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goyalsau: Legendary Member; Posts: 866; Joined: Mon Aug 02, 2010 6:46 pm; Location: Gwalior, India; Thanked: 31 times

by goyalsau » Fri Oct 15, 2010 12:45 am

The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of âˆš2.(x)-x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?

$5.50
$5.10
$5.30
$5.60
$4.50

Saurabh Goyal
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EveryBody Wants to Win But Nobody wants to prepare for Win.

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Source: Beat The GMAT — Problem Solving | Fri Oct 15, 2010 12:45 am

shovan85: Community Manager; Posts: 991; Joined: Thu Sep 23, 2010 6:19 amFollowed by: 24 members; Location: Bangalore, India; Thanked: 146 times

by shovan85 » Fri Oct 15, 2010 1:18 am

IMO D

When Corn (C) increases by 5x/day
Wheat (W) decrease by x(sqrt(2)-1) = .4x/day (approx)

So we can say, per day if W decreases by 4x C increases by 50x

The price diff as of now is 5.80 - 3.20 = $2.60

So this much difference will be overcome someday as we do not know x, however we can say that total 2.60 can be overcome by 50+4 = 54 x (I mean C is moving towards the price of W and vice-versa)

Thus,
54 x --> 2.6
1 x --> 2.6/54
50 x (as C increases by 50x) --> (2.6/54) * 50 = 2.40 (approx)

Thus Answer is $3.2 + $2.4 = $5.60 .

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