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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Fri May 13, 2011 7:32 am

During a sale, the price per pound of raisins was decreased by 40 percent. Simon decides to increase the weight of raisins that he buys so that he spends the same amount on raisins that he would have spent on raisins before the sale. By approximately what percent does Simon increase the weight of the raisins that he buys?

30%

33%

40%

60%

67%

oa-E

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Source: Beat The GMAT — Problem Solving | Fri May 13, 2011 7:32 am

manpsingh87: Master | Next Rank: 500 Posts; Posts: 436; Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members; Thanked: 72 times

by manpsingh87 » Fri May 13, 2011 7:51 am

bblast wrote:During a sale, the price per pound of raisins was decreased by 40 percent. Simon decides to increase the weight of raisins that he buys so that he spends the same amount on raisins that he would have spent on raisins before the sale. By approximately what percent does Simon increase the weight of the raisins that he buys?

30%

33%

40%

60%

67%

oa-E

let price/pound be x and no. of pounds of raisins bought =y;
and assume that he increases the weight of the raisins by z;
as he is spending the same amount, therefore we have;
x*y=0.6x(y+z);
10y=6y+6z;
z=2/3y;
now percentage change in weight = (2/3)y/y*100=66.66% which is approximately 67% hence E

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri May 13, 2011 7:56 am

bblast wrote:During a sale, the price per pound of raisins was decreased by 40 percent. Simon decides to increase the weight of raisins that he buys so that he spends the same amount on raisins that he would have spent on raisins before the sale. By approximately what percent does Simon increase the weight of the raisins that he buys?

30%

33%

40%

60%

67%

oa-E

Let price per pound = 10.
Let number of pounds = 6.
Cost = 10*6 = $60.

Price per pound reduced by 40% = $6.
To spend $60, the number of pounds purchased = (Total cost)/(Reduced price) = 60/6 = 10.

Increase in pounds = 10-6 = 4.
% increase = (Increase in pounds)/(Original pounds)*100 = 4/6 * 100 = 66.67%.

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Whitney Garner: GMAT Instructor; Posts: 273; Joined: Tue Sep 21, 2010 5:37 amFollowed by: 74 members; Location: Durham, NC; Thanked: 154 times; GMAT Score:770

by Whitney Garner » Fri May 13, 2011 9:49 am

bblast wrote:During a sale, the price per pound of raisins was decreased by 40 percent. Simon decides to increase the weight of raisins that he buys so that he spends the same amount on raisins that he would have spent on raisins before the sale. By approximately what percent does Simon increase the weight of the raisins that he buys?

30%

33%

40%

60%

67%

oa-E

Hi bblast!

One final way to solve this is to think generally about the literal equation: T = PQ, where T=total cost, P=price and Q=quantity.

If price falls by 40% (or 2/5), the new price is equivalent to 1-2/5 or 3/5 of the original price (3/5)*P.

Plug this in and now: T = (3/5)P*Q

To counter that (3/5) reduction to the right side, we need to multiply by its reciprocal (5/3, because 3/5 * 5/3 = 1 and then we will be back where we started).

T = (3/5)P*(5/3)Q
T = PQ

That means Q needs to be 5/3 or 166.6% of its original size - this is an increase of approximately 66.7%

Whit

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