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

 It is currently 20 Oct 2019, 04:26 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  A and B can complete a task in 20 days. B and C can c

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

Hide Tags

e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3074
A and B can complete a task in 20 days. B and C can c  [#permalink]

Show Tags

2
13 00:00

Difficulty:   45% (medium)

Question Stats: 67% (02:03) correct 33% (02:11) wrong based on 400 sessions

HideShow timer Statistics

Q.
A and B can complete a task in 20 days. B and C can complete the same task in 30 days. If A and C can complete the task in 40 days, arrange the efficiencies of A, B, and C in descending order.

A. A>B>C
B. A>C>B
C. B>A>C
D. B>C>A
E. C>A>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 _________________

Originally posted by EgmatQuantExpert on 28 Mar 2017, 10:56.
Last edited by EgmatQuantExpert on 07 Aug 2018, 03:24, edited 1 time in total.
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3074
A and B can complete a task in 20 days. B and C can c  [#permalink]

Show Tags

6
3

Method 2

:

The method shown in the previous post is a lengthy method. Especially when we are not asked to find the efficiency. We are just asked to arrange them in descending order.

• Let us try to compare two statements at a time and see if we can infer anything from it?
o A and B can complete the task in 20 days.
o B and C can complete the task in 30 days.
o Let us take the above two statements. Now notice carefully, that B is common in both the statements, right?
 A is just replaced by C in the second statement.
 And what do we notice, when C comes in place of A?
• We see that the time taken to complete the work increases from 20 days to 30 days.
• This means that C works slower than A.
• Hence, A is more efficient than C. (A>C)

• Now let us compare

o B and C can complete the task in 30 days.
o C and A can complete the task in 40 days.
o Now notice carefully, that C is common in both the statements.
 B is just replaced by A in the second statement.
 And what do we notice, when A comes in place of B?
• We see that the time taken to complete the work increases from 30 days to 40 days.
• Thus, that means that A works slower than B.
• Hence, B is more efficient than A.(B>A)

• Combining both the inferences, we can conclude that B>A>C.
• Thus, you can see that even without calculating a single value, we found the answer, by simply observing the data and comparing them.
That’s the power of observation!! :D

Thanks,
Saquib
Quant Expert
e-GMAT

Aiming to score Q50 or higher in GMAT Quant? Attend this webinar on 2nd April to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes. Register

_________________

Originally posted by EgmatQuantExpert on 31 Mar 2017, 03:43.
Last edited by EgmatQuantExpert on 07 Aug 2018, 03:26, edited 1 time in total.
General Discussion
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3074
Re: A and B can complete a task in 20 days. B and C can c  [#permalink]

Show Tags

The official solution has been posted. Looking forward to a healthy discussion.. _________________

Originally posted by EgmatQuantExpert on 28 Mar 2017, 10:57.
Last edited by EgmatQuantExpert on 31 Mar 2017, 03:36, edited 1 time in total.
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3074
A and B can complete a task in 20 days. B and C can c  [#permalink]

Show Tags

1
1
There are a number of ways to solve this.

Let me show you two.

Method 1

:

Given:

• A and B can complete the task in 20 days.
• B and C can complete the task in 30 days.
• C and A can complete the task in 40 days.

Approach and Working Out:

• Let us assume the task to be 120 units. [LCM of 20,30 and 40]
• Therefore, we can say
o Efficiency of A + B = Work/ Time = $$\frac{120}{20}$$ = 6 units/day……….(i)

o Efficiency of B + C = $$\frac{120}{30}$$ = 4 units/day…………(ii)

o Efficiency of C + A = $$\frac{120}{40}$$ = 3 units/day…………(iii)

• If we add these up we get
o 2 (Efficiency of A + B + C) = (6+4+3) = 13

o Efficiency of A + B + C = 6.5 ………..(iv)

• Subtracting (i) from (iv) we get

o Efficiency of C = 0.5 units/day

• Subtracting (ii) from (iv), we get

o Efficiency of A = 2.5 units/day

• And efficiency of B = 3.5 units/day

• Thus, we can arrange the efficiency of A, B and C as B>A>C.

• And the correct answer is Option C.

Thanks,
Saquib
Quant Expert
e-GMAT

Aiming to score Q50 or higher in GMAT Quant? Attend this webinar on 2nd April to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes. Register

_________________

Originally posted by EgmatQuantExpert on 31 Mar 2017, 03:35.
Last edited by EgmatQuantExpert on 07 Aug 2018, 03:28, edited 2 times in total.
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3565
Re: A and B can complete a task in 20 days. B and C can c  [#permalink]

Show Tags

1
EgmatQuantExpert wrote:
Q.
A and B can complete a task in 20 days. B and C can complete the same task in 30 days. If A and C can complete the task in 40 days, arrange the efficiencies of A, B, and C in descending order.

A. A>B>C
B. A>C>B
C. B>A>C
D. B>C>A
E. C>A>B

Thanks,
Saquib
Quant Expert
e-GMAT

Saquib or anyone: I got the correct answer, but I am not sure my method is correct.

--I wrote equations for combined rates (efficiency, i.e. how many days to complete).
A + B = 20 (i)
B + C = 30 (ii)
A + C = 40 (iii)

(ii) B + C = 30
(iii)A + C = 40, which yields

(A + B) + 2C = 70

--We know (A + B) = 20, so
(20) + 2C = 70
C = 25

--Solve for B.
B + C = 30
B = 5

--Solve for A.
A + B = 20
A = 15

B takes 5 days.
A takes 15 days.
C takes 25 days.

Therefore, from most efficient to least: B > A > C, where "greater than" means "more efficient." Answer: C
I looked at Saquib's approaches and mine seemed flabby by comparison. Did I do it wrong? Help?
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3074
Re: A and B can complete a task in 20 days. B and C can c  [#permalink]

Show Tags

2
genxer123 wrote:

Saquib or anyone: I got the correct answer, but I am not sure my method is correct.

--I wrote equations for combined rates (efficiency, i.e. how many days to complete).
A + B = 20 (i)
B + C = 30 (ii)
A + C = 40 (iii)

(ii) B + C = 30
(iii)A + C = 40, which yields

(A + B) + 2C = 70

--We know (A + B) = 20, so
(20) + 2C = 70
C = 25

--Solve for B.
B + C = 30
B = 5

--Solve for A.
A + B = 20
A = 15

B takes 5 days.
A takes 15 days.
C takes 25 days.

Therefore, from most efficient to least: B > A > C, where "greater than" means "more efficient." Answer: C
I looked at Saquib's approaches and mine seemed flabby by comparison. Did I do it wrong? Help?

Hey,

The method that you have used is incorrect. Let me explain by asking you a simple question.
Say A completes a piece of work in 20 days, so A = 20.
And B completes the same work, in 30 days, so B = 30.

Now tell me if A and B work together will they take (20+30) = 50 days? Think about it carefully, when two people will work together, will they complete the work faster or will the take more than the individual time taken by them to complete the work??

Answer the above question and I am sure you will understand why your method is flawed.

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  _________________
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3565
Re: A and B can complete a task in 20 days. B and C can c  [#permalink]

Show Tags

EgmatQuantExpert wrote:
genxer123 wrote:

Saquib or anyone: I got the correct answer, but I am not sure my method is correct.

--I wrote equations for combined rates (efficiency, i.e. how many days to complete).
A + B = 20 (i)
B + C = 30 (ii)
A + C = 40 (iii)

(ii) B + C = 30
(iii)A + C = 40, which yields

(A + B) + 2C = 70

--We know (A + B) = 20, so
(20) + 2C = 70
C = 25

--Solve for B.
B + C = 30
B = 5

--Solve for A.
A + B = 20
A = 15

B takes 5 days.
A takes 15 days.
C takes 25 days.

Therefore, from most efficient to least: B > A > C, where "greater than" means "more efficient." Answer: C
I looked at Saquib's approaches and mine seemed flabby by comparison. Did I do it wrong? Help?

Hey,

The method that you have used is incorrect. Let me explain by asking you a simple question.
Say A completes a piece of work in 20 days, so A = 20.
And B completes the same work, in 30 days, so B = 30.

Now tell me if A and B work together will they take (20+30) = 50 days? Think about it carefully, when two people will work together, will they complete the work faster or will the take more than the individual time taken by them to complete the work??

Answer the above question and I am sure you will understand why your method is flawed.

Thanks,
Saquib
Quant Expert
e-GMAT

Saquib, thank you! Every so often I invert rates. Your question about people working faster together will remind me to check my here-AWOL  logic on hard problems. Thanks again.
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver
Intern  B
Joined: 12 Feb 2016
Posts: 3
Re: A and B can complete a task in 20 days. B and C can c  [#permalink]

Show Tags

3
Less than 20 second solution:

A + B --> 20
C + B --> 30
So, A >> C (1)

B + C --> 30
A + C --> 40
So, B >> A (2)

(1) & (2): B >> A >> C
Hence, option C.
Intern  B
Joined: 25 Mar 2017
Posts: 5
Re: A and B can complete a task in 20 days. B and C can c  [#permalink]

Show Tags

1
I applied the following method. Please let me if the concept is correct.

1. In 20 day; A and B complete the work.
Hence in 1 day work done is: 1/20

Rate of A + rate of B = 1/20
(Similarly)
Rate of A + Rate of C = 1/ 40
Rate of B + Rate of C = 1/30

Now comparing the equations;
1/20> 1/40, so :
Rate of A + rate of B > Rate of A + Rate of C (Minus "rate of A from both sides; we get):
Rate of B > Rate of C

1/30> 1/40, so :
Rate of B + rate of C >. Rate of A + Rate of C (Minus rate of C from both sides we get):
Rate of B> Rate of A

1/20> 1/30, so :
Rate A> Rate C

Combining all inequalities:
B> A> C
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3074
Re: A and B can complete a task in 20 days. B and C can c  [#permalink]

Show Tags

Gargie.D wrote:
I applied the following method. Please let me if the concept is correct.

1. In 20 day; A and B complete the work.
Hence in 1 day work done is: 1/20

Rate of A + rate of B = 1/20
(Similarly)
Rate of A + Rate of C = 1/ 40
Rate of B + Rate of C = 1/30

Now comparing the equations;
1/20> 1/40, so :
Rate of A + rate of B > Rate of A + Rate of C (Minus "rate of A from both sides; we get):
Rate of B > Rate of C

1/30> 1/40, so :
Rate of B + rate of C >. Rate of A + Rate of C (Minus rate of C from both sides we get):
Rate of B> Rate of A

1/20> 1/30, so :
Rate A> Rate C

Combining all inequalities:
B> A> C

Hey Gargie,

Your method is absolutely correct. People do tend to make the mistake of comparing time instead of efficiencies, i.e. rate of doing work.

But you have done it exactly the way I expect a student to do it. :D

Just one suggestion, in questions of high difficulty level, solving the question using fractions sometimes gets cumbersome, so instead of assuming the work to be 1 units, try to assume the work to be the LCM of the time taken by each person, that way you will be solving the question mostly using integers and for me it is easier to solve using integers than fraction/decimals. 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  _________________
Intern  B
Joined: 14 May 2015
Posts: 47
Re: A and B can complete a task in 20 days. B and C can c  [#permalink]

Show Tags

lcm of 20,30,40=120 unit
A+B=120 units/20hr= 6 unit per hr....(1)
B+c=120/30=4......(2)
A+C=120/40=3......(3)
(1)-(2)
A-C=2....(4)
(3)+(4)
A=2.5
B=3.5
C=0.5
B>A>C
VP  P
Joined: 07 Dec 2014
Posts: 1224
Re: A and B can complete a task in 20 days. B and C can c  [#permalink]

Show Tags

EgmatQuantExpert wrote:
Q.
A and B can complete a task in 20 days. B and C can complete the same task in 30 days. If A and C can complete the task in 40 days, arrange the efficiencies of A, B, and C in descending order.

A. A>B>C
B. A>C>B
C. B>A>C
D. B>C>A
E. C>A>B

adding, rate of A+2B+C=20/240
rate of A+C=6/240
subtracting, 2B=14/240
rate of B=7/240
rate of A=12/240-7/240=5/240
rate of C=6/240-5/240=1/240
B>A>C
C
Retired Moderator V
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1332
Location: Viet Nam
Re: A and B can complete a task in 20 days. B and C can c  [#permalink]

Show Tags

1
EgmatQuantExpert wrote:
A and B can complete a task in 20 days. B and C can complete the same task in 30 days. If A and C can complete the task in 40 days, arrange the efficiencies of A, B, and C in descending order.

A. A>B>C
B. A>C>B
C. B>A>C
D. B>C>A
E. C>A>B

Let's call $$A,B,C$$ are the time for each to complete that work. Hence $$\frac{1}{A},\frac{1}{B},\frac{1}{C}$$ are the efficiencies of each.

$$\frac{1}{A}+\frac{1}{B}=\frac{1}{20} \quad (1)$$
$$\frac{1}{B}+\frac{1}{C}=\frac{1}{30} \quad (2)$$
$$\frac{1}{C}+\frac{1}{A}=\frac{1}{40}\quad (3)$$

$$(1) > (2) \implies \frac{1}{A} > \frac{1}{C}$$
$$(2) > (3) \implies \frac{1}{B} > \frac{1}{A}$$
$$(1) > (3) \implies \frac{1}{B} > \frac{1}{C}$$

Hence $$\frac{1}{B}>\frac{1}{A}> \frac{1}{C}$$

The answer is C
_________________
Manager  B
Joined: 02 Aug 2013
Posts: 64
Location: India
WE: Programming (Consulting)
Re: A and B can complete a task in 20 days. B and C can c  [#permalink]

Show Tags

1
I have used below approach. Please let me know if this is correct.

A+B = 20 days --------- (1)
B+C = 30 days --------- (2)
A + C = 40 days --------- (3)
---------------------------
2 (A+B+C) = 90 days
---------------------------

A+B+C = 45 days -------- (4)

I have substituted the value of value of eq (1) , eq (2) and eq (3) in eq (4) one by one.

20 + C = 45 [A+B = 20 days]
C= 25
[C alone can complete work in 25 days]

B + 40 = 45 [ A+C = 40 days]
B=5 days
[B alone can complete work in 5 days]

A+ 30 = 45 [B+C = 30]
A=15 days
[A alone can complete work in 15 days]

Hence, B>A>C

Ans : C
Senior Manager  P
Joined: 02 Apr 2014
Posts: 468
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34 GPA: 3.5
Re: A and B can complete a task in 20 days. B and C can c  [#permalink]

Show Tags

A + B = 1/20 ---(1)
B + C = 1/30 ---(2)
(1)-(2) => A - C = (1/20) - (1/30) = 1/60
A + C = 1/40
solving => A = 1/48
so A alone takes 48 days to complete.

computing C:
so two As => A + A ->will take 24 days to complete,
but given that A + C -> 40 days, this means C is slower than A => A > C

computing B:
two As => A + A -> 24 days to complete,
but given that A + B -> 20 days, this mean B is faster than A => B > A

B > A > C => option (C)
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8109
Location: United States (CA)
Re: A and B can complete a task in 20 days. B and C can c  [#permalink]

Show Tags

EgmatQuantExpert wrote:
Q.
A and B can complete a task in 20 days. B and C can complete the same task in 30 days. If A and C can complete the task in 40 days, arrange the efficiencies of A, B, and C in descending order.

A. A>B>C
B. A>C>B
C. B>A>C
D. B>C>A
E. C>A>B

Since A and B can complete a task in 20 days but B and C can complete the same task in 30 days, A must be more efficient than C.

Since B and C can complete the same task in 30 days but A and C can complete the task in 40 days, B must be more efficient than A.

Therefore, their efficiencies in descending order is B, followed by A, followed by C.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

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

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15287
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: A and B can complete a task in 20 days. B and C can c  [#permalink]

Show Tags

Hi All,

We're told that A and B can complete a task in 20 days. B and C can complete the same task in 30 days and A and C can complete the task in 40 days. We're asked to arrange the 'efficiencies' of A, B, and C in descending order. This is actually more of a 'logic question' than a 'math question' - and you can solve it with some basic logical comparisons.

To start, we know:
A and B take 20 days to do a task
B and C take 30 days to do a task
Thus, 'swapping' A for C makes the job take 10 days LONGER, meaning that A is MORE efficient than C (re: A > C).

Next, we know:
A and B take 20 days to do a task
A and C take 40 days to do a task
Thus, 'swapping' B for C makes the job take 20 days LONGER, meaning that B is MORE efficient than C (re: B > C).

Finally, we know:
B and C take 30 days to do a task
A and C take 40 days to do a task
Thus, 'swapping' B for A makes the job take 10 days LONGER, meaning that B is MORE efficient than A (re: B > A).

Combining the three inequalities, we have B > A > C

GMAT assassins aren't born, they're made,
Rich
_________________ Re: A and B can complete a task in 20 days. B and C can c   [#permalink] 30 Sep 2018, 21:15
Display posts from previous: Sort by

A and B can complete a task in 20 days. B and C can c

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

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