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

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)