BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Manhattan Advanced Quant

Expert replies
by gmat_for_life » Thu May 26, 2016 9:43 am
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
Join the discussion
Source: — Problem Solving |

by [email protected] » Thu May 26, 2016 10:12 am
Hi Amit,

This question could be solved rather easily by TESTing THE ANSWERS. Since you're asking about the algebraic approach you used, you made a small error in your calculations. $18 can be used to buy cheap socks OR 3 fewer pairs of expensive socks. In your calculation, you assume that BOTH are purchased for $18, but that's not the case. If you change your $18 to $36, then you can continue with the algebra and get the correct answer.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Join the discussion

by gmat_for_life » Thu May 26, 2016 10:55 am
Thanks a lot Rich!

That was so silly of me indeed! Should have noticed the wordings of the question properly.

Regards,
Amit
Join the discussion

by Matt@VeritasPrep » Thu May 26, 2016 2:27 pm
Algebraically you'd have

(2x - 1) * (a - 3) = 18

and

x * a = 18

The first equation is really

2ax - a - 6x + 3 = 18

We want to solve for a, so we'll sub out a*x = 18 and x = 18/a, giving

2*18 - a - 6*(18/a) + 3 = 18

0 = a - 108/a - 21

0 = a² - 21a - 108

0 = (a - 12) * (a - 9)

So a = 9 or a = 12, and we're set.
Join the discussion