In a certain clothing store, the most expensive pair of socks sells for one dollar less than
twice the price of the cheapest pair of socks. A customer notices that for exactly $18, she can
buy three fewer pairs of the most expensive socks than the cheapest socks. What could be the
number of pairs of the cheapest socks she could have purchased?
(A) 3
(B) 5
(C) 6
(D) 12
(E) 36
[spoiler]The OA to this question is Option D. Could you please analyze my solution and let me know whats wrong?
Let the cost of cheap pairs be =x
Cost of Expensive pair=(2x-1)
Number of cheap socks=(a)
Number of Expensive socks=(a-3)
Therefore ax+(a-3)(2x-1)=18
which implies a=(6x+15)/(3x-1)
if we substitute x as 6, a would be equal to 3. Thus I arrived at A as the answer.[/spoiler]
Regards,
Amit
twice the price of the cheapest pair of socks. A customer notices that for exactly $18, she can
buy three fewer pairs of the most expensive socks than the cheapest socks. What could be the
number of pairs of the cheapest socks she could have purchased?
(A) 3
(B) 5
(C) 6
(D) 12
(E) 36
[spoiler]The OA to this question is Option D. Could you please analyze my solution and let me know whats wrong?
Let the cost of cheap pairs be =x
Cost of Expensive pair=(2x-1)
Number of cheap socks=(a)
Number of Expensive socks=(a-3)
Therefore ax+(a-3)(2x-1)=18
which implies a=(6x+15)/(3x-1)
if we substitute x as 6, a would be equal to 3. Thus I arrived at A as the answer.[/spoiler]
Regards,
Amit
