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

Question

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

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

pushpitkc · Answer

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)

rulingbear · Answer

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.

ScottTargetTestPrep · Answer

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

Hellohello12 · Answer

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.

testcracker · 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 or shortcut to work it out, please say to me ..

thanks in advance ...

rulingbear · Answer

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,

testcracker · Answer

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 ..

rulingbear · 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 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 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 ..

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.

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

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

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