1、If 5252+=+x x ,then x can equal which of the following? ( ) (A) 51(B) 54(C) 1(D) 25(E) 5 2、,962-=+x x If what is the value of 34-x ?( )(A)-5(B)-9(C) -15(D) -18(E) -213、,1455==tk and t If what is the value of k ?( ) (A)451(B)91(C) 51(D) 5(E) 9 4、The average of x and y is 5 and the average of y x ,,and z is 8.What is the value of z ?( )(A) 19(B) 14(C) 13(D) 11(E) 35、If ,8212-=x x what is the value of x ?( )(A) 2(B) 3(C) 4(D) 5(E) 66、In the xy -plane,the equation of line l is 52+=x y .If line m is the reflection of line l in the axis x -,what is the equation of line m ?( )(A) 52--=x y (B) 52+-=x y (C)52-=x y (D)521--=x y (E)521+-=x y 7、If ()s x a =++12,what is 1+x ,in terms of s and a ? ( ) (A) a s 2(B) 2a s -(C) 2a s +(D) a s -2(E) a s +28、If ,12325+==+y x and x y what is the value of y ?9、Let the operation *and ∆ be defined for all real numbers a and b as follows: b a b a b a b a 4*,3+=+=∆?,4*)5()5(4y of value the is what y y IF =∆1、If 32=y x ,what is the value of y x 23?( ) (A) 31 (B) 32 (C) 1 (D) 23 (E) 492、If1624=x ,then =x ( ) (A) 1 (B) 2 (C) 4 (D) 8 (E) 123、 How much greater than 2-r is 5+r ? ( )(A) 2 (B) 3 (C) 5 (D) 6 (E) 74、?75,4273n of is what is n of IF ( ) (A)70 (B) 45 (C) 30 (D) 185、If and y x 7322=+24=xy ,what is the value of ()2y x +? ( ) (A) 73 (B) 97 (C) 100 (D) 121 (E) 1446、If ,1,52+-x x and 83-x are all integers and 1+x is the median of these integers, which of the following could be a value for x ? ( )(A) 5 (B) 7 (C) 9 (D) 10 (E) 117、If 02<<y x ,which of the following is greatest ? ( )(A) x 2- (B) ()y x +-2 (C) x 2 (D) 0 (E) y -8、If 1013<+b ,which of the following CANNOT be the value of b ? ( )(A) -1 (B) 0 (C) 1 (D) 2 (E) 39、If 30 percent of 40 percent of a positive number is equal to 20 percent of w percent of the same number, what is the value of w ? ( )(A) 80 (B) 60 (C) 50 (D) 15 (E) 1010、If ()()2121--=+b a b a ,which of the following must be true? ( ) (A) 0=b (B) 1=+b a (C) 1=-b a (D) 122=+b a (E)122=-b a1、)()2(,23)(2=-=f then x nonzero all for x x x f IF(A)11/2 (B)7/2 (C) —1/2 (D) —5/2 (E) —72、It takes 4 complete turns of a crank to raise a window 2 inches. At this rate, how many turns does it take to raise the same window 213inches?( ) (A)3.5 (B) 7 (C)12 (D)14 (E)353、In the figure, 1==BD AD ,3=DC ,090=∠ADB . What is the value of BCD ∠?(A) 15 (B) 20 (C) 25 (D) 30A D C x(第3题图) (第4题图)4、In the right triangle above, if 3=x ,what is the value of y ?( )(A) 13 (B) 15 (C)4(D) 17 (E) 55、In the figure above,the circle is tangent to sides BC and AD of the 128--by rectangle ABCD .What is the area of the circle? ( )(A) π16 (B) π20 (C) π36 (D) π64 (E) π96nCl0x0y m(第5题图)(第6题图)6、In the figure above , 90>⊥x and n l .Which of the following must be true ?( )(A) 90<y (B) 90>y (C)90=y (D) m n ⊥ (E) m l //7、Let the operation be defined by b a b a b a -+=* for all numbers a and b ,where b a ≠.If x *22*1=, what is the value of x ?1、If x?of value the is What ,21723=+x ( ) (A)4 (B) 5 (C)9(D)12 (E) 152、In the xy-plane ,the line with equation 105-=x y crosses the x-axis at the point with coordinates ),(b a .What is the value of a ? ( )(A) 10- (B) 2- (C)0(D) 2 (E) 566 60300303、What is the perimerer of the figure above? ( )(A) 24 (B)25 (C) 28 (D)30 (E)364、If m is the greatest prime factor of 38 and n is the greatest prime factor of 100, what is the value of n m + ? ( )(A) 7 (B) 12 (C) 24 (D)29 (E) 44Q030P R5、In the figure above ,QR is the arc of a circle with center P , if the length of arc QR is π6, what is the area of sector PQR? ( )(A) π108 (B) π72 (C) π54 (D) π36 (E) π96、There are 75 more women than men enrolled in Linden College .If there are n men enrolled ,then ,in terms of n ,what percent of those enrolled are men ? ( )(A) %75+n n (B)%752+n n (C)%)752(100+n n (D)%75100+n n (E)%752100+n n 7、If ?,0,,k to equal s i following the of which rv and kr v v xr ≠==( )(A) 1 (B) x /1 (C) 1-x (D) x (E) 1+x8、If ? x of value the is what ,1,2122=+=-y x and y x9、Let the function h(x) be defined by,9)2(,414)(2m m h if x x h =+=? m of value possible one is what1、If 1593+=+x x ,what is the value of x ? ( )(A) 1 (B) 2 (C) 3 (D) 4 (E) 82、There is the same number of boys and girls on a school bus when it departs from school. Atthe first stop. 4 boys get of the bus and nobody gets on. After the first stop , there are twice as many girls as boys on the bus. How many girls are on the bus? ( )(A) 4 (B) 6 (C)8 (D) 12 (E)163、In the figure, there line segments meet at a point to form three angles. What is the value of ?x ( )2x4x 3x(A) 20 (B) 36 (C)40 (D) 45 (E) 604、Positive integers ,,y x and z satisfy the equations 3121=-xand 16=z y .If y z >,whatis the value of ?z x +( )(A) 5 (B) 7 (C) 11 (D) 13 (E) 155、If p is an integer and 3is the remainder when 72+p is divided by 5, then p could be ( )(A) 2 (B) 3 (C) 4 (D) 5 (E) 66、Stacy noted that she is both the 12th tallest and the 12th shortest student in her class. If everyone in the class is of a different height, how many students are in the class? ( )(A) 22 (B) 23 (C) 24 (D) 25 (E) 347、The price of a telephone was first increased by 10 percent and then the new price was decreased by 25 percent. The final price was what percent of the initial price ? ( )(A) 78% (B) 80% (C) 82.5% (D) 85% (E) 87.5%8、When the number w is multiplied by 4, the result is the same as when 4 is added to w . What is the value of w 3?( ) (A) 43 (B) 1 (C) 34 (D) 3 (E) 4 9、The lengths of the sides of a right triangle are consecutive even integers, and the length of the shortest side is x . Which of the following equations could be used to find x ?( )(A) 21+=++x y x (B) ()()22221+=++x x x (C) ()()22242+=++x x x (D) 42+=++x x x (E) ()()422++=x x x10、If x is an integer greater than 1and if xx y 1+=, which of the following must be true ?(1) x y ≠ (2) y is an integer (3) 2x xy >( )(A)(1) only (B)(3) only (C)(1) and (2) only (D)(1) and (3) only (E)(1)(2) and (3)1、If ?,65,52t of terms in equal r does what t s s r ==( ) (A)t 2512 (B)t 56 (C) t 3 (D) t 15 (E) t 30 2、For which of the following function is ?)3()3(f f >-( )(A) 24)(x x f =(B)4)(=x f (C)xx f 4)(= (D) 34)(x x f -= (E) 4)(4+=x x f 3、If Y is the midpoint of XZ ,which of the following must be true? ( )XZ YZ 21)1(=XY XZ 221)2(=XZ XY =2)3( (A)(1) only (B)(2) only (C) (3) only (D)(1) and (2) (E)(1) and (3)4、For what value of x is the FALSE statement about ?)3(322x x <( )(A)-3 (B)0 (C)31 (D) 1 (E) For no value of x 5、For how many ordered pairs of positive integers ),(y x is ?632<+y x ( )(A)1 (B)2 (C)3 (D) 5 (E) 76、If x and y are positive consecutive odd integers, where y x <,which of the following is equal to ?22x y -( )(A)2x (B)4x (C)2x+2 (D)2x+4 (E)4x+47、If the average of x and y is k ,which of the following is the average of x,y and z? ( )(A)32z k + (B)22z k + (C) 3z k + (D) 2z k + (E) 3)(2z k + 8、When 15 is divided by the positive integer k ,the remainder is 3.For how many different values of k is this true? ( )(A)1 (B)2 (C)3 (D) 4 (E) 59、When the number t is multiplied by 4, the result is the same as when 4 is added to t . What is the value of 3t?( )(A) 43 (B) 1 (C) 34 (D) 3 (E) 4 10、In the xy-plane, line l passes through the origin and is perpendicular to the line k y x =+4 ,where k is a constant.If the two lines intersect at the point )1,(+t t ,what is the value oft?1、If 158=+k ,then k =( )(A) 7 (B) 49 (C) 529 (D)7 (E) 23 2、If m and k are positive numbers and m k m 1001012=-,what is 1-m in terms of k ? ( ) (A)10k (B) 90k (C) 10k (D) k 101 (E)k901 3、If a,b,and c are different positive integers and =++=⋅⋅c b a c b a then 222,64222（ ）(A)14 (B)17 (C) 21 (D) 28 (E)344、If 20 percent of x equals 80 percent of y ,which of the following expresses y in terms of x ?( )(A)x of y %16=(B)x of y %25= (C)x of y %60= (D)x of y %100=(E) x of y %400=5、The numerator of a certain fraction is 5 less than the denominator. If the fraction is equal to43,what is the denominator of this fraction ?( )(A) 8 (B) 12 (C) 16 (D) 20 (E) 246、In the xy- plane,the center of a circle has coordinates (3,-7).If one endpoint of a diameter of the circle is (-2,-7).What are the coordinates of the other endpoint of this diameter?( )(A)(-7,-7) (B)(-2,-2) (C) (3,-2) (D)(8,-2) (E)(8,-7)7、If 10<<x , which of the following statemengts must be true ? ( )(1) 32x x > (2) 2x x > (3) 3x x > (A)(1) only (B)(3) only (C)(1) and (2) only (D)(1) and (3) only (E)(1)(2) and (3)8、Let the function f be defined by ().1+=x x f If (),202=p f what is the value of ()p f 31、If x+3=a,then 2x+9=( )(A)a+3 (B)a+6 (C)2a (D)2a+3 (E)2a+62、If 21=x ,what is the value of ?111-+x x ( ) (A)-4 (B)0 (C)1 (D)2 (E)33、How old was a person exactly 1 year ago if exactly x years ago the person was y years old ? ( )(A)y-1 (B)y-x-1 (C)x-y-1 (D)y+x+1 (E)y+x-14、A,B and C are points on a line in that order ,if AB=30 and BC is 20 more than AB ,what does AC equal ? ( )(A)50 (B)60 (C)70 (D)80 (E) 905、If 10<<n , which of the following statemengts must be true ? ( ) (A)2n n n <<(B)n n n <<2 (C)2n n n << (D)n n n <<2 (E)n n n <<26、In a poll, 35 people were in favor of building a new library, 14 people were against it, and 1 person had no opinion. What fraction of those polled were in favor of building a new library?（ ） (A) 107 (B) 32 (C) 73 (D)31 (E) 1037、If85310=-=-k k ,What is the value of k ?8、If b a 2+is equal to 125 percent of b 4,what is the value of?b a9、What is the value of x in the figure above?65° lm︒x 20° 10、In the -xy coordinate plane,the distance between point ()18,10B and point ()3,x A is 17.What is one possible value of x ?1、If1624=x ,then =x ( ) (A) 1 (B) 2 (C) 4 (D) 8 (E) 122、,1455==tk and t If what is the value of k ?( ) (A)451 (B)91 (C) 51 (D) 5 (E) 9 3、If ,8212-=x x what is the value of x ?( )(A) 2 (B) 3 (C) 4 (D) 5 (E) 64、If c b a ,,,and f are four nonzero numbers then all of the following proportions are equivalent EXCEPT( ) (A)c b f a =(B)a b c f =(C)bf a c = (D)f b c a = (E) f b bc af = 5、 If 2,3,8===-z and z y y x ,what is the value of x ?( )(A)-14 (B) -2 (C) 2 (D) 3 (E)146、Todd is older than Marta but younger than Susan. If i , m and s represent the ages in years of Todd .Marta and Susan respectively, which of the following is true ?( )s i m A <<.i m s B <<.m i s C <<.s m i D <<.ms i E <<. 7、If the areas of two regions are equal and the sum of the areas of the regions is 5.What is the areas of one region ?( )(A) 0 (B) 25 (C) 45(D) 5 (E) 10 8、Let S be the set of all integers that can be written as 12+n . Where n is a nonzero integer. Which of the following integers is in S ?( )(A) 16 (B) 28 (C) 35 (D) 39 (E) 509、Let the operation be defined by b a b a b a ++=∆2for all numbersa andb ,If x x ∆=∆12, what is the value of x ?1、If 18)4(3=-n ,what is the value of ?n ( ) 314)(A 332)(B 6)(C 10)(D 22)(E2、?75,4273n of is what is n of IF ( ) (A)70 (B) 45 (C) 30 (D) 183、If a x x 24=and 0≠x ,what is the value of ?a ( )(A) 8 (B) 4 (C) 221)(D 41)(E 4、In the xy-coordinate plane line l is perpendicular to the y-axis and passes through the point (5,-3). Which of the following is an equation of line l ? ( )0)(=x A 5)(=x B 3)(-=y C 53)(+=+x y D 53)(+=-x y E5、If and y x 7322=+24=xy ,what is the value of ()2y x -? ( ) (A) 25 (B) 97 (C) 100 (D) 121 (E) 1446、If 40))((4=-+y x y x and 20=-y x . What is the value of y x + ?7、A recipe for chili for 20 people requires 4 pounds of beans. At this rate how many pounds of beans are required to make chili for 150 people ?8、When the positive even integer n is increased by 50 percent of itself ,the result is between 16 and 20 .What is one possible value of n ?9、The perimeter of a rectangular plot of land is 250 meters .If the length of one side of the plot is 40 meters , what is the area of the plot in square meters ?1、If 30 percent of m is 40.What is 15 percent of m ? ( )(A) 15 (B) 20 (C) 25 (D) 30 (E) 352、and x If 80≤≤ 31≤≤-y , which of the following gives the set of all possible values of xy ( )(A) 4=xy (B)240≤≤xy (C) 111≤≤-xy (D) 241≤≤-xy (E) 248≤≤-xy3、According to a certain recipe ，25 pounds of flour are needed to make 300 rolls.At this rate how many pounds of flour are needed to make 12 rolls? ( )(A) 1 (B) 2 (C) 3 (D) 4 (E) 64、If 10=xy , what is the value of 22y yx ⋅⋅?( ) (A) 5 (B) 8 (C) 10 (D) 12 (E) 205、If 30=+y x and 8>x , then which of the following must be true ? ( ) (A)0>y (B)22<y (C)22=y (D)22>y (E)30<x6、If k is a positive integer divisible by 3 ,and if 60<k , what is the greatest possible value of k ?( )(A) 55 (B) 56 (C) 57 (D) 58 (E) 597、If the average (arithmetic mean) of 6,6,12,16, and x is equal to x . What is the value of x ?( )(A) 6 (B) 8 (C) 9 (D) 10 (E) 118、How many seconds are there in m minutes and s seconds ? ( )(A) s m +60 (B) s m 60+ (C) )(60s m + (D) 60s m + 9、If 0)2)(22(=--x x ,what are all the possible values of x ? ( )(A) 0 only (B) 1 only (C) 2 only (D) 1 and 2 only (E) 0,1 and 210、If 93y x =, what is x in terms of y ?( ) (A)y (B) 2y (C) 3y (D) 6y (E) 12y 11、 If 8)3(2=-x , what does 33+-x x equal ?12、When twice a number is decreased by 3 , the result is 253. What is the number ?1、If 21523=+a ,what is the value of a ?( ) (A) 4 (B) 8 (C) 9 (D)12 (E) 152、If 022=--x x ,what are all the possible values of x ? ( )(A) 0 only (B) -1 only (C) 2 only (D) -1 and 2 only (E) 0,-1 and 23、How many integers in the set of all integers from 1 to 100 inclusive are not the square of an integer ? ( )(A) 19 (B) 50 (C) 81 (D) 89 (E) 904、If n is a negative number. Which of the following must be positive ? () (A) 2n(B) n 2 (C) 2+n (D) 2-n (E) n -25、The ratio 1.2 to 1 is equal to which of the following ratios ? ( )(A) 1 to 2 (B) 12 to 1 (C) 5 to 6 (D) 6 to 5 (E) 6 to 506、If 1)4(3=-m ,what is the value of ?m ( )313)(A 326)(B 6)(C 10)(D 22)(E7、If 1624=x ,then =x ( )(A) 1 (B) 2 (C) 4 (D) 8 (E) 128、If 21=x ,what is the value of ?1221-+x x9、If a xx 23=and 0≠x ,what is the value of ?12+a10、If 40))((=-+y x y x and 20=-y x . What is the value of y x 32+ ?1、If x+1=m,then 2x+3=( )(A)m+3 (B)m+6 (C)2m (D)2m+1 (E)2m+32、If 18)42(3=-n ,what is the value of ?n ( )5)(A 4)(B 6)(C 10)(D 22)(E3、,11332==+tk and t If what is the value of k ?( ) (A)451 (B)91 (C) 51 (D) 5 (E) 9 4、? x of value the is what 3,3,52f ，===-z and z y x y I ( )(A)-14 (B) -2 (C) 2 (D) 3 (E)145、A,B and C are points on a line in that order ,if AB=15 and BC is 20 more than AB ,what does AC equal ? ( )(A)50 (B)60 (C)70 (D)80 (E) 906、If and y x 922=+2=xy ,what is the value of ()2y x -? ( ) (A) 4 (B) 5 (C) 6 (D) 7 (E) 87、According to a certain recipe ，25 pounds of flour are needed to make 300 rolls.At this rate how many pounds of flour are needed to make 36 rolls? ( )(A) 1 (B) 2 (C) 3 (D) 4 (E) 68、If the average of 3,4,6,7, and x is equal to x . What is the value of x ?( )(A) 4 (B) 5 (C)6 (D)7 (E)89、If k is a positive integer divisible by 5 ,and if 60<k , what is the greatest possible value of k ?( )(A) 50 (B) 51 (C) 55 (D) 56 (E) 5810、If 8)3(2=-x , what does 362++x x equal ? ( ) (A) 1 (B) 2 (C) 3 (D) 4 (E) 511、If 42=+y x and 223=-y x . What is the value of y x + ?12、Let the operation be defined by y x y x y x ++=∆2for all numbersx and y ,If a a ∆=∆32, what is the value of 2a+1?(A) 6 (B)7 (C) 8 (D)9 (E)102、If )1(656565+=x , then =x ( )(A)10 (B)11 (C) 100 (D)101 (E)1.0013、If p n 3=, for what value of p is p n = ?( )(A) 0 (B)1/3 (C) 1 (D)3 (E)n can never equal p4、If 123102)(,m m m m m y x ==⋅, what is the value of y x + ?( )(A) 8 (B)9 (C) 10 (D)11 (E)125、If a and b are positive integers and 722=-b a , what is the value of a ?( )(A) 3 (B)4 (C) 5 (D) 6 (E) 76、Which of the following numbers is between 1/5 and 1/4 ?( )(A) 0.14 (B) 0.15 (C) 0.19 (D) 0.21 (E) 0.267、If n represents an odd integer, which of the following expressions represents an even integer ?( )(A) n+2 (B) 2n-1 (C) 3n-2 (D) 3n+2 (E) 5n+18、The following are coordinates of points in the xy-plane,which of these points is nearest the origin ?( )(A) (0,-1) (B) (0,1/2) (C) (1/2,-1/2) (D) (1/2,1/2) (E) (-1,-1) 9、If b a b a 4,161==, what is the value of b a 32+ ?10、Let x be defined as x x x -=2! for all value of x .If !)2(!-=a a ,what is the value of 2a+3 ?(A)10 (B)11 (C) 12 (D)13 (E)142、If )12(11121-=x , then =x ( )(A)5 (B)6 (C) 7 (D)8 (E)93、If 12-=p n , for what value of p is p n = ?( )(A) 0 (B)1/2 (C) 1 (D)3 (E)n can never equal p4、If 123102)(,a a a a a y x ==⋅, what is the value of y x -2 ?( )(A) 14 (B)13 (C) 10 (D)11 (E)125、If and y x 922=+2=xy ,what is the value of ()2y x +? ( ) (A) 11 (B)12 (C) 13 (D) 14 (E) 156、If the average of 3,4,6,7, and x is equal to x . What is the value of x+2?( )(A) 4 (B) 5 (C)6 (D)7 (E)87、If n represents an odd integer, which of the following expressions represents an even integer ?( )(A) n+4 (B) 2n-3 (C) 3n-4 (D) 3n (E) 3n+18、The following are coordinates of points in the xy-plane, which of these points is the farthest origin ?( )(A) (0,-1) (B) (1,-1) (C) (2,0) (D) (3/2,1/2) (E) (-1,1)9、If x y and y x 2,164==, what is the value of y x 32+ ?10、Let x be defined as 1*2+-=x x x for all value of x . If *)1(*+=m m ,what is the value of 2m+1 ?。
