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

It is currently 19 Apr 2019, 23:27

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.

Close

Request Expert Reply

Confirm Cancel

Three men, Alpha,Beta, and Gamma, working together, do a job in 6 hour

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54372
Three men, Alpha,Beta, and Gamma, working together, do a job in 6 hour  [#permalink]

Show Tags

New post 14 Mar 2019, 23:29
2
7
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

38% (02:36) correct 62% (03:22) wrong based on 47 sessions

HideShow timer Statistics

Three men, Alpha,Beta, and Gamma, working together, do a job in 6 hours less time than Alpha alone, in 1 hour less time than Beta alone, and in one-half the time needed by Gamma when working alone. Let h be the number of hours needed by Alpha and Beta, working together to do the job. Then h equals:


(A) \(\frac{5}{2}\)

(B) \(\frac{3}{2}\)

(C) \(\frac{4}{3}\)

(D) \(\frac{5}{4}\)

(E) \(\frac{3}{4}\)

_________________
Intern
Intern
avatar
B
Joined: 27 Sep 2018
Posts: 37
Re: Three men, Alpha,Beta, and Gamma, working together, do a job in 6 hour  [#permalink]

Show Tags

New post 15 Mar 2019, 01:15
1
Let time taken by alpha, beta and gamma be = x hrs
Time taken by alpha = x+6 hrs
Time taken by beta = x+1 hrs
Time taken by gamma = 2x hrs
Also,
1/(x+6) + 1/(x+1) + 1/2x = 1/x
Solving for x we get x= 2/3. (i)

Now atq h is no of hours needed by alpha and gamma for job
So, 1/h = 1/(x+6) + 1/(x+1)
Solving for h by substituting x =2/3 (from I)
we get h 4/3 hrs

Posted from my mobile device
CEO
CEO
User avatar
P
Joined: 18 Aug 2017
Posts: 3001
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: Three men, Alpha,Beta, and Gamma, working together, do a job in 6 hour  [#permalink]

Show Tags

New post 16 Mar 2019, 01:19
2
Bunuel wrote:
Three men, Alpha,Beta, and Gamma, working together, do a job in 6 hours less time than Alpha alone, in 1 hour less time than Beta alone, and in one-half the time needed by Gamma when working alone. Let h be the number of hours needed by Alpha and Beta, working together to do the job. Then h equals:


(A) \(\frac{5}{2}\)

(B) \(\frac{3}{2}\)

(C) \(\frac{4}{3}\)

(D) \(\frac{5}{4}\)

(E) \(\frac{3}{4}\)


let total time of A+B+G= x hrs
so time for A= x+6
B=x+1
and G= 2x

combing all
1/x+6 + 1/x+1 + 1/2x = x
x = 2/3
given
A+B = h
1/x+6 + 1/x+1 = 1/h
x = 2/3
or say
h = 20/15 ; 4/3
IMO C
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Intern
Intern
avatar
B
Joined: 24 Feb 2019
Posts: 1
Re: Three men, Alpha,Beta, and Gamma, working together, do a job in 6 hour  [#permalink]

Show Tags

New post 18 Mar 2019, 07:28
Could please anyone help me :
How did you find x in the first place?
Thank you

Posted from my mobile device
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 5807
Location: United States (CA)
Re: Three men, Alpha,Beta, and Gamma, working together, do a job in 6 hour  [#permalink]

Show Tags

New post 19 Mar 2019, 19:07
1
Bunuel wrote:
Three men, Alpha,Beta, and Gamma, working together, do a job in 6 hours less time than Alpha alone, in 1 hour less time than Beta alone, and in one-half the time needed by Gamma when working alone. Let h be the number of hours needed by Alpha and Beta, working together to do the job. Then h equals:


(A) \(\frac{5}{2}\)

(B) \(\frac{3}{2}\)

(C) \(\frac{4}{3}\)

(D) \(\frac{5}{4}\)

(E) \(\frac{3}{4}\)


We can let their combined rate = 1/x; thus:

Alpha’s rate = 1/(x + 6)

Beta’s rate = 1/(x + 1)

Gamma’s rate = 1/(2x)

Let’s solve for x, using the equation:

1/(x + 6) + 1/(x + 1) + 1/(2x) = 1/x

To rid the equation of fractions, we can multiply the equation by 2x(x + 1)(x + 6):

2x^2 + 2x + 2x^2 + 12x + x^2 + 7x + 6 = 2x^2 + 14x + 12

5x^2 + 21x + 6 = 2x^2 + 14x + 12

3x^2 + 7x - 6 = 0

(3x - 2)(x + 3) = 0

x = 2/3 or x = -3

Since x can’t be negative, x = 2/3. Therefore, Alpha’s rate = 1/(2/3 + 6) = 1/(20/3) = 3/20 and Beta’s rate = 1/(2/3 + 1) = 1/(5/3) = 3/5. Their combined rate is 3/20 + 3/5 = 3/20 + 12/20 = 15/20 = 3/4. Therefore, h = 1/(3/4) = 4/3 hours.

Answer: C
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Intern
Intern
avatar
B
Joined: 07 Jul 2018
Posts: 46
CAT Tests
Re: Three men, Alpha,Beta, and Gamma, working together, do a job in 6 hour  [#permalink]

Show Tags

New post 22 Mar 2019, 12:44
Can anyone help me with this, Where did I go wrong?

(1)ta+tb+tc = ta - 6
(2)ta+tb+tc = tb - 1
(3)ta+tb+tc = tc/2

h= ta + tb

(4)ta+tb+(tc/2) = 0 [from (3)]
Therefore: h + (tc/2) = 0

Adding (1) + (2)
2(ta+tb) + 2tc = (ta+tb) - 7
2h + 2tc = h-7
tc = (-h-7)/2

Substituting tc in (4)

We get h + [(-h-7)]/4 = 0
h = 7/3

Did I do algebra wrong or is there a concept problem?

Thanks.
Manager
Manager
avatar
B
Joined: 11 Jun 2018
Posts: 72
GMAT 1: 500 Q39 V21
Re: Three men, Alpha,Beta, and Gamma, working together, do a job in 6 hour  [#permalink]

Show Tags

New post 05 Apr 2019, 06:47
chetan2u, Gladiator59, Bunuel, how do we solve this question by substituting values?
Manager
Manager
avatar
B
Joined: 09 Nov 2015
Posts: 50
Three men, Alpha,Beta, and Gamma, working together, do a job in 6 hour  [#permalink]

Show Tags

New post 11 Apr 2019, 04:44
Let the time taken for all three men working together to complete the job be T hrs.
Then the time taken by Alpha (A), Beta (B) or Gamma (G), working alone, is (T+6), (T+1) and (2T) hrs respectively.
When all three men work together to complete the job in T hrs, G's contribution is only half of the job (since he takes 2T hrs to do the whole job). Therefore, the remaining half of the job is done by A and B. So A and B together can do half of the job in T hrs or the whole job in 2T hrs (h=2T) or (1/2T) of the job in 1 hr. So, A and B's combined rate is (1/2T).
We know that A's and B's individual rates are [1/T+6)] and [1/(T+1)] respectively.
So we have another expression for their combined rate which is [1/(T+6)] + [1/(T+1)]
Therefore, [1/(T+6)] + [1/(T+1)]=(1/2T)---> (2T+7)/(T+6))(T+1)=(1/2T)---> 3T^2 + 7T - 6 = 0.
The value of T can be calculated either by factorizing or employing the quadratic equation formula.
T=2/3
h=2T=4/3 Ans: C

This approach is slightly faster since it saves some time while substituting the value of T to get 'h'.
GMAT Club Bot
Three men, Alpha,Beta, and Gamma, working together, do a job in 6 hour   [#permalink] 11 Apr 2019, 04:44
Display posts from previous: Sort by

Three men, Alpha,Beta, and Gamma, working together, do a job in 6 hour

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

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

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®.