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

 It is currently 20 Sep 2018, 17:25

### 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

# Four staff members at a certain company worked on a project.

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49271
Four staff members at a certain company worked on a project.  [#permalink]

### Show Tags

08 Oct 2012, 01:47
14
16
00:00

Difficulty:

35% (medium)

Question Stats:

77% (01:55) correct 23% (05:33) wrong based on 1085 sessions

### HideShow timer Statistics

Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?

(A) 80
(B) 96
(C) 160
(D) 192
(E) 240

Practice Questions
Question: 56
Page: 159
Difficulty: 600

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 49271
Re: Four staff members at a certain company worked on a project.  [#permalink]

### Show Tags

08 Oct 2012, 01:48
6
18
SOLUTION

Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?

(A) 80
(B) 96
(C) 160
(D) 192
(E) 240

A:B:C:D=2x:3x:5x:6x, for some positive number x. Total time 2x+3x+5x+6x=16x.

If 2x = 30 then 16x = 240;
If 3x = 30 then 16x = 160;
If 5x = 30 then 16x = 96;
If 6x = 30 then 16x = 80;

Only answer choices which is not obtained is 192.

_________________
##### General Discussion
Senior Manager
Joined: 24 Aug 2009
Posts: 476
Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: Four staff members at a certain company worked on a project.  [#permalink]

### Show Tags

08 Oct 2012, 02:59
3
Let the time taken is 2x, 3x , 5x & 6x
Total time taken 16x
Any one of 2x, 3x , 5x & 6x equals 30 .
So 16x can take any of the below mentioned values -
30*16/2 , 30*16/3, 30*16/5 , 30*16/6
240 , 160, 96, 80
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Senior Manager
Joined: 15 Jun 2010
Posts: 329
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Re: Four staff members at a certain company worked on a project.  [#permalink]

### Show Tags

08 Oct 2012, 03:31
3
Let the time taken as 2x, 3x , 5x & 6x
Total time taken 16x
Any one of 2x, 3x , 5x & 6x equals 30 and x can be 15, 10, 6 and 5 respectively.
Now for all values of X (15,10,6 & 5) 16x will be
= 16*15 = 240 (E)
= 16*10 = 160 (C)
= 16*6 = 96 (B)
= 16*5 =80 (A)

_________________

Regards
SD
-----------------------------
Press Kudos if you like my post.
Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

Senior Manager
Joined: 06 Aug 2011
Posts: 348
Re: Four staff members at a certain company worked on a project.  [#permalink]

### Show Tags

08 Oct 2012, 10:19
1
Ohh 13 the edition question luk little trickier than 12th...i didnt buy 13th yet..

well.. +1 to all above me

very nice question bunuel ..

2x, 3x, 5x, 6x...sum=16x

we r taking X as total no of hours..

2/16x=30 ...x=240

3/16x=30=then x can be =160

5/16x= 30 ...then x can be =96

6/16x= 30..then x can be =80..

D is the only choice which can not X value..
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 608
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
Re: Four staff members at a certain company worked on a project.  [#permalink]

### Show Tags

09 Oct 2012, 21:57
2
Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x.
But we are told that one of these individual works is 30hrs. hence, possible scenarios, if
(1)2x =30 => 16x = 240 (2) 3x =30 => 16x = 160 (3) 5x =30 => 16x = 96 (4) 6x =30 => 16x = 80
Hence Answer is D 192 which can not be any of these.
Another alternate is to backsolve,
for options A to E, Answer/16 should give us a multiplication factor (which is denoted by x in first solution). Since this multiplication factor should be present for individual work also, 30 should be divisible by this to give individual work ratio of any out of 2,3,5,6.
eg. 80/16 =5 and 30/5 =6 or 240/16=15 and 30/15=2, but 192/16=12 and 30/12 =2.5 (not one of the ratios)
This leaves us with choice D again.

Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?

(A) 80
(B) 96
(C) 160
(D) 192
(E) 240

Practice Questions
Question: 56
Page: 159
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

_________________

Lets Kudos!!!
Black Friday Debrief

Intern
Joined: 04 Aug 2009
Posts: 10
Re: Four staff members at a certain company worked on a project.  [#permalink]

### Show Tags

11 Oct 2012, 14:41
1
Hi Bunuel,

If we change this question to say that the ratios are still the same i.e 2, 3, 5 and 6 but the prompt says that the the sum of the hours worked by two of the workers is 121 and then we are asked to find the sum of total hours worked by all the workers. Would this be still a valid variation provided we restrict the number of hours in integers only?

Math Expert
Joined: 02 Sep 2009
Posts: 49271
Re: Four staff members at a certain company worked on a project.  [#permalink]

### Show Tags

11 Oct 2012, 14:51
Hi Bunuel,

If we change this question to say that the ratios are still the same i.e 2, 3, 5 and 6 but the prompt says that the the sum of the hours worked by two of the workers is 121 and then we are asked to find the sum of total hours worked by all the workers. Would this be still a valid variation provided we restrict the number of hours in integers only?

Yes.

Given: A:B:C:D=2x:3x:5x:6x, for some positive integer x and the sum of the hours worked by two of the workers is 121.

Since the only sum which gives integer value for x is 5x+6x=121 --> x=11, then total time is 16x=16*11.

Hope it helps.
_________________
Senior Manager
Status: Final Countdown
Joined: 17 Mar 2010
Posts: 476
Location: India
GPA: 3.82
WE: Account Management (Retail Banking)
Re: Four staff members at a certain company worked on a project.  [#permalink]

### Show Tags

12 Oct 2012, 01:23
1
Given Ratios- 2:3:5:6
2x+3x+4x+5x=16x
lets check one by one with ACs, and when we come to D;
16x=192
=>x=12
if you put x= 12 in any individual's value (2x,3x,5x,6x) 30 can not be acheived.

_________________

" Make more efforts "
Press Kudos if you liked my post

Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 669
Location: United States (CA)
Age: 38
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GRE 1: Q168 V169
WE: Education (Education)
Re: Four staff members at a certain company worked on a project  [#permalink]

### Show Tags

10 May 2016, 18:22
2
Attached is a visual that should help.
Attachments

Screen Shot 2016-05-10 at 5.52.54 PM.png [ 56.16 KiB | Viewed 13286 times ]

_________________

Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching, both in-person (San Diego, CA, USA) and online worldwide, since 2002.

One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong).

You can download my official test-taker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y94hlarr Date of Birth: 09 December 1979.

GMAT Action Plan and Free E-Book - McElroy Tutoring

Contact: mcelroy@post.harvard.edu

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3516
Location: United States (CA)
Re: Four staff members at a certain company worked on a project.  [#permalink]

### Show Tags

08 Feb 2017, 19:50
1
Bunuel wrote:
Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?

(A) 80
(B) 96
(C) 160
(D) 192
(E) 240

We are given that the amounts of time that the four members worked on the project were in the ratio 2 to 3 to 5 to 6. A straightforward approach is to create a ratio with x multipliers. The ratio becomes: 2x : 3x : 5x : 6x, in which 2x was person 1’s time, 3x was person 2’s time, 5x was person 3’s time, and 6x was person 4’s time.

From this information, we can determine that the total time worked by all the members is the sum of our ratios: 2x + 3x + 5x + 6x = 16x.

We are also given that one of the members worked for 30 hours. Thus, we can create 4 different equations to get 4 different possible x values.

Option 1) If Person 1 was the individual who worked 30 hours, then 2x = 30 and x = 15

Option 2) If Person 2 was the individual who worked 30 hours, then 3x = 30 and x = 10

Option 3) If Person 3 was the individual who worked 30 hours, then 5x = 30 and x = 6

Option 4) If Person 4 was the individual who worked 30 hours, then 6x = 30 and x = 5

The above results show the 4 different options for the total number of hours an individual staff member worked.

Now, remember that the entire group worked for 16x hours. We substitute each of the 4 possible values for x into this expression:

Option 1: 16x = (16)(15) = 240 hours

Option 2: 16x = (16)(10) = 160 hours

Option 3: 16x = (16)(6) = 96 hours

Option 4: 16x = (16)(5) = 80 hours

The only value that we did not get was 192 hours, so D is the correct answer.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Joined: 24 May 2016
Posts: 19
Location: Germany
Re: Four staff members at a certain company worked on a project  [#permalink]

### Show Tags

03 Jun 2017, 00:57
2
Brute Force:
You know the ratio is 2x:3x:5x:6x =16x
Now you can set 16x equal to all the answer options and see which one when you calculate through the options yields 30. So each option except one does contain one member that worked 30 hours.
For A) x yields 5 so 6*5=30 -->wrong
B) x yields 6 5*6= 30 -->wrong
C) x yields 10 3*10=30 --> wrong
D) x yields 12 when you calculate through you see nothing yields 30 --> bingo
E) x yields 15 2*15 =30 -->wrong
The moment you figured out D does not yield a 30 you can stop working
Manager
Joined: 02 Jan 2017
Posts: 80
Location: Pakistan
Concentration: Finance, Technology
GMAT 1: 650 Q47 V34
GPA: 3.41
Re: Four staff members at a certain company worked on a project  [#permalink]

### Show Tags

18 Dec 2017, 07:58
1
BANON wrote:
Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?

A. 80
B. 96
C. 160
D. 192
E. 240

Concept Involved

Take any Ratio: $$\frac{A}{B}$$ = $$\frac{3}{4}$$
Becomes $$\frac{A}{B}$$ = $$\frac{3x}{4x}$$

Since its a Ratio we do not know the total elements, values represent. But we do know this
Total = 3x +4x= 7x
It will be some multiple of 7

Using this concept as iteration we can
Total for entire staff as : 2x + 3x + 5x + 6x= 16x
Total will be some multiple of sixteen

Since we have total hours (30) for one of the staff members, we will get four different multipliers.
2x=30 : x=15
3x=30 : x=10
5x=30 : x=6
6x=30 : x=5

Using these multipliers By Trial and error you would quickly realise Answer is D
Manager
Joined: 31 Jul 2017
Posts: 124
Location: Tajikistan
Concentration: Finance, Economics
Schools: Booth '21, CBS '21
GMAT 1: 690 Q48 V35
GRE 1: Q164 V162
GPA: 3.85
WE: Accounting (Investment Banking)
Re: Four staff members at a certain company worked on a project.  [#permalink]

### Show Tags

22 Jun 2018, 06:29
I tested each case to arrive to the answer.
Case 1)
2:3:5:6 (assume 30 h is the least number of hours worked, then multiple is 15)
30:45:75:95, total number is 240 (cross E)
Case 2) (assume 30 h is the second least number of hours worked, then multiple is 10)
2:3:5:6
20:30:50:60, total number of hours is 160 (cross C)
Case 3) (assume 30 h is the second greatest number of hours worked, then multiple is 6)
2:3:5:6
12:18:30:36, total number of hours is 96 (cross B)
Case 4) (assume 30 h is the greatest number of hours worked, then multiple is 5)
2:3:5:6
10:15:25:30, total number of hours is 80 (cross A).
Now, we are left with D, which is the correct answer
Re: Four staff members at a certain company worked on a project. &nbs [#permalink] 22 Jun 2018, 06:29
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne 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®.