy] size(300); draw((0,-10)--(0,10),EndArrow); // Comments this line out for reading purposes //draw((0,0)--(16,0),EndArrow); draw((0,0)--(16,0),arrow=Arrow(TeXHead));//smaller arrowhead picture temp; label(temp,"Temperature ($^\circ$C)"); add(rotate(90)*temp,(-2,0)); picture mon; label(mon,"Mon."); add(rotate(90)*mon,(2,7.3)); picture tues; label(tues,"Tues."); add(rotate(90)*tues,(4,4.3)); picture Wed; label(Wed,"Wed."); add(rotate(90)*Wed,(6,5.3)); picture Thurs; label(Thurs,"Thurs."); add(rotate(90)*Thurs,(8,5.4)); //picture Fri; //label(Fri,"Fri."); //add(rotate(90)*Fri,(10,9)); MP(90,"\textup{ Fri.}",(10,8),N);//MarkPoint(Rotation,Label,Coordinates) textup(upright no-italics) draw((-0.3,-8)--(0.3,-8)); draw((-0.3,-6)--(0.3,-6)); draw((-0.3,-4)--(0.3,-4)); draw((-0.3,-2)--(0.3,-2)); draw((-0.3,2)--(0.3,2)); draw((-0.3,4)--(0.3,4)); //draw((-0.3,6)--(0.3,6)); //draw((-0.3,8)--(0.3,8)); path Tick=((-.3,0)--(.3,0));draw(shift(0,6)*Tick);draw(shift(0,8)*Tick); dot((2,6)); dot((4,3)); dot((6,4)); dot((8,4)); dot((10,8)); draw((1.8,-3.8)--(2.2,-3.8)--(2.2,-4.2)--(1.8,-4.2)--cycle); draw((3.8,-5.8)--(4.2,-5.8)--(4.2,-6.2)--(3.8,-6.2)--cycle); draw((5.8,-1.8)--(6.2,-1.8)--(6.2,-2.2)--(5.8,-2.2)--cycle); draw((7.8,-4.8)--(8.2,-4.8)--(8.2,-5.2)--(7.8,-5.2)--cycle); //draw((9.8,0.2)--(10.2,0.2)--(10.2,-0.2)--(9.8,-0.2)--cycle); path Square=((-.2,-.2)--(-.2,.2)--(.2,.2)--(.2,-.2)--cycle); filldraw(shift(10,0)*Square,white);// this hides the x-axis behind white filling -- try green label("-8",(-0.3,-8),W); label("-6",(-0.3,-6),W); label("-4",(-0.3,-4),W); label("-2",(-0.3,-2),W); label("0",(-0.3,0),W); label("2",(-0.3,2),W); label("4",(-0.3,4),W); label("6",(-0.3,6),W); label("8",(-0.3,8),W); dot((12,-6.5)); label("Daily High",(12,-6.5),E); draw((11.8,-7.7)--(11.8,-7.3)--(12.2,-7.3)--(12.2,-7.7)--cycle); label("Daily Low",(12,-7.5),E); [/asy]

Solution

On each day, the temperature range is the difference between the daily high and daily low temperatures. On Monday, the range is $6 - (-4) = 10$ degrees Celsius. On Tuesday, the range is $3 - (-6) = 9$ degrees Celsius. On Wednesday, the range is $4 - (-2) = 6$ degrees Celsius. On Thursday, the range is $4 - (-5) = 9$ degrees Celsius. On Friday, the range is $8 - 0 = 8$ degrees Celsius. The day with the greatest range is Monday. Therefore, the answer is $A$.

See Also

2005 CEMC Gauss (Grade 7) (Problems • Answer Key • Resources)
Preceded by
Problem 10 		Followed by
Problem 12
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
CEMC Gauss (Grade 7)
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