M-GMAT question

[Stormgal]

A Bushel and a Peck

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 cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?

(A) $4.50
(B) $5.10
(C) $5.30
(D) $5.50
(E) $5.60

[Jello]

My answer is A

How about OG?

[gmatguyIL]

Is it E ?

Heres how I approached this problem. Please feel free to critique my approach!

Assumed x=1. Eyeballed the difference.
In 50 days, price of corn=320+(50*5)=570
wheat = 580-(50*.41)=559.5 (since sqrt(2)-1=0.41)

In 48 days, corn = 320+(48*5)=560
wheat=580-(48*.41)=560.32

[smtripathi]

For me, it seems to be E.
Here is how i went abt this prob:
Price(corn)=3.2+5x
Price(W)=5.80-Sqrt(2)x+x

so , when the price of Wheat = price of corn:
3.2+5x=5.8-sqrt(2)x+x
==>4x+sqrt(2)x=2.6
==>x=2.6/(4+sqrt(2))
==>x~5.65
hence E.

What is OA

[Stormgal]

We can find a ratio between the rates of increase and decrease for the corn and wheat:



To get rid of the radical sign in the denominator, we can multiply top and bottom by and simplify:



This ratio indicates that for every cent that the price of wheat decreases, the price of corn increases by cents. So if the price of wheat decreases by x cents, the price of corn will increase by cents.

Since the difference in price between a peck of wheat and a bushel of corn is currently $2.60 or 260 cents, the amount by which the price of corn increases plus the amount by which the price of wheat decreases must equal 260 cents. We can express this as an equation:

Amount Corn Increases + Amount Wheat Decreases = 260

We can then rewrite this word equation using variables. Let c be the decrease in the price of wheat in cents:



Notice that the radical 2 was replaced with its approximate numerical value of 1.4 because the question asks for the approximate price. We need not be exact in this particular instance.

If c = 20, we know that the price of a peck of wheat had decreased by 20 cents when it reached the same level as the increased price of a bushel of corn. Since the original price of a peck of wheat was $5.80, its decreased price is $5.80 - $0.20 = $5.60.

(By the same token, since c = 20, the price of a bushel of corn had increased by 20() cents when it reached the same level as the decreased price of a peck of wheat. This is equivalent to an increase of approximately 240 cents. Thus the increased price of a bushel of corn = $3.20 + $2.40 = $5.60.)

The correct answer is E.

[gmatguyIL]

Storm, this may be the "correct" approach to solving it in high school. This approach may take a while to think, formulate and solve in a GMAT. Is this the official explanation for the problem ?

[Stormgal]

Originally Posted by gmatguyIL

Storm, this may be the "correct" approach to solving it in high school. This approach may take a while to think, formulate and solve in a GMAT. Is this the official explanation for the problem ?

Yes, sir.

[greycellz]

Since the rate of decrease is way too less compared to the increase (.414 v/s 5) plug in the greatest value in the answer (5.6)
For the price corn to be 5.6, the increase from 3.2 is 240 cents. Thus no. of days elapsed:
240/5 = 48. In 48 days, the price of wheat would be: 5.8 - 48*.414 ~ 5.6
answer. E

(Assume x to be 1)

[Sargataur]

i alo agree that manhattan;s appraoch to the question is not the irght one..thx for sharing the question storm

[Vakul]

my approach:

320 + 5x = 580 - .41x; x = # of days after price is same;

solving for x; x is approximately 48, thus the requiremd price is 320 + 5 * 48 = 560 cents = $5.6

took about 2 mins to solve