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A company makes and sells two products, P and Q. The costs per unit of

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A company makes and sells two products, P and Q. The costs per unit of making and selling P and Q are $8.00 and $9.50, respectively, and the selling prices per unit of P and Q are $10.00 and $13.00, respectively. In one month the company sold a total of 834 units of these products. Was the total profit on these items more than $2,000?

(1) During the month, more units of P than units of Q were sold.
(2) During the month, at least 100 units of Q were sold.
[Reveal] Spoiler: OA

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Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink]

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Bunuel wrote:
A company makes and sells two products, P and Q. The costs per unit of making and selling P and Q are $8.00 and $9.50, respectively, and the selling prices per unit of P and Q are $10.00 and $13.00, respectively. In one month the company sold a total of 834 units of these products. Was the total profit on these items more than $2,000?

(1) During the month, more units of P than units of Q were sold.
(2) During the month, at least 100 units of Q were sold.

Kudos for a correct solution.


p+q = 834
we need to know whether 2p + 3.5q > 2,000
(1) During the month, more units of P than units of Q were sold.
=> p>q
=> 2p + 3.5q >5.5q
But we do not know the value of q => insufficient
(2) During the month, at least 100 units of Q were sold.
=> q>=100, p <=734
=> 2p + 3.5q >= 2p + 350
Insufficient
(1) + (2): p>834/2 = 417 => 2p + 3.5q >= 2p + 350 >834+350

Do not know the valute of 2p + 3.5q

Insufficient

Ans: E

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Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink]

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Profit per unit of P = 10-8 = 2
Profit per unit of Q = 13-9.5 = 3.5

Let number of units of P sold = p
number of units of Q sold = q
Total number of units sold ,p+q= 834

is 2p + 3.5 q > 2000 ?

1.
p> q
If p = 834
then 2p = 1668 < 2000

If p = 418 , q = 416
2* 418 + 416 * 3.5 , which will be greater than 2000

Insufficient

2.
q=100
100 * 3.5 + 734* 2 <2000


If q= 834
834*3.5 > 2000

Combining
Still insufficient
Answer E

We can also solve this using weighted average
If total profit in selling 834 items is 2000
Then profit per item = 2000/ 834 = 2.4

2 --2.4-----3.5

1. If the p=number of units of P sold is equal to number of units of Q=q, then profit per item will be the average of 2 and 3.5 that is 2.75 .
If p is marginally greater than q , then profit per item will be marginally less than 2.75.
As p increases , then profit per item will move towards 2 .

Not sufficient

2.Similarly , when q is equal to 100 or marginally greater than 100 , then profit per item will be near 2 . The distance will be in the inverse proportion of number of items sold.
When q increases , profit per unit will per unit will increase and reach 3.5 (when q will reach 834)

Combining, we get
Still insufficient
Answer E
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Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink]

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I think the answer is 'A,' I am unsure why 'E' is the answer. The stem basically asks is "2P + 3.5Q > 2,000" and the stem also states 834 unites were sold. Stmt A states that "p > q" so the lowest values to make that statement true is 418 (p) and 416 (q) which gives us 836 + 1,456 which is greater than 2,000.

Where is the hole in my thinking?

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Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink]

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AS7x wrote:
I think the answer is 'A,' I am unsure why 'E' is the answer. The stem basically asks is "2P + 3.5Q > 2,000" and the stem also states 834 unites were sold. Stmt A states that "p > q" so the lowest values to make that statement true is 418 (p) and 416 (q) which gives us 836 + 1,456 which is greater than 2,000.

Where is the hole in my thinking?



AS7x ,

Statement1 : p> q
p can take any value from 418 to 834 .Let's consider the below 2 cases-


Case 1.If p = 834
then 2p = 1668 < 2000

Case 2.If p = 418 , q = 416
2* 418 + 416 * 3.5 , which will be greater than 2000

Hope it helps!! :)
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Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink]

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Bunuel, Skywalker18 :
My biggest problem is understanding the implied inequality. It takes me sometime to grab the direction of inequalities and then form equations. It's specific to these types of problems involving "word problems+DS+inequality" combo. I think I need more practice. Can you please suggest more similar problems? Thanks again

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Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink]

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A company makes and sells two products, P and Q. The costs per unit of making and selling P and Q are $8.00 and $9.50, respectively, and the selling prices per unit of P and Q are $10.00 and $13.00, respectively. In one month the company sold a total of 834 units of these products. Was the total profit on these items more than $2,000?

(1) During the month, more units of P than units of Q were sold.
(2) During the month, at least 100 units of Q were sold.

In the original condition, it is the question frequently given in the Gmat Math test, which is "2 by 2" like the table below.
첨부
In the above a+b=834, there are 2 variables(a,b) and 1 equation(a+b=834), which should match with the number of equations. So you need 1 more equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer
In 1), despite a>b, a,b)=(450,384) -> yes, (a,b)=(750, 134) -> no, which is not sufficient.
In 2), despite b>=100, (a,b)=(450,384) -> yes, (a,b)=(750, 134) -> no, which is not sufficient.
In 1) & 2), (a,b)=(450,384) -> yes, (a,b)=(750, 134) -> no, which is not sufficient. Therefore, the answer is E.


-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink]

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New post 15 Dec 2015, 21:27
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A company makes and sells two products, P and Q. The costs per unit of making and selling P and Q are $8.00 and $9.50, respectively, and the selling prices per unit of P and Q are $10.00 and $13.00, respectively. In one month the company sold a total of 834 units of these products. Was the total profit on these items more than $2,000?

(1) During the month, more units of P than units of Q were sold.
(2) During the month, at least 100 units of Q were sold.

In the original condition, it is the question frequently given in the Gmat Math test, which is "2 by 2" like the table below.
Attachment:
GCDS Bunuel     A company makes and sells two products (20151215).jpg
GCDS Bunuel A company makes and sells two products (20151215).jpg [ 32.29 KiB | Viewed 10771 times ]

In the above a+b=834, there are 2 variables(a,b) and 1 equation(a+b=834), which should match with the number of equations. So you need 1 more equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer
In 1), despite a>b, a,b)=(450,384) -> yes, (a,b)=(750, 134) -> no, which is not sufficient.
In 2), despite b>=100, (a,b)=(450,384) -> yes, (a,b)=(750, 134) -> no, which is not sufficient.
In 1) & 2), (a,b)=(450,384) -> yes, (a,b)=(750, 134) -> no, which is not sufficient. Therefore, the answer is E.


-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink]

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New post 13 Jun 2016, 08:19
Skywalker18 wrote:
Profit per unit of P = 10-8 = 2
Profit per unit of Q = 13-9.5 = 3.5

Let number of units of P sold = p
number of units of Q sold = q
Total number of units sold ,p+q= 834

is 2p + 3.5 q > 2000 ?

1.
p> q
If p = 834
then 2p = 1668 < 2000

If p = 418 , q = 416
2* 418 + 416 * 3.5 , which will be greater than 2000

Insufficient

2.
q=100
100 * 3.5 + 734* 2 <2000


If q= 834
834*3.5 > 2000

Combining
Still insufficient
Answer E

We can also solve this using weighted average
If total profit in selling 834 items is 2000
Then profit per item = 2000/ 834 = 2.4

2 --2.4-----3.5

1. If the p=number of units of P sold is equal to number of units of Q=q, then profit per item will be the average of 2 and 3.5 that is 2.75 .
If p is marginally greater than q , then profit per item will be marginally less than 2.75.
As p increases , then profit per item will move towards 2 .

Not sufficient

2.Similarly , when q is equal to 100 or marginally greater than 100 , then profit per item will be near 2 . The distance will be in the inverse proportion of number of items sold.
When q increases , profit per unit will per unit will increase and reach 3.5 (when q will reach 834)

Combining, we get
Still insufficient
Answer E

Using 2p+3.5q>2000 and knowing that p+q=834 we can substitute q for p and get one equation with one variable: p=834-q => 1668-2q+3.5q>2000 Hence the question basically asks if 1.5q>332 => q>221. Using both statement together it is clear that q can be less that 221 or more than 221.
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Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink]

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Bunuel wrote:
A company makes and sells two products, P and Q. The costs per unit of making and selling P and Q are $8.00 and $9.50, respectively, and the selling prices per unit of P and Q are $10.00 and $13.00, respectively. In one month the company sold a total of 834 units of these products. Was the total profit on these items more than $2,000?

(1) During the month, more units of P than units of Q were sold.
(2) During the month, at least 100 units of Q were sold.



Here is now I will approach it:

Profit on per unit of P = $2
Profit on each unit of Q = $3.50
The company sold a total of 834 units.
If all units were P, revenue = 834 * 2 = 1668
If all units were Q, revenue = 834 *3.5 = more than 2400

Had they been split evenly between P and Q, it would have sold 417 units of each.
This would give a revenue of 417*2 + 417*3.5 = 834 + (something above 1200) = more than 2000

(1) During the month, more units of P than units of Q were sold.
There were more units of P. If say there were 418 units of P and 416 of Q, the revenue would remain more than 2000. If there were mostly P sold, revenue would go below 2000. Not sufficient.

(2) During the month, at least 100 units of Q were sold.
100 units of Q give an additional 100*1.5 = 150 dollars only. So a split such as 734-100 would give a revenue of 1668+ 150 (less than 2000).
Again P and Q split could be anything such as 417-417 in which case revenue would be more than 2000.
Not sufficient

Using both statements, the split of P-Q can be 418-416 (more than 200 revenue) or 734-100 (revenue less than 2000)

Answer (E)
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Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink]

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Bunuel wrote:
A company makes and sells two products, P and Q. The costs per unit of making and selling P and Q are $8.00 and $9.50, respectively, and the selling prices per unit of P and Q are $10.00 and $13.00, respectively. In one month the company sold a total of 834 units of these products. Was the total profit on these items more than $2,000?

(1) During the month, more units of P than units of Q were sold.
(2) During the month, at least 100 units of Q were sold.


From the stem we get:

Profit of P = 10 – 8 = 2
Profit of Q = 13 – 9.5 = 3.5

P + Q = 834 => 2P = 2(834 – Q) => 2P = 1668 – 2Q

Question : 2P + 3.5Q > 2000 ?
Substitute 2P in the question: (1668 – 2Q) + 3.5Q > 2000?

The question becomes: is Q > 221.3?

1) P > Q = > 417 > Q > 0, INSUFFICIENT
2) Q > 100 => INSUFFICIENT
1 and 2 => 417 > Q> 100 => INSUFFICIENT. If Q is 300 the answer is YES; if Q is 200 the answer is NO.

Answer is E
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Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink]

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Hello together,

I understand the question and I understand the way to get the result as well.
But my problem is, that I need too much time on such tasks. Because I have to build up the equations.
Does anybody know a strategy to recognize the result due to hidden clues in a minimum of the time? Like "if in both satements are something with "at least" or "more than" it is not solvable"?

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Re: A company makes and sells two products, P and Q. The costs per unit of   [#permalink] 11 Nov 2017, 04:32
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