A shoe store purchased 50 pairs of running shoes and sold some of them

Question

A shoe store purchased 50 pairs of running shoes and sold some of them at $P per pair. The store sold each of the remaining pairs at $5, where S < P. If the store's average profit per pair of these running shoes was $6, what was the value of S?

(1) The store sold 28 pairs of the running shoes at $P per pair.
(2) P = 108

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Attachment:

2024-01-24_13-34-04.png

stne · Accepted Answer

Correct question:

A shoe store purchased 50 pairs of running shoes and sold some of them at $P per pair. The store sold each of the remaining pairs at $5, where S < P. If the store's average profit per pair of these running shoes was $6, what was the value of S?

(1) The store sold 28 pairs of the running shoes at $P per pair.
(2) P = 108

Show Spoiler

Attachment:

2024-01-24_13-34-04.png

Avg profit : Total profit/ 50  =  6  or Total profit  = 300

Total profit : Sales Revenue - Total cost

Sales revenue  = x*p + (50-x)s

Total cost :  50*c

(1) The store sold  28  pairs of the running shoes at $P per pair.

28p +22s -50c = 300

One equation three unknowns.

INSUFF.

(2) P = 108

108x +(50-x)s -50c =300

One equation three unknowns.

INSUFF.

1+2

108*28 + 22s-50c=300

We don't know  c  hence we cannot get the value of  s .

INSUFF.

Ans E

Hope it helped.

gmatophobia · Answer

One way is to solve algebraically, another approach is to use a number line. Solving using the number line approach. Let's assume that the cost price of each pair of shoes is $C. As the store made a profit, we can infer that P > C. On a number line, we can represent P and C as shown below. Screenshot 2024-01-28 201348.png The question also tells us that the value of S is less than P. Hence, we know that S lies to the left of P. We do not have enough information to conclude whether S lies to the left of C, or to the right of C, or at C. Screenshot 2024-01-28 201650.png ...the store's average profit per pair of these running shoes was $6 ... Inference : (C + 6) lies between C and S. Screenshot 2024-01-28 202816.png Statement 1 (1) The store sold 28 pairs of the running shoes at $P per pair. Inference: 28 pairs are sold at $P, and 14 pairs are sold at $S. We don't know the value of P and C. Hence, we don't know how far P is from C or C+6. Hence, we cannot determine the value of S. The statement alone is not sufficient. Eliminate A and D. Statement 2 (2) P = 108 While we know the value of P, the statement provides us with no information on the cost price or the number of pairs sold at this price. Hence, the statement alone is not sufficient. Eliminate B. Combined The statements combined are also not sufficient as we can't still determine the distance between C + 6 and P as the value of C is not known to us. For different values of C, we will arrive at different values of S. Hence, the statements combined are also not sufficient. Option E

KarishmaB · Answer

Using the data of both statements, we find

Number of pairs bought = 50
28 were sold at $108 each
22 were sold at $S each
Overall profit per pair = $6

To use the information of overall profit per pair, we need to know the profit per pair for the 28 shoes sold at $108. Since we don't have the cost price of each pair, we do not know the profit per pair for the 28 shoes. 
Hence we cannot find the value of S and both statements together are not sufficient.

Answer (E)

Let's see how changes in cost price will change the value of S.

Say Cost Price = $91 per shoe
Total cost price = 91 * 50 = 4550
Total selling price = 4550 + 6*50 = 4850
Selling price of 28 shoes = 108*28 = 3024
Selling price of 22 shoes = (4850 - 3024)/22 = $83 = S

Say Cost Price = $80.
Total cost price = 80 * 50 = 4000
Total selling price = 4000 + 6*50 = 4300
Selling price of 28 shoes = 108*28 = 3024
Selling price of 22 shoes = (4300 - 3024)/22 = $58 = S

soumyab12 · Answer

Thanks, I too solved it like this but at the end I thought sometimes even if there are 2 variables, 1 equation is enough to get the answer because there's only 1 solution. Can someone help with how we can eliminate that possibility without solving for the various possibilities? I took way too long because I was trying to see if we can get a unique solution from the last eqn

A shoe store purchased 50 pairs of running shoes and sold some of them

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