Difference between revisions of "1988 AHSME Problems/Problem 11"
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==Solution== | ==Solution== | ||
| − | + | We simply have to divide the present population by the original, and whichever one is the largest have the greatest percent change. City <math>\text{A}</math> is | |
| − | + | <math>\frac{50}{40}=1.25</math>. City <math>\text{B}</math> is <math>\frac{70}{50}=1.4</math>. City <math>\text{C}</math> is <math>\frac{100}{70} \approx 1.42</math>. City <math>\text{D}</math> is <math>\frac{130}{100}=1.3</math>. City <math>\text{E}</math> is <math>\frac{160}{120} \approx 1.33</math>. City <math>\text{C}</math> has the greatest value, so the answer is <math>\boxed{\text{C}}</math>. | |
== See also == | == See also == | ||
Latest revision as of 17:25, 21 November 2017
Problem
![[asy] defaultpen(linewidth(0.7)+fontsize(10)); pair A=(5,0), B=(7,0), C=(10,0), D=(13,0), E=(16,0); pair F=(4,3), G=(5,3), H=(7,3), I=(10,3), J=(12,3); dot(A); dot(B); dot(C); dot(D); dot(E); dot(F); dot(G); dot(H); dot(I); dot(J); draw((0,0)--(18,0)^^(0,3)--(18,3)); draw((0,0)--(0,.5)^^(5,0)--(5,.5)^^(10,0)--(10,.5)^^(15,0)--(15,.5)); draw((0,3)--(0,2.5)^^(5,3)--(5,2.5)^^(10,3)--(10,2.5)^^(15,3)--(15,2.5)); draw((1,0)--(1,.2)^^(2,0)--(2,.2)^^(3,0)--(3,.2)^^(4,0)--(4,.2)^^(6,0)--(6,.2)^^(7,0)--(7,.2)^^(8,0)--(8,.2)^^(9,0)--(9,.2)^^(10,0)--(10,.2)^^(11,0)--(11,.2)^^(12,0)--(12,.2)^^(13,0)--(13,.2)^^(14,0)--(14,.2)^^(16,0)--(16,.2)^^(17,0)--(17,.2)^^(18,0)--(18,.2)); draw((1,3)--(1,2.8)^^(2,3)--(2,2.8)^^(3,3)--(3,2.8)^^(4,3)--(4,2.8)^^(6,3)--(6,2.8)^^(7,3)--(7,2.8)^^(8,3)--(8,2.8)^^(9,3)--(9,2.8)^^(10,3)--(10,2.8)^^(11,3)--(11,2.8)^^(12,3)--(12,2.8)^^(13,3)--(13,2.8)^^(14,3)--(14,2.8)^^(16,3)--(16,2.8)^^(17,3)--(17,2.8)^^(18,3)--(18,2.8)); label("A", A, S); label("B", B, S); label("C", C, S); label("D", D, S); label("E", E, S); label("A", F, N); label("B", G, N); label("C", H, N); label("D", I, N); label("E", J, N); label("1970", (0,3), W); label("1980", (0,0), W); label("0", (0,1.5)); label("50", (5,1.5)); label("100", (10,1.5)); label("150", (15,1.5)); label("Population in thousands", (9,-3)); [/asy]](http://latex.artofproblemsolving.com/3/e/7/3e74f88b7e27fbc4ebf856f9b6a0866d8e64c6be.png)
On each horizontal line in the figure below, the five large dots indicate the populations of cities 
and 
in the year indicated.
Which city had the greatest percentage increase in population from 
to 
?
Solution
We simply have to divide the present population by the original, and whichever one is the largest have the greatest percent change. City 
is
. City 
is 
. City 
is 
. City 
is 
. City 
is 
. City has the greatest value, so the answer is 
.
See also
| 1988 AHSME (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 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
