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

 It is currently 25 Mar 2019, 21:19

### 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 certain cake recipe states that the cake should be baked in a pan 8

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53831
A certain cake recipe states that the cake should be baked in a pan 8  [#permalink]

### Show Tags

07 Dec 2017, 05:36
2
1
00:00

Difficulty:

35% (medium)

Question Stats:

59% (01:35) correct 41% (01:36) wrong based on 56 sessions

### HideShow timer Statistics

A certain cake recipe states that the cake should be baked in a pan 8 inches in diameter. If Jules wants to use the recipe to make a cake of the same depth but 12 inches in diameter, by what factor should he multiply the recipe ingredients?

(A) 2 1/2
(B) 2 1/4
(C) 1 1/2
(D) 1 4/9
(E) 1 1/3

_________________
Senior SC Moderator
Joined: 22 May 2016
Posts: 2581
A certain cake recipe states that the cake should be baked in a pan 8  [#permalink]

### Show Tags

Updated on: 07 Dec 2017, 09:41
1
Bunuel wrote:
A certain cake recipe states that the cake should be baked in a pan 8 inches in diameter. If Jules wants to use the recipe to make a cake of the same depth but 12 inches in diameter, by what factor should he multiply the recipe ingredients?

(A) 2 1/2
(B) 2 1/4
(C) 1 1/2
(D) 1 4/9
(E) 1 1/3

We need the volumes of the two cake pans. Either: just calculate difference in area because only two of the three lengths change; or assign a value for height (depth of the pan) and run the numbers.

You can calculate for square or a round pan. I chose square.

Area only

A square cake pan with an 8-inch diagonal will have sides that = $$\frac{8}{\sqrt{2}}$$ inches

Area = $$\frac{8}{\sqrt{2}} * \frac{8}{\sqrt{2}} =(\frac{64}{2})=32$$ square inches

Sides of cake pan with 12-inch diagonal have length:$$\frac{12}{\sqrt{2}}$$ inches

Area of cake pan with 12-inch diagonal:
$$\frac{12}{\sqrt{2}}* \frac{12}{\sqrt{2}}=(\frac{144}{2})=72$$ square inches

The increase factor of both cake pan volume and recipe:$$\frac{72}{32}=\frac{9}{4}=$$

$$2\frac{1}{4}$$

Volume

Pick a depth (height) - it does not change, so it does not matter what you pick.

First pan is 8 inches in diameter. Let height = 2 inches

The sides of the pan, in length = $$\frac{8}{\sqrt{2}}$$ inches

Volume of original pan, L*H*W, is $$\frac{8}{\sqrt{2}} *\frac{8}{\sqrt{2}} * 2= (\frac{64*2}{2})=64$$ cubic inches

When the pan's diameter is 12 inches, its sides =$$\frac{12}{\sqrt{2}}$$ inches
Height = 2 inches

Volume of 12-inch diameter pan is L*H*W:

$$\frac{12}{\sqrt{2}} * \frac{12}{\sqrt{2}} * 2 = (\frac{12*2}{2})=144$$ cubic inches

By what factor has volume increased (= factor by which recipe must be increased)?

$$\frac{144}{64}=\frac{18}{8}=\frac{9}{2}=$$

$$2\frac{1}{4}$$

_________________
Do I dare
Disturb the universe?
(—T. S. Eliot)
Absolutely.

For moderator-guided sentence correction questions including many official questions,
go to SC Butler (two Sentence Correction questions per day from Nov 7 to Mar 1).
SC Butler is here: https://gmatclub.com/forum/project-sc-butler-get-2-sc-questions-everyday-281043.html

Originally posted by generis on 07 Dec 2017, 09:11.
Last edited by generis on 07 Dec 2017, 09:41, edited 2 times in total.
Math Expert
Joined: 02 Aug 2009
Posts: 7446
A certain cake recipe states that the cake should be baked in a pan 8  [#permalink]

### Show Tags

07 Dec 2017, 09:25
3
Bunuel wrote:
A certain cake recipe states that the cake should be baked in a pan 8 inches in diameter. If Jules wants to use the recipe to make a cake of the same depth but 12 inches in diameter, by what factor should he multiply the recipe ingredients?

(A) 2 1/2
(B) 2 1/4
(C) 1 1/2
(D) 1 4/9
(E) 1 1/3

Hi genxer123
even the round pan will give you an answer..
round pan means it is cylinderical and by increasing diameter we are increasing the VOLUME..

volume of cylinder is $$pi*r^2h$$....
here radius are $$\frac{12}{2}=6$$ and $$\frac{8}{2}=4$$
ans = $$\frac{V_{12}}{V_8} = \frac{pi*6^2*h}{pi*4^2*h}=\frac{36}{16}=\frac{9}{4}=2\frac{1}{4}$$

B
_________________
Senior SC Moderator
Joined: 22 May 2016
Posts: 2581
A certain cake recipe states that the cake should be baked in a pan 8  [#permalink]

### Show Tags

07 Dec 2017, 09:37
chetan2u wrote:
Bunuel wrote:
A certain cake recipe states that the cake should be baked in a pan 8 inches in diameter. If Jules wants to use the recipe to make a cake of the same depth but 12 inches in diameter, by what factor should he multiply the recipe ingredients?

(A) 2 1/2
(B) 2 1/4
(C) 1 1/2
(D) 1 4/9
(E) 1 1/3

Hi genxer123
even the round pan will give you an answer..
round pan means it is cylinderical and by increasing diameter we are increasing the VOLUME..

volume of cylinder is $$pi*r^2h$$....
here radius are $$\frac{12}{2}=6$$ and $$\frac{8}{2}=4$$
ans = $$\frac{V_{12}}{V_8} = \frac{pi*6^2*h}{pi*4^2*h}=\frac{36}{16}=\frac{9}{4}=2\frac{1}{4}$$

B

I stand corrected. My arithmetic was off on the round pan. Nice catch - thanks!
_________________
Do I dare
Disturb the universe?
(—T. S. Eliot)
Absolutely.

For moderator-guided sentence correction questions including many official questions,
go to SC Butler (two Sentence Correction questions per day from Nov 7 to Mar 1).
SC Butler is here: https://gmatclub.com/forum/project-sc-butler-get-2-sc-questions-everyday-281043.html
Intern
Joined: 14 Sep 2017
Posts: 3
Re: A certain cake recipe states that the cake should be baked in a pan 8  [#permalink]

### Show Tags

07 Dec 2017, 10:13
84pi/40 pi

my ans is 2.1 closest to B but why isnt it just the same??
Senior SC Moderator
Joined: 22 May 2016
Posts: 2581
A certain cake recipe states that the cake should be baked in a pan 8  [#permalink]

### Show Tags

07 Dec 2017, 12:09
Bunuel wrote:
A certain cake recipe states that the cake should be baked in a pan 8 inches in diameter. If Jules wants to use the recipe to make a cake of the same depth but 12 inches in diameter, by what factor should he multiply the recipe ingredients?

(A) 2 1/2
(B) 2 1/4
(C) 1 1/2
(D) 1 4/9
(E) 1 1/3

nabiharaza wrote:
84pi/40 pi

my ans is 2.1 closest to B but why isnt it just the same??

nabiharaza , I think your arithmetic might be incorrect, but I can't tell because I don't have your steps. How did you get $$84\pi$$ and $$40\pi$$?

Let's say you want to take the changed volume approach (you can just check changed area, see my post above).

Choose any height for the round pan. It does not change. Let h = 3

A circular pan with an 8-inch diameter has a radius of 4 inches. Its volume, that of a cylinder:

$$\pi r^2h = \pi(16)(3) = 48\pi$$

A circular pan with a 12-inch diameter has a radius of 6 inches. h = 3. Its volume is

$$\pi r^2h = \pi(36)(3) = 108\pi$$

Increase factor?
$$\frac{108\pi}{48\pi}=\frac{9}{4}$$ (divide LHS by 12)

= $$2 \frac{1}{4}$$

_________________
Do I dare
Disturb the universe?
(—T. S. Eliot)
Absolutely.

For moderator-guided sentence correction questions including many official questions,
go to SC Butler (two Sentence Correction questions per day from Nov 7 to Mar 1).
SC Butler is here: https://gmatclub.com/forum/project-sc-butler-get-2-sc-questions-everyday-281043.html
Non-Human User
Joined: 09 Sep 2013
Posts: 10216
Re: A certain cake recipe states that the cake should be baked in a pan 8  [#permalink]

### Show Tags

01 Mar 2019, 04:09
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: A certain cake recipe states that the cake should be baked in a pan 8   [#permalink] 01 Mar 2019, 04:09
Display posts from previous: Sort by