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Math Expert V
Joined: 02 Sep 2009
Posts: 59590
A company makes and sells two products, A, and B. The costs per unit  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 41% (02:46) correct 59% (02:22) wrong based on 51 sessions

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Competition Mode Question

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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Intern  S
Joined: 30 Nov 2017
Posts: 47
GMAT 1: 690 Q49 V35 Re: A company makes and sells two products, A, and B. The costs per unit  [#permalink]

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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
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5446
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
A company makes and sells two products, A, and B. The costs per unit  [#permalink]

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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.
Manager  S
Joined: 23 Nov 2018
Posts: 239
GMAT 1: 650 Q49 V28 GPA: 4
A company makes and sells two products, A, and B. The costs per unit  [#permalink]

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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

_________________

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.
Senior Manager  P
Joined: 07 Mar 2019
Posts: 436
Location: India
GMAT 1: 580 Q43 V27 WE: Sales (Energy and Utilities)
Re: A company makes and sells two products, A, and B. The costs per unit  [#permalink]

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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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Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
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Senior Manager  P
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Schools: Ross '22, ISB '20, NUS '20
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Re: A company makes and sells two products, A, and B. The costs per unit  [#permalink]

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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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Intern  B
Joined: 21 Sep 2016
Posts: 21
Re: A company makes and sells two products, A, and B. The costs per unit  [#permalink]

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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.

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Senior Manager  G
Joined: 25 Jul 2018
Posts: 391
Re: A company makes and sells two products, A, and B. The costs per unit  [#permalink]

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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

Posted from my mobile device
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WE: Analyst (Commercial Banking)
Re: A company makes and sells two products, A, and B. The costs per unit  [#permalink]

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1

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

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

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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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Joined: 24 Nov 2016
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Re: A company makes and sells two products, A, and B. The costs per unit  [#permalink]

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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. 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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