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The two lines y = x and x = -4 intersect on the coordinate plane. If z

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The two lines y = x and x = -4 intersect on the coordinate plane. If z  [#permalink]

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The two lines y = x and x = -4 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?

A. 16
B. 8√2
C. 8
D. 2√2
E. (√2)/3

Kudos for a correct solution.

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Re: The two lines y = x and x = -4 intersect on the coordinate plane. If z  [#permalink]

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New post 17 Jul 2015, 01:51
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Bunuel wrote:
The two lines y = x and x = -4 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?

A. 16
B. 8√2
C. 8
D. 2√2
E. (√2)/3

Kudos for a correct solution.



The area enclosed by the 2 lines and the x-axis is a right triangle with coordinates (0,0), (-4,0) and (-4,-4). Thus z = 0.5*4*4 = 8 ---> 6z = 48 ----> Surface area of a cube with side l = 6l^2

Thus 6l^2 = 48 ---> l =\(2\sqrt{2}\) , D is the correct answer.
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Re: The two lines y = x and x = -4 intersect on the coordinate plane. If z  [#permalink]

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New post 17 Jul 2015, 09:36
Bunuel wrote:
The two lines y = x and x = -4 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?

A. 16
B. 8√2
C. 8
D. 2√2
E. (√2)/3

Kudos for a correct solution.



Line y = x, is a line passing through Ist and IInd Quadrant via origin. And Line x = -4 is a vertical line.
The area intersecting these two lines is a triangle with base = 4 and height = 4. Hence the area, z = 1/2 * 4 * 4 = 8

Given, Surface area of Cube = 6 * side^2 = 6z ==> side^2 = 8
side = 2\sqrt{2}

Option D
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Re: The two lines y = x and x = -4 intersect on the coordinate plane. If z  [#permalink]

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New post 18 Jul 2015, 05:12
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Bunuel wrote:
The two lines y = x and x = -4 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?

A. 16
B. 8√2
C. 8
D. 2√2
E. (√2)/3

Kudos for a correct solution.


Recommendation : Draw the graph in all questions of Co-ordinate Geometry

Answer: Option D
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Re: The two lines y = x and x = -4 intersect on the coordinate plane. If z  [#permalink]

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New post 19 Jul 2015, 12:25
Bunuel wrote:
The two lines y = x and x = -4 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?

A. 16
B. 8√2
C. 8
D. 2√2
E. (√2)/3

Kudos for a correct solution.


800score Official Solution:

The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-4, -4) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(4 × 4) = 8; so z = 8.

The next step requires us to find the length of a side of a cube that has a face area equal to 8. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 8. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 8. Clearly s = √8 = 2√2 , or answer choice (D).
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Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: The two lines y = x and x = -4 intersect on the coordinate plane. If z  [#permalink]

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