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

 It is currently 19 Jun 2018, 07:32

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Harry and Ron can individually build a castle in 20 days and 30 days r

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1505
Harry and Ron can individually build a castle in 20 days and 30 days r [#permalink]

### Show Tags

25 Apr 2017, 01:25
2
00:00

Difficulty:

5% (low)

Question Stats:

83% (01:30) correct 17% (01:48) wrong based on 73 sessions

### HideShow timer Statistics

Q. Harry and Ron can individually build a castle in 20 days and 30 days respectively. Both work together for 6 days, after which Harry and Ron got tired and quit. Hermione decided to complete the castle and worked for 5 days alone to complete the remaining work. Had Hermione worked alone, in how many days would she have built the whole castle?

a. 5 days
b. 10 days
c. 15 days
d. 20 days
e. 30 days

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1505
Harry and Ron can individually build a castle in 20 days and 30 days r [#permalink]

### Show Tags

Updated on: 30 Apr 2017, 01:50
The official solution has been posted. Looking forward to a healthy discussion..
_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Originally posted by EgmatQuantExpert on 25 Apr 2017, 01:25.
Last edited by EgmatQuantExpert on 30 Apr 2017, 01:50, edited 1 time in total.
Intern
Joined: 18 Jul 2016
Posts: 16
Re: Harry and Ron can individually build a castle in 20 days and 30 days r [#permalink]

### Show Tags

25 Apr 2017, 02:10
1
rate of work for
Harry = 1/20
Ron = 1/30

when working together, rate = 1/20 + 1/30 = 5/60 = 1/12
worked for 6 days means they completed 1/12 * 6 work = 1/2

Hermione works for 5 days to complete 1/2 work
so rate of hermione's work = (1/2)/5 = 1/10
hence she can complete the castle in 10 days
_________________

Engineer, Quant score 53 First attempt.

Manager
Joined: 05 Nov 2016
Posts: 87
Re: Harry and Ron can individually build a castle in 20 days and 30 days r [#permalink]

### Show Tags

25 Apr 2017, 19:57
Harry's 6 day work = 6/20
Ron's 6 day work = 6/30
together theri work = 6/20 + 6/30 = 1/2
Remaining work is 1/2 which Hermione completed in 5 days
so the 1 day work by Hermione alone is (1/2)/5 = 1/10
Total days = 10
_________________

Kudos are always welcome ... as well your suggestions

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1505
Re: Harry and Ron can individually build a castle in 20 days and 30 days r [#permalink]

### Show Tags

30 Apr 2017, 01:48
1

Solution

• We are given:

o Time taken by Harry to build the castle $$= 20$$ $$days$$.
o Time taken by Ron to build the castle $$= 30$$ $$days$$.

• Let us assume the work to be $$60$$ $$units$$ (LCM of 20 and 30)

o Efficiency of Harry $$= \frac{60}{20} = 3$$ units/day
o Efficiency of Ron $$= \frac{60}{30} = 2$$ unit/day
• If they work together they can build the castle in $$= \frac{60}{(2+3)} = 10$$ days.

o But they are working for only $$5$$ $$days$$.
o Hence they will complete only half of the work which is $$30$$ $$units$$.

• The remaining half ($$30 units$$) of the work is done by Hemione in $$5$$ $$days$$.
• Thus, Hermione can complete the total work in $$5*2 = 10$$ $$days$$.
• And the correct answer is Option B
.

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Re: Harry and Ron can individually build a castle in 20 days and 30 days r   [#permalink] 30 Apr 2017, 01:48
Display posts from previous: Sort by