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Machine A can produce 50 components a day while Machine B on

by vinni.k » Mon May 01, 2017 10:35 am

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Machine A can produce 50 components a day while Machine B only 40. The monthly maintenance cost for Machine A is $1500 while the cost for Machine B is $550. If each component generates an income of $10, what is the least number of days per month that the plant has to operate to justify the usage of Machine A instead of Machine B?

A. 6
B. 7
C. 9
D. 10
E. 11

OA is D

My Doubt :- Question prompt says "to justify the usage". What does this exactly mean ?
I used the answer choices. I used D first.

For A 50*10*10-1500 = 3500
For B 40*10*10-500 = 3500

Both are same. Is this what justify means? because i thought we need more for A than B. So, i used answer choice E where A = 4000 and B = 3900.

Please clarify

Thank you.
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by DavidG@VeritasPrep » Mon May 01, 2017 10:58 am
vinni.k wrote:Machine A can produce 50 components a day while Machine B only 40. The monthly maintenance cost for Machine A is $1500 while the cost for Machine B is $550. If each component generates an income of $10, what is the least number of days per month that the plant has to operate to justify the usage of Machine A instead of Machine B?

A. 6
B. 7
C. 9
D. 10
E. 11

OA is D

My Doubt :- Question prompt says "to justify the usage". What does this exactly mean ?
I used the answer choices. I used D first.

For A 50*10*10-1500 = 3500
For B 40*10*10-500 = 3500

Both are same. Is this what justify means? because i thought we need more for A than B. So, i used answer choice E where A = 4000 and B = 3900.

Please clarify

Thank you.
Yeah, that question could have been worded a little more clearly. (And an official one would be.) I'm guessing the question-writer's logic was that If we treat "justify" to mean "defend the use of," then we'd need to make at least as much using B as A. An official question would make that crystal clear.
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by vinni.k » Mon May 01, 2017 1:16 pm
DavidG@VeritasPrep wrote:
Yeah, that question could have been worded a little more clearly. (And an official one would be.) I'm guessing the question-writer's logic was that If we treat "justify" to mean "defend the use of," then we'd need to make at least as much using B as A. An official question would make that crystal clear.
Thanks :D
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by Jay@ManhattanReview » Mon May 01, 2017 11:27 pm
vinni.k wrote:Machine A can produce 50 components a day while Machine B only 40. The monthly maintenance cost for Machine A is $1500 while the cost for Machine B is $550. If each component generates an income of $10, what is the least number of days per month that the plant has to operate to justify the usage of Machine A instead of Machine B?

A. 6
B. 7
C. 9
D. 10
E. 11

OA is D

My Doubt :- Question prompt says "to justify the usage". What does this exactly mean ?
I used the answer choices. I used D first.

For A 50*10*10-1500 = 3500
For B 40*10*10-500 = 3500

Both are same. Is this what justify means? because i thought we need more for A than B. So, i used answer choice E where A = 4000 and B = 3900.

Please clarify

Thank you.
Hi vinni.k,

The question is not worded clearly.

One needs to assume that the monthly maintenance cost of $1500 for machine A and $550 for machine B is constant whether the machines are used for less than a month.
There is an error in your computation. Pl. see in red.

For A 50*10*10-1500 = 3500
For B 40*10*10-500 = 3500; it should be $550.
It should be

For A: Net Income in 10 days = 50*10*10-1500 = $3500
For B: Net Income in 10 days = 40*10*10-550 = $3450

Since $3500 > $3450, the usage of Machine A is justified over the usage of Machine B if the plant is to run for at least 10 days.

However, since there is a gap of $50 between $3500 and $3450, you must also check the number of days = 9; it may happen that the usage of Machine A is justified over the usage of Machine B if the plant runs for even 9 days.

For A: Net Income in 9 days = 50*9*10-1500 = $3000
For B: Net Income in 9 days = 40*9*10-550 = $3050

Since $3000 < $3050, it is NOT justified to use Machine A over Machine B is the plan is to run for less than 10 days.

The correct answer is 10 days.

The correct answer: D

Hope this helps!

Relevant book: Manhattan Review GMAT Word Problems Guide

-Jay
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by Jay@ManhattanReview » Mon May 01, 2017 11:43 pm
vinni.k wrote:Machine A can produce 50 components a day while Machine B only 40. The monthly maintenance cost for Machine A is $1500 while the cost for Machine B is $550. If each component generates an income of $10, what is the least number of days per month that the plant has to operate to justify the usage of Machine A instead of Machine B?

A. 6
B. 7
C. 9
D. 10
E. 11

OA is D

My Doubt :- Question prompt says "to justify the usage". What does this exactly mean ?
I used the answer choices. I used D first.

For A 50*10*10-1500 = 3500
For B 40*10*10-500 = 3500

Both are same. Is this what justify means? because i thought we need more for A than B. So, i used answer choice E where A = 4000 and B = 3900.

Please clarify

Thank you.
Let's take the Algebraic route to this question.

Since we wish to just the usage of Machine A over that of Machine B, the net income from the usage of Machine A must be equal or more than that of Machine B.

Say the run of the plan is justified to use Machine A over Machine B if it runs for x days.

Thus,

For A: Net Income in x days = 50*x*10-1500 = 500x - 1500
For B: Net Income in x days = 40*x*10-550 = 400x - 550

500x - 1500 >= 400x - 550

=> 100x >= 950

=> x >= 9.5 days => 10 days

The correct answer: D

Hope this helps!

Relevant book: Manhattan Review GMAT Math Essentials Guide

-Jay
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by ceilidh.erickson » Wed May 03, 2017 11:28 am
David and Jay are right - the wording on this question is really unclear! It's obviously not from a GMAT-like source. This is why BTG asks everyone to post the source of every question, so students know which sources are high-quality and which are not (and also because it's a copyright violation not to post your source).

Where did you find this question?
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by vinni.k » Wed May 03, 2017 12:21 pm
Thank you all for your responses. Source is GMAT club tests

Regards
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by Jeff@TargetTestPrep » Wed Jul 25, 2018 4:38 pm
vinni.k wrote:Machine A can produce 50 components a day while Machine B only 40. The monthly maintenance cost for Machine A is $1500 while the cost for Machine B is $550. If each component generates an income of $10, what is the least number of days per month that the plant has to operate to justify the usage of Machine A instead of Machine B?

A. 6
B. 7
C. 9
D. 10
E. 11
We are given that Machine A can produce 50 components per day, and that each component brings revenue of $10 per component. Thus, we know that Machine A's daily revenue is (50)(10) = 500. We are also given that Machine A's maintenance fee is $1500 per month.

Machine B produces 40 components per day and each component brings revenue of $10 per component. Thus, we know that Machine B's daily revenue is (40)(10) = 400. Machine B's maintenance fee is $550 dollars per month.

Since we need to justify the usage of Machine A, we need to determine the minimum number of days it will take until Machine A's profit is greater than Machine B's profit. We can let t = the number of days until this happens and create the following inequality:

50(10)(t) - 1500 > 40(10)(t) - 550

500t - 1500 > 400t - 550

100t > 950

t > 9.5

Thus, the minimum number of days needed is 10.

Answer: D

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