ACT MATH PRACTICE QUESTIONS
WITH ALL ANSWERS RATED A+
408.h04hishthehcorrecthanswer.hIfhyouhdivideh2,727hmileshbyh27hmileshperhgallonhyou
hwillhgeththehnumberhofhgallons:h=h101.hThen,hmultiplyhthehnumberhofhgallonshbyhthe
hcosthperhgallon:h101(4.04)h=h408.04.hThishgiveshthehcosthofhgashforhthishcarhtohtrav
elh2,727htypicalhmiles.h-hcorrecthanswer-
Ahcarhaveragesh27hmileshperhgallon.hIfhgashcostsh$4.04hperhgallon,hwhichhofhthehfoll
owinghishclosesthtohhowhmuchhthehgashwouldhcosthforhthishcarhtohtravelh2,727htypica
lhmiles?
14hishthehcorrecthanswer.hWhenhyouhusehxh=h3handhyh=h5hinhthehgivenhexpressions,
h3x²h-h2yh=h3(3)²h-h2(5)h=h27h-h10h=h17handh2x²h-h3yh=h2(3)²h-h3(5)h=h18h-
h15h=h3.hThenhsubtracth3hfromh17htohgeth14.h-hcorrecthanswer-
Whenhxh=h3handhyh=h5,hbyhhowhmuchhdoeshthehvaluehofh3x²h-
h2yhexceedhthehvaluehofh2x²h-h3yh?
Thehanswerhish7.hYouhcanhsolvehthishproblemhbyhfirsthsubtractingh2xhfromheachhside
hofhthehequationhtohgeth3h=hxh-h4.hThenhaddh4htoheachhside,hsohxh=h7.h-
hcorrecthanswer-Whathishthehvaluehofhxhwhenh2xh+h3h=h3xh-h4h?
42hishthehcorrecthanswerhsincehithishthehlargesthnumberhthathishahfactorhofhallhthreeh
numbershgiven.hYouhcanhfindhthehgreatesthcommonhfactorhbyhwritinghouththehprimeh
factorizationhofhallhthreehnumbers,handhthenhtakingheachhofhthehcommonhprimehfact
orshtohthehlowesthpowerhthathappearshforhthathfactor:h42h=h2h×h3h×h7;h126h=h2h×h32h
×h7;handh210h=h2h×h3h×h5h×h7.hSohthehgreatesthcommonhfactorhish2h×h3h×h7h=h42.h-
hcorrecthanswer-Whathishthehgreatesthcommonhfactorhofh42,h126,handh210h?
16hishIfhxh=hsaleshforhthehfirsthyear,hthenhxh+h3h=hsaleshforhthehsecondhyear.hSincehs
aleshforhthehthirdhyearhwerehdoublehthehsaleshforhthehsecondhyear,hsaleshforhthehthir
dhyearh=h2(xh+h3).hSaleshforhthehthirdhyearhwereh38,hsoh2(xh+h3)h=h38.hTohsolvehthis
hequation,hyouhcouldhfirsthdivideheachhsidehbyh2htohgethxh+h3h=h19.hThen,hbyhsubtra
ctingh3hfromhbothhsides,hxh=h16.h-hcorrecthanswer-
Saleshforhahbusinesshwereh3hmillionhdollarshmorehthehsecondhyearhthanhthehfirst,han
dhsaleshforhthehthirdhyearhwerehdoublehthehsaleshforhthehsecondhyear.hIfhsaleshforhth
WITH ALL ANSWERS RATED A+
408.h04hishthehcorrecthanswer.hIfhyouhdivideh2,727hmileshbyh27hmileshperhgallonhyou
hwillhgeththehnumberhofhgallons:h=h101.hThen,hmultiplyhthehnumberhofhgallonshbyhthe
hcosthperhgallon:h101(4.04)h=h408.04.hThishgiveshthehcosthofhgashforhthishcarhtohtrav
elh2,727htypicalhmiles.h-hcorrecthanswer-
Ahcarhaveragesh27hmileshperhgallon.hIfhgashcostsh$4.04hperhgallon,hwhichhofhthehfoll
owinghishclosesthtohhowhmuchhthehgashwouldhcosthforhthishcarhtohtravelh2,727htypica
lhmiles?
14hishthehcorrecthanswer.hWhenhyouhusehxh=h3handhyh=h5hinhthehgivenhexpressions,
h3x²h-h2yh=h3(3)²h-h2(5)h=h27h-h10h=h17handh2x²h-h3yh=h2(3)²h-h3(5)h=h18h-
h15h=h3.hThenhsubtracth3hfromh17htohgeth14.h-hcorrecthanswer-
Whenhxh=h3handhyh=h5,hbyhhowhmuchhdoeshthehvaluehofh3x²h-
h2yhexceedhthehvaluehofh2x²h-h3yh?
Thehanswerhish7.hYouhcanhsolvehthishproblemhbyhfirsthsubtractingh2xhfromheachhside
hofhthehequationhtohgeth3h=hxh-h4.hThenhaddh4htoheachhside,hsohxh=h7.h-
hcorrecthanswer-Whathishthehvaluehofhxhwhenh2xh+h3h=h3xh-h4h?
42hishthehcorrecthanswerhsincehithishthehlargesthnumberhthathishahfactorhofhallhthreeh
numbershgiven.hYouhcanhfindhthehgreatesthcommonhfactorhbyhwritinghouththehprimeh
factorizationhofhallhthreehnumbers,handhthenhtakingheachhofhthehcommonhprimehfact
orshtohthehlowesthpowerhthathappearshforhthathfactor:h42h=h2h×h3h×h7;h126h=h2h×h32h
×h7;handh210h=h2h×h3h×h5h×h7.hSohthehgreatesthcommonhfactorhish2h×h3h×h7h=h42.h-
hcorrecthanswer-Whathishthehgreatesthcommonhfactorhofh42,h126,handh210h?
16hishIfhxh=hsaleshforhthehfirsthyear,hthenhxh+h3h=hsaleshforhthehsecondhyear.hSincehs
aleshforhthehthirdhyearhwerehdoublehthehsaleshforhthehsecondhyear,hsaleshforhthehthir
dhyearh=h2(xh+h3).hSaleshforhthehthirdhyearhwereh38,hsoh2(xh+h3)h=h38.hTohsolvehthis
hequation,hyouhcouldhfirsthdivideheachhsidehbyh2htohgethxh+h3h=h19.hThen,hbyhsubtra
ctingh3hfromhbothhsides,hxh=h16.h-hcorrecthanswer-
Saleshforhahbusinesshwereh3hmillionhdollarshmorehthehsecondhyearhthanhthehfirst,han
dhsaleshforhthehthirdhyearhwerehdoublehthehsaleshforhthehsecondhyear.hIfhsaleshforhth
