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Manager  Joined: 06 Apr 2010
Posts: 101
Company S produces two kinds of stereos: basic and deluxe.  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 71% (02:27) correct 29% (02:56) wrong based on 781 sessions

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Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?

A. 7/17
B. 14/31
C. 7/15
D. 17/35
E. 1/2
Veritas Prep GMAT Instructor V
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Posts: 9983
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17
6
SoniaSaini wrote:
Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
A. 7/17
B. 14/31
C. 7/15
D. 17/35
E. 1/2

I'm not getting how to solve it?

The easiest way would be to assume values:
2/3 were basic, 1/3 were deluxe.
So assume 2 basic and 1 deluxe were produced.
If 5 hrs are needed to make a basic one, 7 hrs are needed to make a deluxe stereo.
Total hrs needed = 2 x 5 + 1 x 7 = 17 out of which 7 were used for deluxe stereo.
So 7/17 is the fraction of time spent in making the deluxe stereo.

Since everything is in fraction terms, i.e. one related to the other, it is pretty easy to assume values and solve. Same should be done when everything is in percentage terms.
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Karishma
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Math Expert V
Joined: 02 Sep 2009
Posts: 60460
Company S produces two kinds of stereos: basic and deluxe.  [#permalink]

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14
9
udaymathapati wrote:
Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 32 were basic and the rest were deluxe. If it takes 57 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
A. 7/17
B. 14/31
C. 7/15
D. 17/35
E. 1/2

udaymathapati please do check the questions when posting. Correct question is as follows:

Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?

A. 7/17
B. 14/31
C. 7/15
D. 17/35
E. 1/2

# of basic stereos was 2/3 of total and # of deluxe stereos was 1/3 of total, let's assume total = 15, then Basic = 10 and Deluxe = 5.

Now, if time needed to produce one Basic stereo is 1 unit than time needed to produce one Deluxe stereo would be 7/5 units. Total time for Basic would be 10*1 = 10 and total time for Deluxe would be 5*7/5 = 7 --> total time for both of them would be 10 + 7 = 17 --> deluxe/total = 7/17.

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Company S produces two kinds of stereos: basic and deluxe.  [#permalink]

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Bunuel wrote:
udaymathapati wrote:
Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 32 were basic and the rest were deluxe. If it takes 57 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
A. 7/17
B. 14/31
C. 7/15
D. 17/35
E. 1/2

udaymathapati please do check the questions when posting. Correct question is as follows:

Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?

A. 7/17
B. 14/31
C. 7/15
D. 17/35
E. 1/2

# of basic stereos was 2/3 of total and # of deluxe stereos was 1/3 of total, let's assume total = 15, then Basic = 10 and Deluxe = 5.

Now, if time needed to produce one Basic stereo is 1 unit than time needed to produce one Deluxe stereo would be 7/5 units. Total time for Basic would be 10*1 = 10 and total time for Deluxe would be 5*7/5 = 7 --> total time for both of them would be 10 + 7 = 17 --> deluxe/total = 7/17.

OHHHHHHHHHH Goshhhhhhhhhhhhhhhhhh Thanx a lot bunuel u were a savior..I would have spent my whole night solving this question i tried every possible way to find out solution...trust me the only last thing i was trying to find out how can i make this question correct from the answer choices.. (

where did u find this question BTW?
Intern  Joined: 18 Aug 2010
Posts: 7

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1
Or if you prefer variables:

Let B be # of basic units and D be # of deluxe units and T(B) and T(D) be the respective production time.

B = 2D => D = B/2
T(D) = 7/5 x T(B)

D x T(D)/[(B x T(B) + D x T(D)]
= (B/2 x 7/5 x T(B))/[(B x T(B)) + B/2 x 7/5 x T(B))
= B x T(B) x (7/10)/[B x T(B) x (7/10 + 1)]
= 7/17
Senior Manager  B
Affiliations: SPG
Joined: 15 Nov 2006
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2
2
we have the following ratios:
basic (b) : deluxe (d)
2 units : 1 unit
5 hrs : 7 hrs

total time taken to produce basic units = 2*5= 10hrs
total time taken to produce deluxe units = 1*7= 7hrs
total time taken = 10+7= 17hrs

so, 7/17

HTH
Manager  Joined: 18 Sep 2009
Posts: 225

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Hai Karishma,

I have a trouble in calculating the time to produce one deluxe stereo. How did you get value 7. I try to calculate in the following manner. (5+5*7/5) . I know it is wrong. Please explain. where i went wrong
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Joined: 16 Oct 2010
Posts: 9983
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1
TomB wrote:
Hai Karishma,

I have a trouble in calculating the time to produce one deluxe stereo. How did you get value 7. I try to calculate in the following manner. (5+5*7/5) . I know it is wrong. Please explain. where i went wrong

I have assumed values here. Let's look at the question again.

Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe.

Ok so if a total of 3 stereos were produced, 2 were basic (because 2/3 are basic) and 1 was deluxe

If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo,

It takes 7/5 as many hours.. So if it takes 5 hrs to produce a basic one, a deluxe one takes 7/5 * 5 = 7 hrs. The question says 7/5 as many hours so you just multiply the hours it takes to produce a basic one with 7/5. Think of it this way - if the question said, "it takes twice as many hours as it takes to produce a basic one..." would you just multiply by 2 or would you follow your method?

then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?

Hours taken for 2 basic stereos = 2*5
Hours taken for 1 deluxe = 1*7
Total hours = 17
Required fraction = 7/17
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Karishma
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Director  Joined: 01 Feb 2011
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B/D = 2/1

lets say time required to produce 1 Basic stereo = 5 hours
=> time required to produced 1 deluxe stereo = 7 hours

total time required to produce B basic stereo's = 5B hours

total time required to produce D deluxe stereo's = 7D hours

ratio of total time required to produce all deluxe stereo's to total time for all stereo's = 7D/(5B+7D) = 7/((5B/D)+7)

=7/17

Manager  B
Joined: 11 Jul 2009
Posts: 89
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assuming total stereo's manufactured=210(7*5*3*2)
deluxe stereo's= 70 and basic=140
7hrs/deluxe stereo and 5 per basic gives 490 hrs to manufacture deluxe and 700 hrs for basic stereo's
therefore 490/(490+700)=7/17
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Kaustubh
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let total stereos = 15

basic:deluxe = 10:5

time taken by deluxe = 7/5*5 = 7 hrs
time taken by basic = 1*10 = 10 hrs

ANS ............ 7/17
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Posts: 60460
Re: Company S produces two kinds of stereos: basic and deluxe.  [#permalink]

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Re: Company S produces two kinds of stereos: basic and deluxe.  [#permalink]

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1
1.Since the denominator in the fraction representing the number of units is 3 , assume a multiple of 3 as the number of units. Let us say 3 units were produced. So 1 was delux and 2 were basic
2. Since the denominator in the fraction representing the time taken to produce a unit is 5, assume a multiple of 5 as the time taken to produce a unit. Let it be 5. So if it takes 5 units of time to produce a basic set, it takes 7/5 * 5 units of time to produce a deluxe set. That is 7 units of time.
3. From (1) and (2) total time spent on basic and deluxe are 2*5 and 1*7 resp which are 10 and 7 units resp
4. Total time spent on both the basic and deluxe sets is 10+ 7 = 17
5. The fraction of time spent on deluxe = 7/17
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Re: Company S produces two kinds of stereos: basic and deluxe.  [#permalink]

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udaymathapati wrote:
Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?

A. 7/17
B. 14/31
C. 7/15
D. 17/35
E. 1/2

In the above Questions, we have fractions 2/3, 7/5 and 1/3. We can assume some values and try solving the questions.
Since in fraction we have 3 and 5, LCM is 15, Let us assume total production to be multiple of 15 ( say 90)
As per question stem, Total production for 90 stereos will be as follows
Basic : 60
Deluxe: 30

Let us take time taken to produce 1 Basic stereo to be 5 hours
For deluxe stereo, it will be 7/5*7= 7 hours

Total time take to produce deluxe stereo as percentage of total production can now be calculated as follows

(30*7)/ (30*7+ 60*5) -----> 210/510 ----> 21/51 i.e 7/17

Ans should be A
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Company S produces two kinds of stereos: basic and deluxe.  [#permalink]

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Bunuel wrote:
udaymathapati wrote:
Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 32 were basic and the rest were deluxe. If it takes 57 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
A. 7/17
B. 14/31
C. 7/15
D. 17/35
E. 1/2

udaymathapati please do check the questions when posting. Correct question is as follows:

Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?

A. 7/17
B. 14/31
C. 7/15
D. 17/35
E. 1/2

# of basic stereos was 2/3 of total and # of deluxe stereos was 1/3 of total, let's assume total=15, then Basic=10 and Deluxe=5.

# of basic stereos was 2/3 of total and # of deluxe stereos was 1/3 of total, let's assume total = 15, then Basic = 10 and Deluxe = 5.

Now, if time needed to produce one Basic stereo is 1 unit than time needed to produce one Deluxe stereo would be 7/5 units. Total time for Basic would be 10*1 = 10 and total time for Deluxe would be 5*7/5 = 7 --> total time for both of them would be 10 + 7 = 17 --> deluxe/total = 7/17.

Hi Bunuel one question:

what does "takes 7/5 as many hours " mean

like it takes 1.4 hours to produce basic units and same time 1.4 takes to produce deluxe units ?

if yes, than why multiplying 1 by 10 to find time to find time we need to divide work by rate no ? thanks Math Expert V
Joined: 02 Sep 2009
Posts: 60460
Re: Company S produces two kinds of stereos: basic and deluxe.  [#permalink]

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dave13 wrote:
Bunuel wrote:
udaymathapati wrote:
Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 32 were basic and the rest were deluxe. If it takes 57 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
A. 7/17
B. 14/31
C. 7/15
D. 17/35
E. 1/2

udaymathapati please do check the questions when posting. Correct question is as follows:

Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?

A. 7/17
B. 14/31
C. 7/15
D. 17/35
E. 1/2

# of basic stereos was 2/3 of total and # of deluxe stereos was 1/3 of total, let's assume total = 15, then Basic = 10 and Deluxe = 5.

Now, if time needed to produce one Basic stereo is 1 unit than time needed to produce one Deluxe stereo would be 7/5 units. Total time for Basic would be 10*1 = 10 and total time for Deluxe would be 5*7/5 = 7 --> total time for both of them would be 10 + 7 = 17 --> deluxe/total = 7/17.

Hi Bunuel one question:

what does "takes 7/5 as many hours " mean

like it takes 1.4 hours to produce basic units and same time 1.4 takes to produce deluxe units ?

if yes, than why multiplying 1 by 10 to find time to find time we need to divide work by rate no ? thanks x times as many as y means x multiplied by y. For example, twice as many as y means 2y. So, if it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, means that if time needed to produce one Basic stereo is 1 unit than time needed to produce one Deluxe stereo would be 1*7/5=7/5 units..

Next, if Basic=10 and Deluxe=5, then time to produce 10 Basic would be 10*1=10 and time to produce 5 Deluxe would be 5*7/5=7
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Re: Company S produces two kinds of stereos: basic and deluxe.  [#permalink]

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udaymathapati wrote:
Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?

A. 7/17
B. 14/31
C. 7/15
D. 17/35
E. 1/2

Lets assume the company produced a total of 90 units, hence units of basic model 60 units & 30 units of deluxe model.

Let the # of hours required to produce one unit of basic model = 10 hours, hence # hours required to produce 1 unit of deluxe model = 14 hours

Now Total # of hours required to produce the 60 units of basic model = 10 * 60 = 600 hours

& Total # of hours required to produce the 30 units of deluxe model = 14 * 30 = 420 hours

So the required fraction of hours out of total hours to produce the deluxe model = 420 / (600 + 420) = 7/17

Thanks,
GyM
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Re: Company S produces two kinds of stereos: basic and deluxe.  [#permalink]

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udaymathapati wrote:
Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?

A. 7/17
B. 14/31
C. 7/15
D. 17/35
E. 1/2

We can let the total number of stereos = 12; thus, 8 are basic and 4 are deluxe.

We can let the number of hours to produce a basic stereo = 10, and thus it takes 7/5 x 10 = 14 hours to produce a deluxe stereo.

The number of hours to produce the deluxe stereos last month was 14 x 4 = 56 hours, and the number of hours to produce the basic stereos was 8 x 10 = 80 hours.

Thus, the time to make the deluxe stereos was 56/(56 + 80) = 56/136 = 7/17 of the total time taken to produce all stereos.

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Re: Company S produces two kinds of stereos: basic and deluxe.  [#permalink]

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time taken deluxe: 7t
time taken basic: 5t

deluxe units: 1
basic units: 2

total time = 5t*2+7t*1
time for deluxe units = 7t*1

7t/17t=7/17
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Company S produces two kinds of stereos: basic and deluxe.  [#permalink]

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Totally algebraic approach:

Time taken to produce a deluxe product: $$\frac{1}{3} * \frac{5}{7}$$
Time taken to produce a basic product: $$\frac{2}{3} * 1$$

So total share of time of $$\frac{deluxe}{basic+deluxe}$$:

$$\frac{\frac{1}{3} * \frac{5}{7}}{\frac{1}{3} * \frac{5}{7} + \frac{2}{3} * 1} = \frac{7}{17}$$ Company S produces two kinds of stereos: basic and deluxe.   [#permalink] 14 Dec 2019, 09:10
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