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

 It is currently 09 Dec 2019, 16:34

### 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 cylindrical tank of radius R and height H must be redesign

Author Message
TAGS:

### Hide Tags

Manager
Joined: 13 Jul 2011
Posts: 78
Concentration: Operations, Strategy
GMAT 1: 680 Q46 V37
WE: Engineering (Telecommunications)
A cylindrical tank of radius R and height H must be redesign  [#permalink]

### Show Tags

24 Oct 2011, 22:17
6
29
00:00

Difficulty:

95% (hard)

Question Stats:

29% (02:51) correct 71% (02:41) wrong based on 606 sessions

### HideShow timer Statistics

A cylindrical tank of radius R and height H must be redesigned to hold approximately twice as much liquid. Which of the following changes would be farthest from the new design requirements?

A. A 100% increase in R and a 50% decrease in H
B. A 30% decrease in R and a 300% increase in H
C. A 10% decrease in R and a 150% increase in H
D. A 40% increase in R and no change in H
E. A 50% increase in R and a 20% decrease in H
Math Expert
Joined: 02 Sep 2009
Posts: 59622
Re: MGMAT Geometry #13, Redesigned Tank  [#permalink]

### Show Tags

18 Apr 2012, 05:08
5
5
GMATD11 wrote:
vaibhav123 wrote:
easy but time consuming...ny 1 with any easy method??

Can any body explain it geometrically.
Thanks

What do you mean geometrically?

A cylindrical tank of radius R and height H must be redesigned to hold approximately twice as much liquid. Which of the following changes would be farthest from the new design requirements?
A. A 100% increase in R and a 50% decrease in H
B. A 30% decrease in R and a 300% increase in H
C. A 10% decrease in R and a 150% increase in H
D. A 40% increase in R and no change in H
E. A 50% increase in R and a 20% decrease in H

The wording makes the question harder than it actually is.

The question basically asks: if we have a cylindrical tank of radius R and height H, then which of the following changes will give a cylindrical tank with the volume with greatest difference from the volume of $$2\pi{r^2}h$$ (twice the original).

Answer E ($$\pi{(1.5r)^2}*(0.8h)=1.8\pi{r^2}h$$) gives the greatest difference from $$2\pi{r^2}h$$.
_________________
##### General Discussion
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9859
Location: Pune, India
Re: A cylindrical tank of radius R and height H must be redesign  [#permalink]

### Show Tags

18 Jul 2013, 23:24
7
2
arjunbt wrote:
A cylindrical tank of radius R and height H must be redesigned to hold approximately twice as much liquid. Which of the following changes would be farthest from the new design requirements?

A. A 100% increase in R and a 50% decrease in H
B. A 30% decrease in R and a 300% increase in H
C. A 10% decrease in R and a 150% increase in H
D. A 40% increase in R and no change in H
E. A 50% increase in R and a 20% decrease in H

The solution I am going to give has already been provided but I am still writing it down to highlight the approximations you could use to save time.

Volume must be doubled.
We know volume of a cylinder $$= \pi * r^2 * h$$
To double the volume, either you double the height 'h' OR you multiply r by $$\sqrt{2}$$ i.e. by 1.41 i.e. increase radius by a little over 40%.
OR you use a combination.

A. A 100% increase in R and a 50% decrease in H
Volume $$= \pi * 4r^2 * \frac{h}{2} = 2* \pi * r^2 * h$$ (matches the design requirement)

B. A 30% decrease in R and a 300% increase in H
Volume $$= \pi * 0.49 r^2 * 4h = \pi * \frac{r^2}{2} * 4h = 2* \pi * r^2 * h$$ (matches the design requirement)
Note that .49 is approximately 0.5 i.e. 1/2

C. A 10% decrease in R and a 150% increase in H
Volume $$= \pi * .81 r^2 * \frac{5}{2}h = 2* \pi * \frac{4}{5}r^2 * \frac{5}{2} h = 2* \pi * r^2 * h$$ (matches the design requirement)
Notice that .81 is approximately .80 i.e. 80% i.e. 4/5

D. A 40% increase in R and no change in H
We discussed it above. A 40% increase in R matches our design requirement.

E. A 50% increase in R and a 20% decrease in H
Volume $$= \pi * 2.25 r^2 * 0.8 h$$
Compare with (C). 2.5*0.8 gives you 2 so 2.25*0.8 will give you less than 2. Hence doesn't match the requirement.
_________________
Karishma
Veritas Prep GMAT Instructor

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9859
Location: Pune, India
Re: A cylindrical tank of radius R and height H must be redesign  [#permalink]

### Show Tags

01 Dec 2013, 21:22
4
1
Karishma, I took R=10 and H=10 and proceeded but I am unable to arrive at a constructive answer. Can you please explain how to proceed using the above values and using substitution method. Thanks in advance .

R = 10
H = 10

We know volume of a cylinder$$= \pi * r^2 * h = 1000\pi$$

A. A 100% increase in R and a 50% decrease in H (R = 20, H = 5)
Volume =$$\pi * 400 * 5 = 2000\pi$$(matches the design requirement)

B. A 30% decrease in R and a 300% increase in H (R = 7, H = 40)
Volume =$$\pi * 49 * 40 = 1960\pi$$ (approximately matches the design requirement)
Note that 49 is approximately 50

C. A 10% decrease in R and a 150% increase in H (R = 9, H = 25)
Volume$$= \pi * 81 * 25 = 2025\pi$$ (approximately matches the design requirement)
Notice that 81 is approximately 80

D. A 40% increase in R and no change in H (R = 14)
Volume$$= \pi * 196 * 10 = 1960 \pi$$ (approximately matches the design requirement)

E. A 50% increase in R and a 20% decrease in H (R = 15, H = 8)
Volume $$= \pi * 225 * 8 = 1800\pi$$ (Does not match)
_________________
Karishma
Veritas Prep GMAT Instructor

Manager
Joined: 17 Sep 2011
Posts: 164
Concentration: Strategy, Operations
Schools: ISB '15
GMAT 1: 720 Q48 V40
GPA: 3.18
WE: Supply Chain Management (Manufacturing)
Re: MGMAT Geometry #13, Redesigned Tank  [#permalink]

### Show Tags

24 Oct 2011, 23:31
2
1
ans is E
volume of cylinder=pi*r^2*H
=>reqd multiplication factor is 2
=>any change in R will cause volume to be multiplied by "square of (1+/- change in fractions)"
=>any change in H will cause vol to b multiplied by (1+/-change)
1. a 100% increase in R and a 50% decrease in H=>4*.5=2=>as required
2. a 30% decrease in R and a 300% increase in H=>.49*4=1.96
3. a 10% decrease in R and a 150% increase in H=>.81*2.5=2.025
4. a 40% increase in R and no change in H=>1.96
5. a 50% increase in R and a 20% decrease in H=>1.8=>max difference from required multiplication factor of 2

very easy qs...but my method took like 3 minutes....anyone with a faster solution?
Intern
Joined: 07 Nov 2011
Posts: 14
Re: MGMAT Geometry #13, Redesigned Tank  [#permalink]

### Show Tags

04 Dec 2011, 09:04
easy but time consuming...ny 1 with any easy method??
Manager
Joined: 10 Nov 2010
Posts: 166
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
Re: MGMAT Geometry #13, Redesigned Tank  [#permalink]

### Show Tags

17 Apr 2012, 23:03
vaibhav123 wrote:
easy but time consuming...ny 1 with any easy method??

Can any body explain it geometrically.
Thanks
Intern
Joined: 09 Jun 2012
Posts: 27
Re: A cylindrical tank of radius R and height H must be redesign  [#permalink]

### Show Tags

18 Jul 2013, 04:52
1
arjunbt wrote:
A cylindrical tank of radius R and height H must be redesigned to hold approximately twice as much liquid. Which of the following changes would be farthest from the new design requirements?
A. A 100% increase in R and a 50% decrease in H
B. A 30% decrease in R and a 300% increase in H
C. A 10% decrease in R and a 150% increase in H
D. A 40% increase in R and no change in H
E. A 50% increase in R and a 20% decrease in H

"Farthest from the new design requirement" denotes highest difference between "twice the volume" (- the actual requirement) and volume given by each of the answer choices (- the new design requirement). Actual required volume is 2*pi*r^2*h.
We need to calculate 2 metrics for each answer choice:
1) Volume of each of the new design requirements and
2) Difference from actual required volume (2*pi*r^2*h)
A)
Volume of new design = pi*(2r)^2 * (.50h) = 2*pi*r^2*h
Difference = 2*pi*r^2*h ~ 2*pi*r^2*h = 0
B)
Volume of new design = pi*(.7r)^2 * (4h) = 1.96 *pi*r^2*h
Difference = 1.96 *pi*r^2*h ~ 2*pi*r^2*h = 0.04 *pi*r^2*h
C)
Volume of new design = pi*(1.4r)^2 * (h) = 2.025*pi*r^2*h
Difference = 2.025*pi*r^2*h ~ 2*pi*r^2*h = 0.025 *pi*r^2*h
D)
Volume of new design = pi*(.9r)^2 * (2.5h) = 1.96*pi*r^2*h
Difference = 1.96 *pi*r^2*h ~ 2*pi*r^2*h = 0.04 *pi*r^2*h
E)
Volume of new design = pi*(1.5r)^2 * (.8h) = 1.8*pi*r^2*h
Difference = 1.8*pi*r^2*h ~ 2*pi*r^2*h = 0.2 *pi*r^2*h

Therefore, the largest difference (farthest design) is 0.2. so the correct choice is E.
Intern
Joined: 09 Jun 2012
Posts: 27
Re: A cylindrical tank of radius R and height H must be redesign  [#permalink]

### Show Tags

18 Jul 2013, 22:09
Also, we can follow the below technique for finding the percentage increase in volume/area.
Say if side of a square increased by 10%. The new area is (1.1*side)^2 = 1.21 (side)^2 = 1.21(Old Volume). Therefore volume increased by 21%.

Similarly, for this question, we can just multiply the numeric part before radius^2 and height after applying appropriate % increase/decrease.
The old volume is pi * r^2 *h. And the required volume is 2*pi * r^2 *h.
Working out option E -> If radius increased by 50% and height decreased by 20%, then new volume = (1.5)^2 * (.80) (Old Volume)=1.8(Old Volume). Whereas required volume is 2*(Old Volume). Hence new design is .2 farther from required design.
Manager
Joined: 07 May 2013
Posts: 87
Re: A cylindrical tank of radius R and height H must be redesign  [#permalink]

### Show Tags

01 Dec 2013, 05:35
Karishma, I took R=10 and H=10 and proceeded but I am unable to arrive at a constructive answer. Can you please explain how to proceed using the above values and using substitution method. Thanks in advance .
Intern
Joined: 07 Oct 2015
Posts: 15
Schools: Copenhagen (A)
Re: A cylindrical tank of radius R and height H must be redesign  [#permalink]

### Show Tags

04 Dec 2015, 10:00
Can't you just use the formula, and multiply it pretty quickly? Took me less than 2 minutes if you just use the percentage increases.

A) 100% increase to R = 2R and 50% decrease to H = .5 H so formula is pi*r^2*h
so 2^2*.5=2

Repeat with each solution and you get E at 1.8.

This worked for me, but is this correct?
Director
Joined: 12 Nov 2016
Posts: 694
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: A cylindrical tank of radius R and height H must be redesign  [#permalink]

### Show Tags

02 Jun 2017, 17:55
Bunuel wrote:
GMATD11 wrote:
vaibhav123 wrote:
easy but time consuming...ny 1 with any easy method??

Can any body explain it geometrically.
Thanks

What do you mean geometrically?

A cylindrical tank of radius R and height H must be redesigned to hold approximately twice as much liquid. Which of the following changes would be farthest from the new design requirements?
A. A 100% increase in R and a 50% decrease in H
B. A 30% decrease in R and a 300% increase in H
C. A 10% decrease in R and a 150% increase in H
D. A 40% increase in R and no change in H
E. A 50% increase in R and a 20% decrease in H

The wording makes the question harder than it actually is.

The question basically asks: if we have a cylindrical tank of radius R and height H, then which of the following changes will give a cylindrical tank with the volume with greatest difference from the volume of $$2\pi{r^2}h$$ (twice the original).

Answer E ($$\pi{(1.5r)^2}*(0.8h)=1.8\pi{r^2}h$$) gives the greatest difference from $$2\pi{r^2}h$$.

Let the radius be 1 and the height be 2- now, the algebraic translation of twice the volume would be

2( (pi)(r)^2(h))
2( (pi)(1)^2(2))

We could simply construct an equation for each of the answer choices- for example

pi * 2(1)^2 (h-1/2h)

Eventually we would be able to arrive at the answer. Bunuel is there a quicker method- perhaps I am not reading into some of the other answers deeply enough- but it seems too time-consuming and inefficient to construct an equation for each answer choice and calculate which has an answer choice has a volume furthest away from the volume of twice the original cylinder's volume- is there a more efficient way of solving this problem?
Manager
Joined: 07 Jun 2018
Posts: 104
A cylindrical tank of radius R and height H must be redesign  [#permalink]

### Show Tags

21 Jul 2018, 10:07
KarishmaB wrote:
Karishma, I took R=10 and H=10 and proceeded but I am unable to arrive at a constructive answer. Can you please explain how to proceed using the above values and using substitution method. Thanks in advance .

R = 10
H = 10

We know volume of a cylinder$$= \pi * r^2 * h = 1000\pi$$

A. A 100% increase in R and a 50% decrease in H (R = 20, H = 5)
Volume =$$\pi * 400 * 5 = 2000\pi$$(matches the design requirement)

B. A 30% decrease in R and a 300% increase in H (R = 7, H = 40)
Volume =$$\pi * 49 * 40 = 1960\pi$$ (approximately matches the design requirement)
Note that 49 is approximately 50

C. A 10% decrease in R and a 150% increase in H (R = 9, H = 25)
Volume$$= \pi * 81 * 25 = 2025\pi$$ (approximately matches the design requirement)
Notice that 81 is approximately 80

D. A 40% increase in R and no change in H (R = 14)
Volume$$= \pi * 196 * 10 = 1960 \pi$$ (approximately matches the design requirement)

E. A 50% increase in R and a 20% decrease in H (R = 15, H = 8)
Volume $$= \pi * 225 * 8 = 1800\pi$$ (Does not match)

Life saver, right here! I almost postponed this one for later. Thanks a lot!
Non-Human User
Joined: 09 Sep 2013
Posts: 13732
Re: A cylindrical tank of radius R and height H must be redesign  [#permalink]

### Show Tags

30 Jul 2019, 05:37
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 cylindrical tank of radius R and height H must be redesign   [#permalink] 30 Jul 2019, 05:37
Display posts from previous: Sort by