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A company makes and sells two products, A, and B. The costs per unit

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A company makes and sells two products, A, and B. The costs per unit  [#permalink]

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New post 01 Nov 2019, 04:11
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A company makes and sells two products, A, and B. The costs per unit of making and selling A and B are $8.00 and $9.50, respectively, and the selling prices per unit of A and B are $10.00 and $12.00, 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 A than units of B were sold.
(2) During the month, at least 100 units of B were sold.

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

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New post 01 Nov 2019, 05:23
1
Given:
COP SP # Profit(Rs/pc)
A--> 8$ 10$ x 2$
B--> 9.5$ 12$ y 2.5$

x+y=834

Q: is 2x+2.5y>2000?

St 1: x>y
max value of x=833
therefore value of y=1
2x+2.5y=833*2+2.5*1=1666+2.5=1668.5. No
max value of y=416
therefore value of x=418
2x+2.5y=418*2+416*2.5=836+832+208=1876.No

Either way answer is No. sufficient

2)y>100
let's say min value of y=100, then x=734
2x+2.5y=1468+250=1710<2000. no
lets say max value of y=833, then x=1
2x+2.5y=2*1+833*2.5=2+1666+416.5>2000. yes
Insufficient.

Ans:A
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A company makes and sells two products, A, and B. The costs per unit  [#permalink]

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New post Updated on: 04 Nov 2019, 01:10
given CP of A&B
and SP of A&B
net price gain of A&B ; 10-8 ; 2$ and 12-9.5 ; 2.5 $
total units sold ; 834 = A+B

#1
During the month, more units of A than units of B were sold.
A+B=834
2*833+2.5*1 = 1668.5 NO
at max of A ; so answer will be NO sufficient

#2
During the month, at least 100 units of B were sold
B>=100 so A can be atleast 734
profit ; 100* 2.5+ 734 * 2 = $1718 NO
734*2.5+100*2 = 2035$ YES
insufficient
IMO A

A company makes and sells two products, A, and B. The costs per unit of making and selling A and B are $8.00 and $9.50, respectively, and the selling prices per unit of A and B are $10.00 and $12.00, 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 A than units of B were sold.
(2) During the month, at least 100 units of B were sold.

Originally posted by Archit3110 on 01 Nov 2019, 06:29.
Last edited by Archit3110 on 04 Nov 2019, 01:10, edited 1 time in total.
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A company makes and sells two products, A, and B. The costs per unit  [#permalink]

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New post Updated on: 04 Nov 2019, 05:26
A+B= 834---eqn 1

is 10A+12B-8A-9.5B>2000?

2A-2.5B>2000?---eqn 2

(1) During the month, more units of A than units of B were sold.
A+B=834
let A= 418-(least value of A) & B=416---- yes (2A+2.5B>2000)

option A is sufficient

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

A+B=834
B=100
A=734
734*2.5+100*2 = 2035 yes
734*2+ 100*2.5 =1718 no

b is insufficient

A is the correct answer
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Originally posted by sampriya on 01 Nov 2019, 06:37.
Last edited by sampriya on 04 Nov 2019, 05:26, edited 1 time in total.
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Re: A company makes and sells two products, A, and B. The costs per unit  [#permalink]

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New post 01 Nov 2019, 06:40
Is something wrong with the statement "The costs per unit of making and selling A and B are $8.00 and $9.50, respectively, and the selling prices per unit of A and B are $10.00 and $12.00, respectively" ??
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Re: A company makes and sells two products, A, and B. The costs per unit  [#permalink]

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New post 01 Nov 2019, 10:04
1
2a+2.5b value greater/lesser than 2000? For 834units

1.During the month, more units of A than units of B were sold.

If we consider

2*833+1*2.5=1668.5...so it can never be >2000
2*418+2.5*416<2000

So its sufficient

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

If b=100 then 734*2+100*2.5<2000

But If b=800 then
34*2+800*2.5>2000


Insufficient


So OA:A

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

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New post 01 Nov 2019, 14:14
1
Let's assume the nos. of product A is a and nos. of product B is b.

From the given info,

Net profit = 2a + 2.5b
And, a+b = 834

1) a>b
In this case minimum possible value of a = 418
=> b = 416
=> net profit = 836 + 1040 < 2000

And max. value of a = 833
=> b = 1
=> net profit = 1666 + 2.5 < 2000

Therefore, option 1 alone is sufficient.

2) b >= 100

If we take minimum value of b = 100,
Then a = 734
And net profit = 1468 + 250 < 2000

And if we take max possible value of b = 833,
Then a = 1
And net profit = 2.5 x 833 + 2 x 1

Although we can calculate the above expression but there is no need to do so since we know that 800x2.5 = 2000. Therefore above expression is greater than 2000.

Since in one case of option 2) we are getting a value less than 2000 and in another case we are getting a value more than 2000 therefore this option alone is not sufficient enough.

Answer is (A)

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

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New post 01 Nov 2019, 15:57
1
(10A —8A) + (12B —9.5B) > 2000
2A+ 2.5B > 2000

—> A+ 1.25B > 1000 ???
—> A+ B= 834

A = 834 —B
834 —B +1.25B > 1000
0.25*B > 166
B > 166/0.25= 664
—> B >664 ???

B= 834 —A
834 —A> 664
A < 170 ???

(Statement1):
A> B —>( always No)

Sufficient

(Statement 2) B >100
Clearly insufficient

The answer is A .

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

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New post 01 Nov 2019, 16:49
1
A is my answer.

Prompt
Profit from product A= $2.00 per unit
Profit from product B= $2.50 per unit

Three situations here:
1. If the average profit is $ 2.25 per unit, # of product A sold=# of product B sold.
2. If the average profit is LESS than $ 2.25 per unit, # of product A sold># of product B sold.
3. If the average profit is GREATER than $ 2.25 per unit, # of product A sold<# of product B sold.

The question asks: is Average profit GRATER than 2000/834 (or almost 2.40 which is greater than $2.25)?
in other words, is the NUMBER of Product B sold is GREATER than the NUMBER of Product A sold?. The third situation above.

Statement 1 Sufficiently says NO to the answer.
Statement 2 is NOT SUFFICIENT
A=734, B=100 [No to main question]
A=1, B=733 [YES to main question]
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Re: A company makes and sells two products, A, and B. The costs per unit  [#permalink]

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New post 01 Nov 2019, 18:47
I would go for A.

How to calculate whether 2.25 is GREATER or LESS than 2000/834 ?
2.25..........................2000/834
834*2.25 ...................2000 [multiplying both by 8.34]
=834*2+834/4 ...........2000
=1668+208...............2000
=1876 which is LESS than 2000.

than means 2.25 is LESS than 2000/834
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Re: A company makes and sells two products, A, and B. The costs per unit  [#permalink]

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New post 02 Nov 2019, 01:33
1
Profit on each item of A = 10 - 8 = $2
Profit on each item of B = 12 - 9.5 = $2.5

(1) During the month, more units of A than units of B were sold.

Profit when A & B are sold equally = 834/2*2 + 834/2*2.5 = 834 + 1042.5 = $1876.5

If A is sold more, Profit will decrease as the profit on A is less than that of B
Eg: If all items sold are A, Profit = 834*2 = $1668

So, we can clearly say that Profit can never be more than $2000 if A > B --> A definite NO --> Sufficient


(2) During the month, at least 100 units of B were sold.
--> Number of B units sold will lie between 100 & 834, inclusive

Case 1: B = 100 & A = 734
--> Profit = 734*2 + 100*2.5 = 1468 + 250 = $1718 (< $2000)

Case 2: B = 834 & A = 0
--> Profit = 0*2 + 834*2.5 = 0 + 2085 = $2085 (> $2000)

Two outcomes are possible --> Insufficient

IMO Option A
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Re: A company makes and sells two products, A, and B. The costs per unit  [#permalink]

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New post 03 Nov 2019, 16:08
1
Quote:
A company makes and sells two products, A, and B. The costs per unit of making and selling A and B are $8.00 and $9.50, respectively, and the selling prices per unit of A and B are $10.00 and $12.00, 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 A than units of B were sold.
(2) During the month, at least 100 units of B were sold.


cost(A;B)=8;9.50
price(A;B)=10;12
profit(A;B)=2;2.5

a+b=834… a=834-b
2a+2.5b>2000
2(a+b)+0.5b>2000
a+b+0.25b>1000
(834-b)+b+0.25b>1000
0.25b>166…b>166/0.25…
find if b>664 is true;

(1) During the month, more units of A than units of B were sold. sufic.

a>834/2…a>417…b<417

ie.
B=660…A=834-660=174
2(174)+2.5(660)>2000?…348+1650>2000?…1998>2000? no

B=664…A=834-664=170
2(170)+2.5(664)>2000?…340+1660>2000?…2000>2000? no

B=665…A=834-665=169
2(169)+2.5(665)>2000?…yes

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

Answer (A)
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Re: A company makes and sells two products, A, and B. The costs per unit   [#permalink] 03 Nov 2019, 16:08
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