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

 It is currently 25 Sep 2018, 16:07

### 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

# A type A employee can complete a task in 2 hours while a type B employ

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49496
A type A employee can complete a task in 2 hours while a type B employ  [#permalink]

### Show Tags

04 May 2017, 05:06
3
4
00:00

Difficulty:

45% (medium)

Question Stats:

70% (02:06) correct 30% (02:04) wrong based on 197 sessions

### HideShow timer Statistics

A type A employee can complete a task in 2 hours while a type B employee needs 6 hours to complete the same task. If a firm needs the task to be completed in one hour and the cost of hiring a type A is 4 times the cost of hiring a type B employee, which combination should the firm choose in order to achieve their goal of one hour at a minimum cost?

A. 6 type B employees
B. 1 type A employee and 3 type B employees
C. 2 type A employees and 1 type B employee
D. 2 type A employees
E. Any of the above combinations

_________________
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 3141
Location: India
GPA: 3.12
A type A employee can complete a task in 2 hours while a type B employ  [#permalink]

### Show Tags

04 May 2017, 06:16
2
2
Let the cost of acquiring the type B employee be C.
Hence, the cost of acquiring the type A employee is 4C.

Since a type A employee does the work in 2 hours, he does half the work in an hour.
Since a type B employee does the work in 6 hours, he will complete 1/6th of the work in an hour.

All the 4 combinations will complete the work
A. 6 type B(6*$$\frac{1}{6}$$th of work)
B. 1 type A($$\frac{1}{2}$$ of the work) and 3 type B(3*$$\frac{1}{6}$$th of the work)
C. 2 type A(2*$$\frac{1}{2}$$ of the work) and 1 type B(1*$$\frac{1}{6}$$th of the work)
In this case the type B employee will do additional work.
D. 2 type A(2*$$\frac{1}{2}$$ of the work)

Cost for completing the work
A. 6*C
B. 4C + 3(C) = 7C
C. 2(4C) + 1(C) = 9C
D. 2(4C) = 8C

Hence, A completes the work the quickest(Option A)
_________________

You've got what it takes, but it will take everything you've got

Manager
Joined: 03 May 2017
Posts: 106
A type A employee can complete a task in 2 hours while a type B employ  [#permalink]

### Show Tags

Updated on: 23 Jul 2017, 12:40
1
Given that the firm needs only 1 hr of work, options C and E can be rid of. This leaves us with options A, B and D.
Type A is worth 3B but cost 4B. For simplicity, if A cost $4/hr, then B cost$3/hr.
A. 6B/6 = $3 B. A/2+3B/6 = 2+ 1.5=$3.5
D. 2A/2 = $4 Hence, A is the answer. Originally posted by rulingbear on 04 May 2017, 14:48. Last edited by rulingbear on 23 Jul 2017, 12:40, edited 3 times in total. Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 3528 Location: United States (CA) Re: A type A employee can complete a task in 2 hours while a type B employ [#permalink] ### Show Tags 06 May 2017, 18:00 Bunuel wrote: A type A employee can complete a task in 2 hours while a type B employee needs 6 hours to complete the same task. If a firm needs the task to be completed in one hour and the cost of hiring a type A is 4 times the cost of hiring a type B employee, which combination should the firm choose in order to achieve their goal of one hour at a minimum cost? A. 6 type B employees B. 1 type A employee and 3 type B employees C. 2 type A employees and 1 type B employee D. 2 type A employees E. Any of the above combinations The easiest way to solve this question is to try each answer choice. We will make sure that the combination in each answer choice gets the job done in 1 hour and compare the costs. Let’s denote the cost to hire a type B employee as x. Since a type A employee costs 4 times as much as a type B employee, the cost to hire a type A employee is 4x. Also, keep in mind that the rate of a type A employee is ½ and the rate of a type B employee is ⅙. A) 6 type B employees Since 6 x (⅙) = 1, 6 type B employees will complete the task in 1 hour. Since each type B employee costs x dollars, this option will cost 6x dollars. B) 1 type A employee and 3 type B employees Since 1 x (½) + 3 x (⅙) = ½ + ½ = 1, 1 type A employee and 3 type B employees will complete the task in 1 hour. Since each type A employee costs 4x dollars and each type B employee costs x dollars, this option will cost 1(4x) + 3(x) = 7x dollars. C) 2 type A employees and 1 type B employee Whatever the cost is, this option will cost more than option D. D) 2 type A employees This option costs 2(4x) = 8x dollars, which is more than either option A or B. This option cannot be the correct answer choice. E) Any of the above combinations This cannot be the correct answer choice, since some of the choices cost less than the others. The lowest cost is option A, 6 type B employees. Answer: A _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Intern Joined: 30 May 2017 Posts: 8 Re: A type A employee can complete a task in 2 hours while a type B employ [#permalink] ### Show Tags 12 Jul 2017, 13:58 2 The approach I used is more abstract (but hopefully just as correct). From the question, we know that A works at a rate of 1/2 per hour while B works at a rate of 1/6 per hour . From this we know that A works three times as fast as B. However, A costs four times as much as B. Therefore, any unit of A is overpriced for the return. Makes most sense economically to go with 6 B employees. Senior Manager Status: love the club... Joined: 24 Mar 2015 Posts: 275 A type A employee can complete a task in 2 hours while a type B employ [#permalink] ### Show Tags Updated on: 24 Jul 2017, 02:24 rulingbear wrote: Given that the firm needs only 1 hr of work, options C and E can be rid of. This leaves us with options A, B and D. Type A is worth 3B but cost 4B. For simplicity, if A cost$4/hr, then B cost $3/hr. A. 6B =$18
B. 2A+B = $13 D. 2A =$8

hi

beautiful I must say

anyway, did you deduce this inference "A cost $4/hr, then B cost$3/hr" from any calculation or from any shortcut...? if from any step by step method - then okay - I know it, but if you know any rule or shortcut to work it out, please say to me ..

Originally posted by gmatcracker2018 on 23 Jul 2017, 11:41.
Last edited by gmatcracker2018 on 24 Jul 2017, 02:24, edited 1 time in total.
Manager
Joined: 03 May 2017
Posts: 106
A type A employee can complete a task in 2 hours while a type B employ  [#permalink]

### Show Tags

Updated on: 24 Jul 2017, 09:10
ssislam wrote:
rulingbear wrote:
Given that the firm needs only 1 hr of work, options C and E can be rid of. This leaves us with options A, B and D.
Type A is worth 3B but cost 4B. For simplicity, if A cost $4/hr, then B cost$3/hr.
A. 6B = $18 B. 2A+B =$13
D. 2A = $8 Hence, D is the answer. hi beautiful I must say anyway, did you deduce this inference "A cost$4/hr, then B cost $3/hr" from any calculation or from any shortcut...? if from any step by step method - then okay - I know it, but if you know any rule of shortcut to work it out, please say to me .. thanks in advance ... Hi ssislam, Thanks, note that I have edited my response as the answer is A, which was already implicit in the statement, "A cost$4/hr, then B cost $3/hr". I just forgot to account for the employees to hours ratio in the options (see my edited post for the correct approach). Now for your question, I am afraid the deduction is rather abstract. However, I will try to help. It is a variant of plugging in numbers. If you understand up to the point that Type A is worth 3B but cost 4B. Therefore A is 4/3 times more expensive than B. I picked 3 and 4 for simplicity as they are simple numbers and are divisible by both 4 and 3. i.e 4/3 * 3= 4, so if B=3, then A =4. Note that you can plug in any values for A and B and you would still get the same answer, as long as you keep in mind the relationship between A and B in term of cost, i.e A = 4/3B. I have found this helpful in solving GMAT questions, as all the applied questions usually have numbers that are easily divisible after careful observation, except for arithmetic questions that are testing peculiar number properties. Even those usually yield elegant and simple solutions after diligent observations, hence why all quant questions are meant to be solved under 2 minutes. Best, Originally posted by rulingbear on 23 Jul 2017, 12:31. Last edited by rulingbear on 24 Jul 2017, 09:10, edited 1 time in total. Senior Manager Status: love the club... Joined: 24 Mar 2015 Posts: 275 A type A employee can complete a task in 2 hours while a type B employ [#permalink] ### Show Tags Updated on: 11 Aug 2017, 12:30 rulingbear wrote: ssislam wrote: rulingbear wrote: Given that the firm needs only 1 hr of work, options C and E can be rid of. This leaves us with options A, B and D. Type A is worth 3B but cost 4B. For simplicity, if A cost$4/hr, then B cost $3/hr. A. 6B =$18
B. 2A+B = $13 D. 2A =$8

hi

beautiful I must say

anyway, did you deduce this inference "A cost $4/hr, then B cost$3/hr" from any calculation or from any shortcut...? if from any step by step method - then okay - I know it, but if you know any rule of shortcut to work it out, please say to me ..

Hi ssislam,

Thanks, note that I have edited my response as the answer is A, which was already implicit in the statement, "A cost $4/hr, then B cost$3/hr". I just forgot to account for the employees to hours ratio in the options (see my edited post for the correct approach).

Now for your question, I am afraid the deduction is rather abstract. However, I will try to help. It is a variant of plugging in numbers. If you understand up to the point that
Type A is worth 3B but cost 4B. Therefore A is 4/3 times more expensive than A. I picked 3 and 4 for simplicity as they are simple numbers and are divisible by both 4 and 3. i.e 4/3 * 3= 4, so if B=3, then A =4. Note that you can plug in any values for A and B and you would still get the same answer, as long as you keep in mind the relationship between A and B in term of cost, i.e A = 4/3B.

I have found this helpful in solving GMAT questions, as all the applied questions usually have numbers that are easily divisible after careful observation, except for arithmetic questions that are testing peculiar number properties. Even those usually yield elegant and simple solutions after diligent observations, hence why all quant questions are meant to be solved under 2 minutes.

Best,

hi
thanks, yes I saw the answer was "A" well before I wrote to you. Actually I was not worried about the answer, but rather was interested in the logic underlying the concept the question is testing.

so, "Type A is worth 3B but cost 4B. Therefore A is 4/3 times as expensive as B "(not A), as you mentioned in your reply, if I am not wrong. this is a concept very handy.

if this were such that, "Type A is worth 2B but cost 4B" then A would be 2 times as expensive as B.
if this were such that "Type A is worth B but cost 4B then A would be 4 times as expensive as B."
if this were such that "Type A is worth 3B but cost 5B then A would be is 5/3 times as expensive as B."
if this were such that "Type A is worth 3B but cost B. Then A would be 1/3 times as expensive(actually less) as B."

is that okay, man ..?

thanks ..

Originally posted by gmatcracker2018 on 24 Jul 2017, 03:10.
Last edited by gmatcracker2018 on 11 Aug 2017, 12:30, edited 2 times in total.
Manager
Joined: 03 May 2017
Posts: 106
A type A employee can complete a task in 2 hours while a type B employ  [#permalink]

### Show Tags

24 Jul 2017, 09:20
hi

beautiful I must say

anyway, did you deduce this inference "A cost $4/hr, then B cost$3/hr" from any calculation or from any shortcut...? if from any step by step method - then okay - I know it, but if you know any rule of shortcut to work it out, please say to me ..

Hi ssislam,

Thanks, note that I have edited my response as the answer is A, which was already implicit in the statement, "A cost $4/hr, then B cost$3/hr". I just forgot to account for the employees to hours ratio in the options (see my edited post for the correct approach).

Now for your question, I am afraid the deduction is rather abstract. However, I will try to help. It is a variant of plugging in numbers. If you understand up to the point that
Type A is worth 3B but cost 4B. Therefore A is 4/3 times more expensive than A. I picked 3 and 4 for simplicity as they are simple numbers and are divisible by both 4 and 3. i.e 4/3 * 3= 4, so if B=3, then A =4. Note that you can plug in any values for A and B and you would still get the same answer, as long as you keep in mind the relationship between A and B in term of cost, i.e A = 4/3B.

I have found this helpful in solving GMAT questions, as all the applied questions usually have numbers that are easily divisible after careful observation, except for arithmetic questions that are testing peculiar number properties. Even those usually yield elegant and simple solutions after diligent observations, hence why all quant questions are meant to be solved under 2 minutes.

Best,[/quote]

hi
thanks, yes I saw the answer was "A" well before I wrote to you. Actually I was not worried about the answer, but rather was interested in the logic underlying the concept the question is testing.

so, "Type A is worth 3B but cost 4B. Therefore A is 4/3 times more expensive than B "(not A), as you mentioned in your reply, if I am not wrong. this is a concept very handy.

if this were such that, "Type A is worth 2B but cost 4B" then A would be 2 times more expensive than is B.
if this were such that "Type A is worth B but cost 4B then A would be 4 times more expensive than is B."
if this were such that "Type A is worth 3B but cost 5B then A would be is 5/3 times more expensive than is B."
if this were such that "Type A is worth 3B but cost B. Then A would be 1/3 times more expensive(actually less) than is B."

is that okay, man ..?

thanks ..[/quote]

HI ssislam,

Your examples are correct. I am glad you found it helpful. I think the concept can be applied to questions on rate, exchange rate, and even speed and average, once you master the idea.
It can also be used with rate boxes if you are familiar with them. I believe that on a higher level this sort of questions demonstrate that GMAT quants are just a more specific version of CR in verbal and that you don't have to be a math guru to excel in GMAT quant.

In fact, I believe the ability to think critically is the sole attribute that can differentiate high scorers (99th percentile) from the rest in both quant and verbal.
Non-Human User
Joined: 09 Sep 2013
Posts: 8189
Re: A type A employee can complete a task in 2 hours while a type B employ  [#permalink]

### Show Tags

03 Sep 2018, 07:28
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.
_________________
Re: A type A employee can complete a task in 2 hours while a type B employ &nbs [#permalink] 03 Sep 2018, 07:28
Display posts from previous: Sort by

# A type A employee can complete a task in 2 hours while a type B employ

## 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®.