During a 10-day craft fair, a print studio sold only posters and

Question

During a 10-day craft fair, a print studio sold only posters and banners. Each poster sold for $18 and cost $10 to produce, while each banner sold for $30 and cost $16 to produce. If the studio sold 110 posters and banners in total during the fair, was its profit from these sales more than $1,200?

(1) The studio used 290 ounces of ink to produce the items sold, with each poster requiring 1 ounce and each banner requiring 4 ounces.

(2) The studio sold more banners than posters.

M47-219

Bunuel · Accepted Answer

GMAT Club Official Solution:

During a 10-day craft fair, a print studio sold only posters and banners. Each poster sold for $18 and cost $10 to produce, while each banner sold for $30 and cost $16 to produce. If the studio sold 110 posters and banners in total during the fair, was its profit from these sales more than $1,200?

(1) The studio used 290 ounces of ink to produce the items sold, with each poster requiring 1 ounce and each banner requiring 4 ounces.

Let b be the number of banners sold. Since 110 items were sold in total, the number of posters sold is 110 - b.

So:

1 * (110 - b) + 4 * b = 290

b = 60

Thus, the studio sold 60 banners and 50 posters.

Each poster gives a profit of $8, and each banner gives a profit of $14. So the total profit is:

50 * 8 + 60 * 14 = 400 + 840 = 1,240

Since 1,240 is more than 1,200, the answer is yes.

Sufficient.

(2) The studio sold more banners than posters.

Since 110 items were sold in total, the smallest possible number of banners is 56.

Since each banner gives more profit than each poster, the total profit is lowest when the number of banners is as small as possible. At 56 banners and 54 posters, the profit is:

56 * 14 + 54 * 8 = 784 + 432 = 1,216

Since even the lowest possible profit is more than $1,200, the answer is yes.

Sufficient.

Answer: D.

paragw · Answer

Let posters = P, banners = B.
P + B = 110
Profit = 8P + 14B. Need to know if profit > 1200.

(1) Ink: P + 4B = 290
Subtract: (P + 4B) − (P + B) = 290 − 110 3B = 180 B = 60, P = 50
Profit = 8(50) + 14(60) = 400 + 840 = 1240 > 1200.
 Sufficient .

(2) B > P and P + B = 110.
Possible: P = 54, B = 56 → Profit = 1216 (>1200) P = 0, B = 110 → Profit = 1540 (>1200)
Since B > P ⇒ B ≥ 56.
Minimum profit occurs at B = 56: Profit = 8(54) + 14(56) = 1216 > 1200.
Always YES.
 Sufficient .

Answer:  D

vasu1104 · Answer

Posters CP= 10 SP=18 sold =x Banners CP= 16 SP=30 Sold=110-x profit = SP -CP x(18-10) + (110-x)(30-16) 8x+ 1540-14x >1200 340> 6x x< 56.6 ? S-1 1 poster need 1 ounce. so for x poster, need x ounce. 1 banner need 4 ounce. so 1110- need 4(110-x) once. so total =290 ounce x + 4(110-x) = 290 x+440-4x =290 150 = 3x x=50 sufficient. S-2 110-x>x 110>2x x<55 if its less than 55 then its less than 56 as well. sufficient. option D

SS990 · Answer

Given:

no. 
 P 
 B 
 110 
 
  CP 
 10 
 16

SP 
 18 
 30

P 
 8 
 14

To find if P>1200

1) sold numbers use ink at P:B=1:4 this is sufficient to answer the number of P and B to det profit

2) B>P i.e B>55 even if B=56 and P=54, we get P>1200 hence this is sufficeint

So the answer is D

MarkGMATMentor · Answer

As on many DS problems, here you can save yourself time by using reasoning rather than immediately calculating.

From the prompt, we know the profit per poster is 18 - 10 = $8

The profit per banner is 30 – 16 = $14

So the question can be restated as:
8p + 14b > $1,200 ?

We also know the posters and banners add to 110:
p + b = 110

Statement 1:

This tells you that 1p + 4b = 290

Now you have two different simultaneous equations with the same two variables. A system of this type can always be solved, giving you values for p and b.

Plugging these values into 8p + 14b will result in a total dollar figure. Either this amount is more than $1,200 (a definite YES) or it isn’t (a definite NO). No need to actually calculate.  Sufficient.

Statement 2:

If the studio sold more banners than posters, a YES is clearly possible. 100 banners at $14 per banner, for example, would give you $1,400 profit, which is already more than $1,200.

But can you get an answer of NO? Try the other extreme. If there were an equal number of posters and banners, the weighted average profit per unit would be $11 (right in the middle of $8 and $14). Then, $11 X 110 = $1,210, which is also more than $1,200. The answer must be YES.  Sufficient.  The answer is D.

(Note that technically, there must be  more  banners than posters. So the total actually must be even more than $1,210.)

Remember to reason your way through DS problems before diving into calculations, and you can save yourself time and potential frustration.

During a 10-day craft fair, a print studio sold only posters and

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