Resolução de Equações Matemáticas

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56. (C) Let x = the lesser number and y = the greater number. The question informa-
tion yields two equations: (1) + =x y3 35; and (2) − =y x5 75, − = −x y5 75. Adding 
(1) + =x y3 35 and (2) − = −x y5 75 yields = −x8 40, = −x 5. Then + =x y3 35 implies 
− + =y3( 5) 35, − + =y15 35, =y 50. Quantity A is 10% of y, which is 10%(50) = 5. 
Quantity B is the absolute value of x, which is − =5 5. The two quantities are equal. Select (C).
57. (D) Solve the equation.
 − = −x x2 5 22 
 − + =x x2 5 2 02 
 − − =x x(2 1)( 2) 0 
 =x 1
2
, 2 
 If =x 1
2
, then Quantity B is greater. If x = 2, then Quantity A is greater. Because you 
found different results (one when Quantity B was greater and one when Quantity A was 
greater), the relationship cannot be determined from the information given. Select (D).
58. (C) The discriminant of a quadratic equation is −b ac42 . Quantity A is 
− = − = −b ac4 1 4(1)(1) 32 2 . Quantity B is − = − − = −b ac4 ( 1) 4(1)(1) 32 2 . The two quantities 
are equal. Select (C).
59. (B) Solve the equation.
 + =x
x
2
2
12 
 + =x x( 2) 24 
 + − =x x2 24 02 
 + − =x x( 6)( 4) 0 
 = −x 6, 4 
 If = −x 6, then Quantity B is greater. If =x 4, then (again) Quantity B is greater. Thus, 
Quantity B is greater.
60. (C) In a coordinate plane, the distance between points x y( , )1 1 and x y( , )2 2 is d = 
− + −x x y y( ) ( )2 1
2
2 1
2 . Quantity A is − + −(5 2) (7 3)2 2 = +3 42 2 = 25 = 5. Quantity B 
is ( )− − + −1 ( 2) (1 5)2 2 = + −3 ( 4)2 2 = 25 = 5. The two quantities are equal. Select (C).
61. (B) In a coordinate plane, the midpoint between points x y( , )1 1 and x y( , )2 2 is 
+ +x x y y
2
,
2
1 2 1 2 . Thus, = +a7 6
2
, + =a 6 14, =a 8 (Quantity A); and = +b7 5
2
, + =b 5 14, 
=b 9 (Quantity B). Quantity B is greater.
06_McCune_Answer.indd 162 2/21/22 4:44 PM