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

 It is currently 16 Oct 2019, 08:34

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

In a particular machine, there are 2 gears that interlock; One gear is

Author Message
TAGS:

Hide Tags

Manager
Joined: 07 Sep 2010
Posts: 249
In a particular machine, there are 2 gears that interlock; One gear is  [#permalink]

Show Tags

16 Aug 2012, 08:32
3
23
00:00

Difficulty:

45% (medium)

Question Stats:

61% (01:42) correct 39% (01:40) wrong based on 884 sessions

HideShow timer Statistics

In a particular machine, there are 2 gears that interlock; One gear is larger in circumference than the other. The manufacturer of the gears guarantees that each gear will last for atleast 6,000,000,000 revolutions. Assuming that there is no slippage between the 2 gears and that when one gear rotates the other gear also rotates, the larger gear is guaranteed to last how many days longer than the smaller gear.

(1) The diameter of the larger gear is twice the diameter of smaller gear.
(2) The smaller gear revolves 600 times per minute.
Director
Joined: 22 Mar 2011
Posts: 590
WE: Science (Education)
Re: In a particular machine, there are 2 gears that interlock; One gear is  [#permalink]

Show Tags

16 Aug 2012, 10:32
7
5
imhimanshu wrote:
In a particular machine, there are 2 gears that interlock; One gear is larger in circumference than the other. The manufacturer of the gears guarantees that each gear will last for atleast 6,000,000,000 revolutions. Assuming that there is no slippage between the 2 gears and that when one gear rotates the other gear also rotates, the larger gear is guaranteed to last how many days longer than the smaller gear.

a) the diameter of the larger gear is twice the diameter of smaller gear.
b) The smaller gear revolves 600 times per minute.

Please put your reasoning across and then I will ask my doubt. I want to see if I am assuming much in this question.

Thanks

(1) We can deduce that the smaller gear makes two rotations while the larger gear makes just one rotation. No information about the speed of revolution, so we cannot establish any connection with time.
Not sufficient.

(2) No information about the larger gear.
Not sufficient.

(1) and (2): The larger gear makes 300 rotations per minute and the smaller gear 600 per minute. So, we can calculate how long it takes in minutes each one to do 6,000,000,000 rotations, take the difference and convert to days...really messy. But being a DS question, you shouldn't spend time on working out the final answer.

Choose Answer C, and move on.
_________________
PhD in Applied Mathematics
Love GMAT Quant questions and running.
General Discussion
Manager
Joined: 25 Jun 2012
Posts: 55
Re: In a particular machine, there are 2 gears that interlock; One gear is  [#permalink]

Show Tags

16 Aug 2012, 20:33
Eva above is pretty much spot-on. Note that the larger gear having a diameter twice as long as the smaller gear's means that the larger will turn once for every 4 times the smaller does, but the logical process remains sound. Do also note that as Eva mentioned, you should not bother working out the "complete" answer to the question; once you figure out that you need both the ratio of circumferences (or diameters/radii) and the turn speed of one gear, you can answer the question.
Director
Joined: 22 Mar 2011
Posts: 590
WE: Science (Education)
Re: In a particular machine, there are 2 gears that interlock; One gear is  [#permalink]

Show Tags

17 Aug 2012, 04:33
DonQuixote wrote:
Eva above is pretty much spot-on. Note that the larger gear having a diameter twice as long as the smaller gear's means that the larger will turn once for every 4 times the smaller does, but the logical process remains sound. Do also note that as Eva mentioned, you should not bother working out the "complete" answer to the question; once you figure out that you need both the ratio of circumferences (or diameters/radii) and the turn speed of one gear, you can answer the question.

Why 4 times? Circumference of the circle is $$\pi*{Diameter}$$.
So, if one of the diameters is twice the other one, circumference is also twice, which means twice more rotations for the smaller gear. No?
_________________
PhD in Applied Mathematics
Love GMAT Quant questions and running.
Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1001
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Re: In a particular machine, there are 2 gears that interlock; One gear is  [#permalink]

Show Tags

17 Aug 2012, 17:16
+1 C

Beautiful question. When the small gear rotates one time, the big gear rotates 1/2 its diameter. Therefore, the big gear rotates 300 times in 1 minute.
With that information, we can calculate the time for both gears when they make 6 x 10^9 times.
_________________
"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings
Manager
Joined: 07 Sep 2010
Posts: 249
Re: In a particular machine, there are 2 gears that interlock; One gear is  [#permalink]

Show Tags

17 Aug 2012, 22:16
1
Though I also found the answer to be C. However, I want to ask one question.

The question states that each gear will last for atleast 6,000,000,000 revolutions.

What if the bigger gear last for 9,000,000,000 and smaller gear will last for 6,000,000,000 revolution. In this scenario, we may not be having definite scenario. Isn't it. So, the answer must be E

imhimanshu wrote:
In a particular machine, there are 2 gears that interlock; One gear is larger in circumference than the other. The manufacturer of the gears guarantees that each gear will last for atleast 6,000,000,000 revolutions. Assuming that there is no slippage between the 2 gears and that when one gear rotates the other gear also rotates, the larger gear is guaranteed to last how many days longer than the smaller gear.

(1) The diameter of the larger gear is twice the diameter of smaller gear.
(2) The smaller gear revolves 600 times per minute.

Please put your reasoning across and then I will ask my doubt. I want to see if I am assuming much in this question.

Thanks
Director
Joined: 22 Mar 2011
Posts: 590
WE: Science (Education)
Re: In a particular machine, there are 2 gears that interlock; One gear is  [#permalink]

Show Tags

17 Aug 2012, 22:26
imhimanshu wrote:
Though I also found the answer to be C. However, I want to ask one question.

The question states that each gear will last for atleast 6,000,000,000 revolutions.

What if the bigger gear last for 9,000,000,000 and smaller gear will last for 6,000,000,000 revolution. In this scenario, we may not be having definite scenario. Isn't it. So, the answer must be E

imhimanshu wrote:
In a particular machine, there are 2 gears that interlock; One gear is larger in circumference than the other. The manufacturer of the gears guarantees that each gear will last for atleast 6,000,000,000 revolutions. Assuming that there is no slippage between the 2 gears and that when one gear rotates the other gear also rotates, the larger gear is guaranteed to last how many days longer than the smaller gear.

(1) The diameter of the larger gear is twice the diameter of smaller gear.
(2) The smaller gear revolves 600 times per minute.

Please put your reasoning across and then I will ask my doubt. I want to see if I am assuming much in this question.

Thanks

the larger gear is guaranteed to last how many days longer than the smaller gear.

The question is about the guaranteed number of days and not about possible scenarios.
_________________
PhD in Applied Mathematics
Love GMAT Quant questions and running.
Manager
Joined: 07 Sep 2010
Posts: 249
Re: In a particular machine, there are 2 gears that interlock; One gear is  [#permalink]

Show Tags

18 Aug 2012, 04:40
Thanks. Makes Sense now..

the larger gear is guaranteed to last how many days longer than the smaller gear.

The question is about the guaranteed number of days and not about possible scenarios.[/quote]
Senior Manager
Joined: 27 Jun 2012
Posts: 350
Concentration: Strategy, Finance
Schools: Haas EWMBA '17
Re: In a particular machine, there are 2 gears that interlock; One gear is  [#permalink]

Show Tags

17 Jan 2013, 01:06
4
2
Each gear has life to 6,000,000,000 revolutions. As both gears are interlocked, smaller gear will have more revolutions and will wear out before the larger one.

(1) The diameter of the larger gear is twice the diameter of smaller gear.
INSUFFICIENT: This means - the circumference of the larger gear is twice that of smaller gear. I.e. 1 revolution of larger gear = smaller gear rotates two times.
Even if we know relative ratio for diameters, we don’t know what rate at they are revolving per minute.
- If the gears are rotating at extreme high speed, they will wear out soon -> hence difference of their life (in minutes) will be smaller.
- If the gears are rotating at extreme slow speed, they will last lot longer -> hence difference of their life (in minutes) will be much larger.
Hence we cannot conclude how many days the gears will last long.

(2) The smaller gear revolves 600 times per minute.
INSUFFICIENT: This information is clearly insufficient. This tells the revolution rate only for smaller gear. No info about larger gear (speed or relative diameter ratio)

Combining (1) & (2)
SUFFICIENT: As we know smaller gear has 600 RPM and 1/2 the diameter than larger one -> the larger gear rotate at half the speed i.e. 300 RPM and hence we can find out how many days they can last long.

We can stop at this point (no need to calculate further during actual exam) but just for sake of curiosity lets calculate further:
No of days larger gear lasts longer than smaller gear = $$\frac{6,000,000,000}{24*60*60 minutes} * (\frac{1}{300}-\frac{1}{600}) = 115.74 days.$$

_________________
Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
VOTE GMAT Practice Tests: Vote Here
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here
Finance your Student loan through SoFi and get $100 referral bonus : Click here Manager Joined: 22 Nov 2010 Posts: 217 Location: India GMAT 1: 670 Q49 V33 WE: Consulting (Telecommunications) Re: In a particular machine, there are 2 gears that interlock; One gear is [#permalink] Show Tags 04 Mar 2013, 02:48 imhimanshu wrote: In a particular machine, there are 2 gears that interlock; One gear is larger in circumference than the other. The manufacturer of the gears guarantees that each gear will last for atleast 6,000,000,000 revolutions. Assuming that there is no slippage between the 2 gears and that when one gear rotates the other gear also rotates, the larger gear is guaranteed to last how many days longer than the smaller gear. (1) The diameter of the larger gear is twice the diameter of smaller gear. (2) The smaller gear revolves 600 times per minute. Please put your reasoning across and then I will ask my doubt. I want to see if I am assuming much in this question. Thanks (1) The diameter of the larger gear is twice the diameter of smaller gear. This means for Bigger gear # of revolution = 6,000,000,000 / pi * 2d Smaller gear # of revolution = 6,000,000,000 / pi * d. But we don't know d (diameter) (2) The smaller gear revolves 600 times per minute. this gives rate of smaller gear. Not sufficient. We can find (6,000,000,000 / pi * d) = 600. We can find d. 1 + 2: Now, we know diameter of Bigger gear we can find Bigger gear # of revolution per min - Smaller gear # of revolution _________________ YOU CAN, IF YOU THINK YOU CAN Intern Joined: 02 Jul 2015 Posts: 34 WE: Investment Banking (Investment Banking) Re: In a particular machine, there are 2 gears that interlock; One gear is [#permalink] Show Tags 01 Dec 2015, 10:56 What if the larger gear revolved faster than the smaller one ? Intern Joined: 05 Apr 2013 Posts: 5 Schools: Wharton '16 (S) Re: In a particular machine, there are 2 gears that interlock; One gear is [#permalink] Show Tags 16 Jan 2016, 00:43 torreadortorment wrote: What if the larger gear revolved faster than the smaller one ? Good point. Could anyone please share thoughts on this? How can the velocities (speed of rotation) be assumed equal for each gear? Math Expert Joined: 02 Aug 2009 Posts: 7958 Re: In a particular machine, there are 2 gears that interlock; One gear is [#permalink] Show Tags 16 Jan 2016, 00:53 anupamisrich wrote: torreadortorment wrote: What if the larger gear revolved faster than the smaller one ? Good point. Could anyone please share thoughts on this? How can the velocities (speed of rotation) be assumed equal for each gear? Hi , it is given that the two gears are interlocked, so both have to move with same speed.. Hope its clear _________________ Director Joined: 04 Jun 2016 Posts: 556 GMAT 1: 750 Q49 V43 Re: In a particular machine, there are 2 gears that interlock; One gear is [#permalink] Show Tags 01 Aug 2016, 04:52 imhimanshu wrote: In a particular machine, there are 2 gears that interlock; One gear is larger in circumference than the other. The manufacturer of the gears guarantees that each gear will last for atleast 6,000,000,000 revolutions. Assuming that there is no slippage between the 2 gears and that when one gear rotates the other gear also rotates, the larger gear is guaranteed to last how many days longer than the smaller gear. (1) The diameter of the larger gear is twice the diameter of smaller gear. (2) The smaller gear revolves 600 times per minute. Please put your reasoning across and then I will ask my doubt. I want to see if I am assuming much in this question. Thanks Given in the stimulus , One gear is bigger than the other. Both gear will work till 6000000 revolution Find the life of the larger gear. Life of gear is a function of revolution they makes. "{They will last till 600000000 revolution-given in the question} Revolution is dependant on the circumference and thus depends on the diameter of the gears. Revolution is also dependant on the rate of revolution of gear per second or per minute or per hour AIM:-Look out for Radius+Rate info (1) The diameter of the larger gear is twice the diameter of smaller gear. We got the relative radius info. We don't have exact radius values. And we are still missing rate of revolution INSUFFICIENT (2) The smaller gear revolves 600 times per minute. Nice:- we got the rate info for smaller one since the smaller one and bigger one are connected so their rate will be same; but this statement doesn't talk about diameter INSUFFICENT COMBINE we have the radius as well as rate info for both gear SUFFICIENT ANSWER IS C _________________ Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired. Intern Joined: 14 Jun 2016 Posts: 15 Location: United States GMAT 1: 700 Q48 V37 WE: Engineering (Pharmaceuticals and Biotech) Re: In a particular machine, there are 2 gears that interlock; One gear is [#permalink] Show Tags 18 Sep 2016, 21:37 imhimanshu wrote: In a particular machine, there are 2 gears that interlock; One gear is larger in circumference than the other. The manufacturer of the gears guarantees that each gear will last for atleast 6,000,000,000 revolutions. Assuming that there is no slippage between the 2 gears and that when one gear rotates the other gear also rotates, the larger gear is guaranteed to last how many days longer than the smaller gear. (1) The diameter of the larger gear is twice the diameter of smaller gear. (2) The smaller gear revolves 600 times per minute. Please put your reasoning across and then I will ask my doubt. I want to see if I am assuming much in this question. Thanks Just looking at the question, (2) is clearly insufficient because you don't know how big the large gear is nor it's revolution rate. (1) you can see the relation of the gears' sizes. However, you can't translate these sizes into time. There's no way to calculate the numbers of days needed for either gear to rotate 6000000000 revs so insufficient. With (1+2) you have the relationship between gear sizes and the time for one gear. Therefore, without doing any calculation, it should be C. Current Student Joined: 28 Nov 2014 Posts: 818 Concentration: Strategy Schools: Fisher '19 (M$)
GPA: 3.71
Re: In a particular machine, there are 2 gears that interlock; One gear is  [#permalink]

Show Tags

21 Oct 2016, 12:05
PrashantPonde wrote:
Each gear has life to 6,000,000,000 revolutions. As both gears are interlocked, smaller gear will have more revolutions and will wear out before the larger one.

(1) The diameter of the larger gear is twice the diameter of smaller gear.
INSUFFICIENT: This means - the circumference of the larger gear is twice that of smaller gear. I.e. 1 revolution of larger gear = smaller gear rotates two times.
Even if we know relative ratio for diameters, we don’t know what rate at they are revolving per minute.
- If the gears are rotating at extreme high speed, they will wear out soon -> hence difference of their life (in minutes) will be smaller.
- If the gears are rotating at extreme slow speed, they will last lot longer -> hence difference of their life (in minutes) will be much larger.
Hence we cannot conclude how many days the gears will last long.

(2) The smaller gear revolves 600 times per minute.
INSUFFICIENT: This information is clearly insufficient. This tells the revolution rate only for smaller gear. No info about larger gear (speed or relative diameter ratio)

Combining (1) & (2)
SUFFICIENT: As we know smaller gear has 600 RPM and 1/2 the diameter than larger one -> the larger gear rotate at half the speed i.e. 300 RPM and hence we can find out how many days they can last long.

We can stop at this point (no need to calculate further during actual exam) but just for sake of curiosity lets calculate further:
No of days larger gear lasts longer than smaller gear = $$\frac{6,000,000,000}{24*60*60 minutes} * (\frac{1}{300}-\frac{1}{600}) = 115.74 days.$$

I am getting the below expression. Can anyone confirm. Thanks!

6 X 10^9/24*60 [1/300- 1/600]

Manager
Joined: 20 Jun 2013
Posts: 50
Location: India
Concentration: Economics, Finance
GMAT 1: 430 Q39 V25
GPA: 3.5
WE: Information Technology (Other)
Re: In a particular machine, there are 2 gears that interlock; One gear is  [#permalink]

Show Tags

20 Jan 2018, 15:55
just one minor point if it can be clarified... in the question it says that ''revolutions'' that the gear will last say n number of revolutions.

but what is required to find out, how may days more larger gear will be.......... i do understand the dynamics of circumference and other things... but how can you assume that in any given day, the gear will keep on rotating 24x365

i mean on some day, there has be to be a rest day also for the machines... request if some one can explain this.... thanks in advance
Non-Human User
Joined: 09 Sep 2013
Posts: 13203
Re: In a particular machine, there are 2 gears that interlock; One gear is  [#permalink]

Show Tags

21 Jan 2019, 22:41
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: In a particular machine, there are 2 gears that interlock; One gear is   [#permalink] 21 Jan 2019, 22:41
Display posts from previous: Sort by