Find all School-related info fast with the new School-Specific MBA Forum

It is currently 20 Aug 2014, 10:50

Flash Sale:

The Economist GMAT Tutor - 15% Off All Courses


Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A certain calculating machine has only three operation butto

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 10 Sep 2012
Posts: 151
Followers: 2

Kudos [?]: 29 [0], given: 17

A certain calculating machine has only three operation butto [#permalink] New post 19 Nov 2012, 16:41
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

57% (02:53) correct 43% (01:33) wrong based on 51 sessions
A certain calculating machine has only three operation buttons, D, R and A. The D operation doubles the number the machine displays, the R operation subtracts 1 from the number the machine displays, and the A operation adds 1 to the number the machine displays. If the machine initially displays the number 2, which of the following operation sequences (read from left to right) would lead to the same final displayed result as the sequence - D R D R D R D R D R D R ?

A. D D D D D D R R R R R R

B. R D R D R D R D R D R D

C. A D D D D D

D. D D D D D A

E. D D D D D D D A





I have the solution and I will post if there are any inquiries, however I want to see how you guys are able to do this under 2 minutes, I could not figure it out. and I don't think the solution is that great at doing it under 2 either.
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Aug 2014, 08:25, edited 2 times in total.
Moved to PS forum.
4 KUDOS received
Director
Director
User avatar
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 646
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
Followers: 35

Kudos [?]: 353 [4] , given: 23

GMAT ToolKit User Premium Member
Re: A certain calculating machine has only three operation butto [#permalink] New post 19 Nov 2012, 17:18
4
This post received
KUDOS
anon1 wrote:
A certain calculating machine has only three operation buttons, D, R and A. The D operation doubles the number the machine displays, the R operation subtracts 1 from the number the machine displays, and the A operation adds 1 to the number the machine displays. If the machine initially displays the number 2, which of the following operation sequences (read from left to right) would lead to the same final displayed result as the sequence -

D R D R D R D R D R D R ?
-----choices
D D D D D D R R R R R R
R D R D R D R D R D R D
A D D D D D
D D D D D A
D D D D D D D A
I have the solution and I will post if there are any inquiries, however I want to see how you guys are able to do this under 2 minutes, I could not figure it out. and I don't think the solution is that great at doing it under 2 either.

While solving this under 1 miunte is possible.. typing surely isnt... I better get kudos for this :-D

Reading question carefully is very important!

We have D, which doubles the number. A and R which add or substract 1.
Now given sequence:
D R D R D R D R D R D R
We can take a look and know that this has to be an odd number, (Note second last D will make whatever number before that even and R will make it odd).

Now quickly go through answer choices, option B and C end with doubling operation, so these numbers will be even. Eliminate.
Remaining A, D and E
Look at A. After last doubling operation, there are 6 substractions. Therefore reduces even (6) from an even number (formed due to operation D)... we get even. Eliminate A.
Choice D and E both end with odd numbers. so cant be eliminated in this way.

Again lets take a look at given sequence in question. There are 6 doubling operation and some substractions. Ans choice has 7 doubling operation and no substraction, therefore E would be much larger than original sequence.

We are left with D. Lets party with D because.......

..Ans D it is!!
_________________

Lets Kudos!!! ;-)
Black Friday Debrief

Current Student
avatar
Joined: 26 Sep 2012
Posts: 6
Schools: CBS '15 (M)
GMAT Date: 11-27-2012
Followers: 0

Kudos [?]: 0 [0], given: 15

Re: A certain calculating machine has only three operation butto [#permalink] New post 20 Nov 2012, 04:24
Are we sure that the answer choice D is copied correctly from the problem? I only count five doubling operations. If it were six it would be correct.
Manager
Manager
avatar
Joined: 10 Sep 2012
Posts: 151
Followers: 2

Kudos [?]: 29 [0], given: 17

Re: A certain calculating machine has only three operation butto [#permalink] New post 20 Nov 2012, 15:10
fastcompany wrote:
Are we sure that the answer choice D is copied correctly from the problem? I only count five doubling operations. If it were six it would be correct.


Yes it is copied correctly, in D, there are 5 doubling operations.
Manager
Manager
avatar
Joined: 10 Sep 2012
Posts: 151
Followers: 2

Kudos [?]: 29 [0], given: 17

Re: A certain calculating machine has only three operation butto [#permalink] New post 20 Nov 2012, 15:25
Wow VIPS, brilliant work. That was very innovative insight that you used to solve the problem. The solution didn't even have that. Your ability to recognize those even/odds really was quite impressive.

Here is the solution, as you can see, is much more arduous


------official solution

To efficiently solve this question, you have to understand what the D-R operations actually do. Calculate the result of the seven times D-R, step by step:

2 -> 4 -> 3

-> 6 -> 5

-> 10 -> 9

-> 18 -> 17

-> 34 -> 33

-> 66 -> 65

The intermediate results, after each D-R, are 3,5,9,17,33,65. These numbers follow a pattern - they are all one greater than the powers of two, 2,4,8,16,32,64.

Thus, 65 is 2×2×2×2×2×2+1, i.e., five times D, followed by an A.

[[continue]]

Alternative explanation - Plug in the initial number of 2 into the answer choices, and eliminate those that do not reach the same result of 65:

(A) D D D D D D R R R R R R - the 6 Ds get you to 26 = 64, and the series of Rs reduces the result below 65.

(B) R D R D R D R D R D R D - yields a repeating pattern of 1 - 2 - 1 - 2...

(C) A D D D D D - The first A raises the initial number to 3, and the Ds ensure that the result is a multiple of 3. Since 65 is not divisible by 3, POE this answer choice.

(E) D D D D D D D A - 7 Ds is already too big - 28 = 256.
SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 2073
Followers: 179

Kudos [?]: 35 [0], given: 0

Premium Member
Re: A certain calculating machine has only three operation butto [#permalink] New post 09 Mar 2014, 02:13
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Senior Manager
Senior Manager
User avatar
Joined: 21 Oct 2013
Posts: 410
Followers: 7

Kudos [?]: 272 [0], given: 222

Re: A certain calculating machine has only three operation butto [#permalink] New post 03 Aug 2014, 04:12
1
This post was
BOOKMARKED
A certain calculating machine has only three operation buttons, D, R and A. The D operation doubles the number the machine displays, the R operation subtracts 1 from the number the machine displays, and the A operation adds 1 to the number the machine displays. If the machine initially displays the number 2, which of the following operation sequences (read from left to right) would lead to the same final displayed result as the sequence - D R D R D R D R D R D R ?

A): D D D D D D R R R R R R
B): R D R D R D R D R D R D
C): A D D D D D
D): D D D D D A
E): D D D D D D D A
Intern
Intern
avatar
Joined: 21 Jul 2014
Posts: 39
Schools: Sloan '17
Followers: 0

Kudos [?]: 17 [0], given: 3

Re: A certain calculating machine has only three operation butto [#permalink] New post 03 Aug 2014, 08:56
goodyear2013 wrote:
A certain calculating machine has only three operation buttons, D, R and A. The D operation doubles the number the machine displays, the R operation subtracts 1 from the number the machine displays, and the A operation adds 1 to the number the machine displays. If the machine initially displays the number 2, which of the following operation sequences (read from left to right) would lead to the same final displayed result as the sequence - D R D R D R D R D R D R ?

A): D D D D D D R R R R R R
B): R D R D R D R D R D R D
C): A D D D D D
D): D D D D D A
E): D D D D D D D A



This is how I solved this problem:

First I tried to figure out what the original sequence result is. I didn't have to do a lot of calculating before noticing a pattern. Each R was 2x-1, so I just did every other letter. Yes, there is an algebraic way to simplify further, but in the interest of time, I didn't bother with trying to figure that out for such simple arithmetic.

From that, I got that my goal is 65. Now I had to find the correct answer choice. I start with C and move up or down depending on if I need a higher answer.

Answer choice C = (2+1)(2^5) = 96 --> too high. So I look for something that could be smaller. Option D looks smaller than C since it is powers of 2 and then adding one, instead of powers of 3.

D = 2^6 + 1

Powers of 2 should be something that is pretty easy to remember (especially if you work with computers). I know 2^6 = 64. Add 1 = 65. I have my answer: D!

For these types of questions, I find that rather than complicating it with a lot of theory, it is better to just jump into it if you are good at doing simple arithmetic in your head (or with limited scratch paper). Saves a lot of time and prevents you from making strategic errors.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24384 [0], given: 2677

Re: A certain calculating machine has only three operation butto [#permalink] New post 12 Aug 2014, 08:26
Expert's post
goodyear2013 wrote:
A certain calculating machine has only three operation buttons, D, R and A. The D operation doubles the number the machine displays, the R operation subtracts 1 from the number the machine displays, and the A operation adds 1 to the number the machine displays. If the machine initially displays the number 2, which of the following operation sequences (read from left to right) would lead to the same final displayed result as the sequence - D R D R D R D R D R D R ?

A): D D D D D D R R R R R R
B): R D R D R D R D R D R D
C): A D D D D D
D): D D D D D A
E): D D D D D D D A


Merging similar topics. Please refer to the discussion above.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: A certain calculating machine has only three operation butto   [#permalink] 12 Aug 2014, 08:26
    Similar topics Author Replies Last post
Similar
Topics:
A certain calculating machine has only three operation goodyear2013 0 03 Aug 2014, 08:56
2 Three machines operating independently, simultaneously, and kiseki 4 09 Oct 2013, 18:23
A Co. has 2 types of machines, type R and S. Operating at a mexicanhoney 2 02 Oct 2007, 14:20
2 Experts publish their posts in the topic A company has two types of machines, type R and type S. Oper above720 4 08 Feb 2007, 21:57
A company has two types of machines, type R and S. Operating MBAHopeful 3 25 Dec 2005, 15:22
Display posts from previous: Sort by

A certain calculating machine has only three operation butto

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.