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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  [#permalink]

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25 Oct 2015, 09:04
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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. _________________ ##### Most Helpful Expert Reply Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 9772 Location: Pune, India Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink] ### Show Tags 13 Jun 2016, 23:16 18 7 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)

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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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25 Oct 2015, 11:20
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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

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
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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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25 Oct 2015, 10:11
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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 Intern Joined: 30 Sep 2015 Posts: 3 Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink] ### Show Tags 01 Nov 2015, 15:41 4 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? Verbal Forum Moderator Status: Greatness begins beyond your comfort zone Joined: 08 Dec 2013 Posts: 2426 Location: India Concentration: General Management, Strategy Schools: Kelley '20, ISB '19 GPA: 3.2 WE: Information Technology (Consulting) Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink] ### Show Tags 01 Nov 2015, 20:47 4 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!! _________________ When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long Manager Joined: 15 Dec 2015 Posts: 50 Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink] ### Show Tags 15 Dec 2015, 00:07 1 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8125 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink] ### Show Tags 15 Dec 2015, 22:25 2 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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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 02 Dec 2014 Posts: 353 Location: Russian Federation Concentration: General Management, Economics GMAT 1: 640 Q44 V33 WE: Sales (Telecommunications) Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink] ### Show Tags 13 Jun 2016, 09:19 1 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. _________________ "Are you gangsters?" - "No we are Russians!" Manager Status: GMAT Coach Joined: 05 Nov 2012 Posts: 141 Location: Peru GPA: 3.98 Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink] ### Show Tags 27 Oct 2016, 09:51 8 5 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.

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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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11 Nov 2017, 05:32
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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]

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24 Jan 2018, 04:41
Bumping Bunuel chetan2u niks18 for an alternate solution.
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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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24 Jan 2018, 11:43
Bumping Bunuel chetan2u niks18 for an alternate solution.

As this DS question has lot of information in the question stem, you need to use every information possible before moving on to the statements.

As it turns out my approach to this question was the same as posted by cledgard above.

the question boils down to whether q>221.3 and then reading both the statements become simple.

There might be other simpler approaches which other experts might be able to explain.
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A company makes and sells two products, P and Q. The costs per unit of  [#permalink]

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18 Apr 2018, 15:40
Given:
P + Q = 834
Profit P = $2 Profit Q =$3.5

i) P > Q. The official guide says no information about quantity of P or Q is provided; hence, this is incorrect. I disagree. You do not need either variable to solve for this. The max P can achieve is when Q is 0 (i.e. P = 834 units sold). Hence, total profit will be 834 * $2 =$1668. This by itself is sufficient to answer that the profit is not more than $2k. However, nothing says that Q = 0; thus, let's try the other extreme (i.e. min value of P which occurs when P and Q are as close as possible or 834 / 2 + 1 = P and 834 / 2 - 1 = Q (P > Q). Here, profit = p_min (418) *$2 + q_max (416) * $3.50 =$2292 which is > $2k. Since we receive 2 different answers that make the stem T (case 1) and F (case 2), this statement is insufficient. _________________ If this helped, please give kudos! Veritas Prep GMAT Instructor Joined: 01 Jul 2017 Posts: 79 Location: United States Concentration: Leadership, Organizational Behavior Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink] ### Show Tags 09 Oct 2018, 15:26 Let's talk strategy here. Many explanations of Quantitative questions focus blindly on the math, but remember: the GMAT is a critical-thinking test. For those of you studying for the GMAT, you will want to internalize strategies that actually minimize the amount of math that needs to be done, making it easier to manage your time. The tactics I will show you here will be useful for numerous questions, not just this one. My solution is going to walk through not just what the answer is, but how to strategically think about it. Ready? Here is the full "GMAT Jujitsu" for this question: The target of this question is "total profit", and we know that profit is equal to the selling price minus the cost. Thus, the profit per unit for product P would be $$_P = 10-8 = 2$$, and the profit per unit for product Q would be $$_Q = 13-9.5 = 3.5$$. The total profit would therefore be (where $$P$$ and $$Q$$ represent the number of units of each product): $$T=P(_P )+Q(_Q)$$ $$T=P(2)+Q(3.5)$$ Now that we have set up the basic equation, we need to pause in our discussion here. Many people spend too much time on Data Sufficiency questions because they think they need to get to the bitter end. The question asks “Was the total profit on these items more than$2,000.00?” This is a “Yes/No” question – a very common structure for Data Sufficiency problems. The fundamental trap for problems like these is to bait you into thinking that you actually need to solve for every value. You don’t. As soon as you have enough information to conclude whether you can come up with only one answer to the question, you can move on. For “Yes/No” questions, if you can think of two situations (or two variable inputs) that are consistent with all of the problem’s constraints but come up with different answers to the question, you know a statement is insufficient. In my classes, I call this strategy “Play Both Sides.”

Let’s analyze each statement, and you will see what I mean. Statement #1 tells us that there are more units of $$P$$ than there are units of $$Q$$. Now, look at the shape of the equations. From the question stem, we know that $$P+Q=834$$. “834” is a bit of a messy number, so approximating this would make our analysis a lot easier. First, let’s assume that $$P$$ is roughly equal to $$Q$$, making both values around $$400$$. Thus,

$$T=P(2)+Q(3.5)≈400(2)+400(3.5)≈800+1400≈2200$$

So, it is possible to exceed $$2,000$$, and we know we can answer “Yes” to the question. The next question we ask ourselves is: Can we play both sides? Is it possible to have a solution where the total is under $$2,000$$? If $$P$$ dominated the relationship (in other words, if $$P$$ were around $$800$$, then we would have less than $$2,000$$. After all, $$800*2$$ is only equal to $$1,600$$. We are not even close to the boundary of $$2,000$$, so approximating is sufficient here. Since one scenario would clearly give us a combined profit of less than $$2,000$$ while the other would give a total profit of more than $$2,000$$, Statement #1 is insufficient by itself.

Statement #2 tells us that $$Q$$ is “at least 100 units.” We have already shown by our analysis of Statement #1 that if $$Q$$ is around $$400$$, then the total will exceed $$2,000$$. There is no reason to redo this. As we “Play Both Sides”, we already know that there is a solution where $$Q$$ is “at least 100 units” that allows us to answer [color=#00a651]“Yes”[/color] to the original question. So, we need to know if we can show that the total may be less than $$2,000$$. The phrase “at least” is massive leverage. This is a minimum amount, so let’s see what a minimum amount would do – in other words, if $$Q=100$$. Again, approximating here is more enough. If $$Q=100$$, then $$P≈700$$. Thus:

$$T≈700(2)+100(3.5)≈1400+350≈1750$$

Since we can also show that the total can be less than $$2,000$$, we have “played both sides” and Statement #2 is insufficient.

We now need to look at combining them to see if they are sufficient. But we have already done all the analysis we need. The hypothetical situations we created for Statements #1 and #2 show two possibilities where (1) P can be greater than Q and (2) Q is at least 100. Since we can “play both sides” of this Yes/No question even when the statements are simultaneously true, the answer is “E”.

Now, let’s look back at this problem from the perspective of strategy. This problem can teach us several patterns seen throughout the GMAT. First, minimize your math. You only need to do enough math to prove the answer to the question. With Yes/No questions, this often means “playing both sides” – coming up with two possible solutions that follow the rules of the problem, but give different answers to the question. Second, notice how approximation can often cut through otherwise messy math. This saves time and energy, allowing you to focus on other, potentially harder, questions. And that is how you think like the GMAT.
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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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13 Oct 2019, 20:42
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. VeritasKarishma Bunuel chetan2u MathRevolution What does this language mean : costs per unit of making and selling P and Q are$8.00 and $9.50 cost of making and selling P is 8 this is Cost Price, i understand but what does this mean? should not it be the cost of making only? sellling cost is sp ,right ? Math Expert Joined: 02 Aug 2009 Posts: 8150 Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink] ### Show Tags 13 Oct 2019, 20:55 1 vanam52923 wrote: 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.

VeritasKarishma Bunuel chetan2u MathRevolution
What does this language mean :
costs per unit of making and selling P and Q are $8.00 and$9.50

cost of making and selling P is 8
this is Cost Price, i understand but what does this mean?
should not it be the cost of making only?
sellling cost is sp ,right ?

Cost of making and selling would mean two items - one the actual cost of material and labour AND second the cost of selling incurred in transporting or advertisement or packing or whatever it may be etc
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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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13 Oct 2019, 20:58
chetan2u wrote:
vanam52923 wrote:
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. VeritasKarishma Bunuel chetan2u MathRevolution What does this language mean : costs per unit of making and selling P and Q are$8.00 and $9.50 cost of making and selling P is 8 this is Cost Price, i understand but what does this mean? should not it be the cost of making only? sellling cost is sp ,right ? Cost of making and selling would mean two items - one the actual cost of material and labour AND second the cost of selling incurred in transporting or advertisement or packing or whatever it may be etc thankyou so much Director Joined: 24 Nov 2016 Posts: 748 Location: United States Re: A company makes and sells two products, P and Q. The costs per unit of [#permalink] ### Show Tags 17 Oct 2019, 04:35 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.

volume: 834=p+q; p=834-q;
unit profit p: 10-8=2; q: 13-9.5=3.5

for profit > 2000:
2p+3.5q>2000
2(834-q)+3.5q>2000
-2q+3.5q>2000-1668
1.5q>332…q>664/3~221
q>~221 or p<~613

(1) During the month, more units of P than units of Q were sold. insufic.

if p sold 600, q sold 834-600=234>221, then profit > 2000
if p sold 700, q sold 834-700=134<221, then profit < 2000

(2) During the month, at least 100 units of Q were sold. insufic.

if p sold 600, q sold 834-600=234>221, then profit > 2000
if p sold 700, q sold 834-700=134<221, then profit < 2000

(1&2): insufic.

if p sold 600, q sold 834-600=234>221, then profit > 2000
if p sold 700, q sold 834-700=134<221, then profit < 2000

Re: A company makes and sells two products, P and Q. The costs per unit of   [#permalink] 17 Oct 2019, 04:35
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