GRE-Math-Questions-to-Know-by-Test-Day-2nd-Edition_pag172

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Answers ‹ 163
62. (D) The slope between points x y( , )1 1 and x y( , )2 2 is −
−
y y
x x
2 1
2 1
. The slope of 
the line through x y( , ) and −( 5,5) is −
− −
y
x
5
5
. If =x y( , ) (0,1), then Quantity A is 
−
− −
= −
− −
=
−
= −y
x
5
5
5 1
5 0
4
5
0.8. In this case, Quantity B is greater. If =x y( , ) (1,5), then 
Quantity A is −
− −
= −
− −
=
−
=y
x
5
5
5 5
5 1
0
6
0. In this case, the two quantities are equal. Because 
you found different results (one where Quantity B was greater and one where the quantities 
were equal), the relationship cannot be determined from the information given. Select (D).
63. (A) Two lines that are perpendicular have slopes that are negative reciprocals of each 
other. The slope between points x y( , )1 1 and x y( , )2 2 is −
−
y y
x x
2 1
2 1
. The slope between (2,3) and 
k( ,4) is −
−
=
−k k
4 3
2
1
2
. Rewrite + =x y3 10 in slope-intercept form as = − +y x3 10. Hence, 
the slope of the line with equation + =x y3 10 is −3, which has negative reciprocal 1
3
. Thus, 
−
=
k
1
2
1
3
, − =k 2 3, =k 5. Quantity A is greater.
64. (C) Substitute = −y x x2 into = −y x 1 and solve.
 − = −x x x 12 
 − + =x x2 1 02 
 − =x( 1) 02 
 =x 1 (Quantity A)
 The two quantities are equal. Select (C).
65. (B) In triangle KLM, LM is opposite the largest angle, so it is longer than KM . Quantity B 
is greater.
66. (A) Let AX = x = the width of the river. Right triangles AXY and ACB are similar 
because they have common angle A. Set up a proportion based on corresponding sides and 
solve.
+
= =x
x 30
60
80
3
4
 
 = +x x4 3( 30) 
 = +x x4 3 90 
 =x 90 (Quantity A)
 Quantity A is greater. Tip: Simplifying 60
80
 to lowest terms 3
4
 makes the calculations 
easier to do in this problem.
06_McCune_Answer.indd 163 2/21/22 4:44 PM