A tricky word problem

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billzhao: Senior | Next Rank: 100 Posts; Posts: 80; Joined: Mon Feb 02, 2009 6:36 am; Thanked: 10 times

by billzhao » Tue Feb 24, 2009 2:03 am

My answer is (E). OA is (C). Please help to explain. Thanks.

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Source: Beat The GMAT — Problem Solving | Tue Feb 24, 2009 2:03 am

sureshbala: Master | Next Rank: 500 Posts; Posts: 319; Joined: Wed Feb 04, 2009 10:32 amFollowed by: 9 members; Location: Delhi; Thanked: 84 times

by sureshbala » Tue Feb 24, 2009 3:35 am

Let C1 and C2 be the respective cost prices of the first and second share.

Given that 120%(C1)=96, so C1 = 80
Also 80%(C2) = 96 , so C2 = 120.

Hence both the stocks are purchased for 200$ and both of them are sold for 192$. So a loss of 8$

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You can also remember a small note here...

When two articles are sold at the same price and if the gain % (say x%) on one article is same as the loss % (x%)on the other article, then overall there always will be a loss and the overall loos% = (x^2)/100 %.

Coming this problem, since the gain % = loss % = 20%, the overall loss = 4%.

So 96%(C1+C2) = 192.
Hence C1+C2 = 200.

Thus there will be a loss of 8$ in the entire transaction.

Another small note.....

When two articles are purchased at the same price and if the gain % (say x%) from the sale of one article is same as the loss % (x%) incurred from the sale of the other article, then overall there will neither profit nor loss

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