GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 11 Dec 2019, 15:46

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

A number of equal sized baseballs are stored in a box with a width of

Author Message
TAGS:

Hide Tags

Senior Manager
Joined: 25 Sep 2018
Posts: 471
Location: United States (CA)
Concentration: Finance, Strategy
GMAT 1: 640 Q47 V30
GPA: 3.97
WE: Investment Banking (Investment Banking)
A number of equal sized baseballs are stored in a box with a width of  [#permalink]

Show Tags

21 Oct 2018, 14:06
1
4
00:00

Difficulty:

55% (hard)

Question Stats:

60% (02:06) correct 40% (02:19) wrong based on 95 sessions

HideShow timer Statistics

A number of equal sized baseballs are stored in a box with a width of 18 inches and a length of 24 inches. If each ball is the same size, and they are lined up tangent to each other in the box, what is the maximum number of balls that can fit in the bottom layer of the box?

(1) The surface area of each ball is $$64\pi$$ inches^2
(2) If the diameter of each ball were 4 inches less, the maximum number of balls that could fit into the box would be 4 times the number of balls that currently fit into the box.

_________________
Why do we fall?...So we can learn to pick ourselves up again
Manager
Joined: 13 Oct 2013
Posts: 132
Concentration: Strategy, Entrepreneurship
Re: A number of equal sized baseballs are stored in a box with a width of  [#permalink]

Show Tags

21 Oct 2018, 14:41
stmt 1

surface area of each ball =4 pi r^2=64pi
=> r=4 inches

Length of the box is 24 inches , so maximum 3 balls (length wise) and 2 balls (width wise)
total 3* 2 = 6 balls in bottom layer can fit

sufficient

stmt 2:
if diameter is 4 inches less, that means now diameter is 8-4 = 4 inches , we can calculate the number of balls on bottom layer that is 6 balls (length wise) and 4 balls widh wise
so total 6 *4 =24 balls in bottom layer can fit

sufficient

Ans D

As height is not given, question only asks about bottom layer .
Math Expert
Joined: 02 Aug 2009
Posts: 8302
Re: A number of equal sized baseballs are stored in a box with a width of  [#permalink]

Show Tags

21 Oct 2018, 19:19
2
Abhi077 wrote:
A number of equal sized baseballs are stored in a box with a width of 18 inches and a length of 24 inches. If each ball is the same size, and they are lined up tangent to each other in the box, what is the maximum number of balls that can fit in the bottom layer of the box?
1) The surface area of each ball is $$64\pi inches^2$$
2) If the diameter of each ball were 4 inches less, the maximum number of balls that could fit into the box would be 4 times the number of balls that currently fit into the box.

We are looking for the radius of each ball..

1) The surface area of each ball is $$64\pi inches^2$$
So $$4*π*r^2=64*π......r=4$$
So dia is 4*2=8 and number of the ball that will fit in is 24/8=3 along one side and 18/8=2.zyz so 2 along other side
Sufficient

2) If the diameter of each ball were 4 inches less, the maximum number of balls that could fit into the box would be 4 times the number of balls that currently fit into the box.
Let the dia be x, new dia is x-4...
$$\frac{18*24}{(x-4)^2}$$=$$4*\frac{18*24}{x^2}$$
So (x-4)^2*4=x^2.....$$4x^2-32x+64=x^2.......3x^2-32x+64=0.......$$
$$3x^2-24x-8x+64=0.....(3x(x-8)-8(x-8)=0.....(3x-8)(x-8)=0$$

Now X can be 8/3 or 8 but 8/3-4 will be negative so not possible...
Again sufficient

D

sunita123, you are reading info of statement I in solving II by taking initial DIA as 8
_________________
Manager
Joined: 13 Oct 2013
Posts: 132
Concentration: Strategy, Entrepreneurship
Re: A number of equal sized baseballs are stored in a box with a width of  [#permalink]

Show Tags

22 Oct 2018, 22:09
Thank you Chetan2u for pointing out the mistake ..

Can you please explain how did you arrive at this -

18∗24(x−4)218∗24(x−4)2= 4∗18∗24x2

Thank you !

chetan2u wrote:
Abhi077 wrote:
A number of equal sized baseballs are stored in a box with a width of 18 inches and a length of 24 inches. If each ball is the same size, and they are lined up tangent to each other in the box, what is the maximum number of balls that can fit in the bottom layer of the box?
1) The surface area of each ball is $$64\pi inches^2$$
2) If the diameter of each ball were 4 inches less, the maximum number of balls that could fit into the box would be 4 times the number of balls that currently fit into the box.

We are looking for the radius of each ball..

1) The surface area of each ball is $$64\pi inches^2$$
So $$4*π*r^2=64*π......r=4$$
So dia is 4*2=8 and number of the ball that will fit in is 24/8=3 along one side and 18/8=2.zyz so 2 along other side
Sufficient

2) If the diameter of each ball were 4 inches less, the maximum number of balls that could fit into the box would be 4 times the number of balls that currently fit into the box.
Let the dia be x, new dia is x-4...
$$\frac{18*24}{(x-4)^2}$$=$$4*\frac{18*24}{x^2}$$
So (x-4)^2*4=x^2.....$$4x^2-32x+64=x^2.......3x^2-32x+64=0.......$$
$$3x^2-24x-8x+64=0.....(3x(x-8)-8(x-8)=0.....(3x-8)(x-8)=0$$

Now X can be 8/3 or 8 but 8/3-4 will be negative so not possible...
Again sufficient

D

sunita123, you are reading info of statement I in solving II by taking initial DIA as 8
VP
Joined: 14 Feb 2017
Posts: 1321
Location: Australia
Concentration: Technology, Strategy
GMAT 1: 560 Q41 V26
GMAT 2: 550 Q43 V23
GMAT 3: 650 Q47 V33
GMAT 4: 650 Q44 V36
GMAT 5: 650 Q48 V31
GMAT 6: 600 Q38 V35
GPA: 3
WE: Management Consulting (Consulting)
Re: A number of equal sized baseballs are stored in a box with a width of  [#permalink]

Show Tags

16 May 2019, 02:43
The source of this is Target Test Prep. Please update, mods. Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 59674
Re: A number of equal sized baseballs are stored in a box with a width of  [#permalink]

Show Tags

16 May 2019, 03:03
dcummins wrote:
The source of this is Target Test Prep. Please update, mods. Bunuel

Done. Thank you. Could you please use Report a Problem button for such kind of issues? Thank you.
_________________
Intern
Joined: 11 Apr 2019
Posts: 2
Re: A number of equal sized baseballs are stored in a box with a width of  [#permalink]

Show Tags

24 May 2019, 13:55
If the height of the box is 0.5 inches.The ball would not fit.
Therefore i marked "E"
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9869
Location: Pune, India
Re: A number of equal sized baseballs are stored in a box with a width of  [#permalink]

Show Tags

25 May 2019, 01:44
ayusharora96 wrote:
If the height of the box is 0.5 inches.The ball would not fit.
Therefore i marked "E"

It is apparent in the question that the height of the box is irrelevant. The words "bottom layer" clarify that one could stack balls on top of each other in the box.
_________________
Karishma
Veritas Prep GMAT Instructor

Re: A number of equal sized baseballs are stored in a box with a width of   [#permalink] 25 May 2019, 01:44
Display posts from previous: Sort by