ankitongmat wrote:
Guys these are the questions from the new GMAT prep . Please help me solve.
Dear
ankitongmat,
I'm happy to help.
In the future, I will ask you to post only one question per post.
Q1. For a display, identical cube boxes are stacked in square layers. Each layer consists of cubic boxes arranged in rows that form a square and each layer has 1 fewer row and 1 fewer box in each remaining row than the layer directly below it. If the bottom layer has 81 boxes and the top layer has only 1 box, how many boxes are there in display ?
236
260
269
276
285The first row has 9 x 9 = 81 cubes; the second row has 8 x 8 = 64 cubes; the third row has 7 x 7 - 49 cubes, and so forth.
Total = 81 + 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1
let's make the arithmetic easy:
Total = (
64 + 36) + (
25 + 16 + 9) + (
49 + 1) + 81 + 4 =
100 +
50 +
50 + 81 + 4 = 285
Answer =
(E)Q2. If a rectangular region has perimeter P inches and area A square inches , is the region square ?
(1) P = 4/3 * A
(2) P = 4 * A^1/2Let's say the rectangular region x by y.
Area = x*y
Perimeter = 2x + 2y
The question is: does x = y?
(1)
P = 4/3 * A3P = 4A
3(2x + 2y) = 4xy
6x + 6y = 4xy
3x + 3y = 2xy
This is one equation with two unknowns. If we required x = y, we could solve for a unique solution. If we required, say x = 2y, we would solve for another unique solution. There's no reason to wade through all that algebra. It's enough to see that different requirement lead to different solutions, and there is nothing from this that requires that x = y. Therefore, this statement, alone and by itself, is
insufficient.
(2)
P = 4 * A^1/2Square both sides, to get rid of the radical
2x + 2y = 4[(xy)^(1/2)]
Divide everything by 2
x + y = 2[(xy)^(1/2)]
Now, square both sides
(x + y)^2 = 4xy
For the left term, squaring the quantity (x + y) see this blog:
http://magoosh.com/gmat/2013/three-alge ... -the-gmat/(x^2) + 2xy + (y^2) = 4xy
Subtract 4xy from both sides:
(x^2) - 2xy + (y^2) = 0
This is another important algebra equation from that same blog, and it simplifies to:
(x - y)^2 = 0
Take a square root
x - y = 0
x = y
So this statement absolutely requires that x = y, which means that the rectangular region is indeed a square. Therefore, this statement, alone and by itself, is
sufficient.
Answer =
(B)BTW, here's a blog with more "is it a square?" DS questions.
http://magoosh.com/gmat/2012/gmat-geome ... -a-square/Does all this make sense?
Mike
_________________
Mike McGarry
Magoosh Test Prep