GRE-Math-Questions-to-Know-by-Test-Day-2nd-Edition_pag243

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426. (C), (D)
x x
x x
x x
x x
3 ( 3) 6
3 9 6 0
3 2 0
( 1)( 2) 0
2
2
− − =
− + − =
− + =
− − = 
 x = 1 (C) or x = 2 (D)
427. (A), (D) Check the answer choices. (A) 6
3
(2 3)
3
2 3
3
2 3 2
8
4
8
4
8 8
4
8 4 4= ⋅ = ⋅ = ⋅ ≠ , False; 
(B) 5
5
5
6
2
4= , True; (C) 12
4
(3 4)
4
3 4
4
3
4
4
4
4
4 4
4
4= ⋅ = ⋅ = , True; (D) 4
2
(2 )
2
2
2
2 2
5
3
2 5
3
10
3
7 2= = = ≠ , 
False; (E) 9
3
81
81
1
2
4
= = , True; (F) 4
2
(2 )
2
2
2
2
3
3
2 3
3
6
3
3= = = , True.
428. (A), (F) Check the answer choices. (A) ( 6) 2 1 1
2
1 1
16
1 1
16
0 4
4
− + = + = + =− ( 6) 2 1 1
2
1 1
16
1 1
16
0 4
4
− + = + = + =− , 
True; (B) 6(3 ) 6. 1
3
6
27
2
9
2
9
3
3
= = = ≠ −− , False; (C) 10 1
10
1
100
1002
2
= = ≠ −−10 1
10
1
100
1002
2
= = ≠ −− , False; 
(D) 4 4 4 16 1
16
5 3 2⋅ = = ≠− , False; (E) (2 ) 2 23 2 6= ≠− − , False; (F) (2 ) 2 162 2 4= =− − , True.
429. (A), (B), (C) On the GRE, measures (e.g., lengths) are greater than 0. Thus, 
x2 30 0− > , which implies x 15.> Select (A), (B), and (C) because these values are not 
greater than 15.
430. (B), (D) The area is length times width = x x x x( 3)( 9) 6 272+ − = − − . Select (D). 
By inspection, eliminate (A) and (E). Select (B) because x( 3) 362− − = x x6 9 362 − + − = 
x x6 272 − − . Eliminate (C) because x x x x x( 3) 18 6 9 18 6 92 2 2− − = − + − = − − .
431. (C), (E) Eliminate (A) because when x = 4, x 4 4 4 16 4 12 02 2− = − = − = ≠ . 
Eliminate (B) because when x = 4, x 4 16 82 2= = ≠ . Select (C) because when x = 4, 
x 16 4 16 16 16 02 2− = − = − = and when x = 4− , x 16 ( 4) 16 16 16 02 2− = − − = − = . Elimi-
nate (D) because when x = 4− , x x8 162 − + = ( 4) 8( 4) 162− − − + = 16 32 16 0+ + ≠ .
 Select (E) because when x = 4, x2 2(4) 2 16 322 2= = ⋅ = and when x = 4− , 2x2 = 2(−4)2 = 
x2 2( 4) 2 16 322 2= − = ⋅ = .
432. (C), (D) Recall that for a quadratic equation ax2 + bx + c = 0, the sum of its roots = 
−b/a and the product of its roots = c/a. Rewrite the given equation in standard quadratic 
form as x2 + 6x + 4 = 0, where a = 1, b = 6, and c = 4, yielding −b/a = –6 and c/a = 4. 
Because –6 and 4 are real numbers, the roots must be two real numbers or two irrational 
conjugate pairs, such as +x y and −x y . Thus, the two answer choices are either (A) 
and (B), (C) and (D), or (E) and (F). Eliminate (A) and (B) because −10 − 4 = −14, not 
−6. Select (C) and (D) because − + − − = −3 5 3 5 6 and ) )( (− + − − = − =3 5 3 5 9 5 4. 
You have found two roots, so move on to the next question.
433. (B), (C) The graph of the equation Ax Ay Cx Dy F 02 2+ + + + = ; A 0≠ is a circle. By 
inspection, select (B) and (C).
07_McCune_Answer.indd 234 2/21/22 4:39 PM