PS bushel price

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sarwan: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Wed May 26, 2010 3:26 amFollowed by: 1 member

by sarwan » Tue Aug 10, 2010 7:08 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 {sqrt(2x)- x} 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

Ans: E

Pls explain the reason.

Last edited by sarwan on Wed Aug 11, 2010 7:51 pm, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Tue Aug 10, 2010 7:08 am

kmittal82: Master | Next Rank: 500 Posts; Posts: 324; Joined: Mon Jul 05, 2010 6:44 amFollowed by: 3 members; Location: London; Thanked: 70 times

by kmittal82 » Tue Aug 10, 2010 7:13 am

What is 'x' ?

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sarwan: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Wed May 26, 2010 3:26 amFollowed by: 1 member

by sarwan » Wed Aug 11, 2010 7:51 pm

kmittal82 wrote:What is 'x' ?

X is an any variable.

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Asif: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Thu May 20, 2010 5:08 amFollowed by: 1 member; Location: Dhaka

by Asif » Wed Aug 11, 2010 8:09 pm

If the answer is E then the question needs little modification, I am not sure though. Instead of the price of wheat decreasing at a rate "square root (2x)-x" it needs to be "square root(2)x-x". If considered the latter one the problem can be solved in the following way:

320 + 5x = 580 - .41x (all prices converted to cents)

x = # of days after price is same

x is approximately 48

Therefore, the required price is 320 + 5 * 48 = 560 cents or $5.6

Answer: E

Request for any other explanation.

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aarati: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Thu Aug 05, 2010 3:15 am

by aarati » Wed Aug 11, 2010 10:27 pm

Asif wrote:If the answer is E then the question needs little modification, I am not sure though. Instead of the price of wheat decreasing at a rate "square root (2x)-x" it needs to be "square root(2)x-x". If considered the latter one the problem can be solved in the following way:

320 + 5x = 580 - .41x (all prices converted to cents)

x = # of days after price is same

x is approximately 48

Therefore, the required price is 320 + 5 * 48 = 560 cents or $5.6

Answer: E

Request for any other explanation.

thank u Asif, can u explain me little bit clear please...

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sarwan: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Wed May 26, 2010 3:26 amFollowed by: 1 member

by sarwan » Thu Aug 12, 2010 10:36 pm

Asif wrote:If the answer is E then the question needs little modification, I am not sure though. Instead of the price of wheat decreasing at a rate "square root (2x)-x" it needs to be "square root(2)x-x". If considered the latter one the problem can be solved in the following way:

320 + 5x = 580 - .41x (all prices converted to cents)

x = # of days after price is same

x is approximately 48

Therefore, the required price is 320 + 5 * 48 = 560 cents or $5.6

Answer: E

Request for any other explanation.

Hi Asif,

Thanks for your reply.
may be question is wrong as I also thought before posting this problem.
because if we will consider this as a right question then equation will be in this way:

320 + n(5x) = 580 - m(.41x)

where n => total # of days in which price of a bushel of corn has been increased
and m=> total # of days in which price of wheat has been decreased

and thus, We can't solve for 3 variables

Actually, I am trying to count total price of total number of days for these two (corn and wheat)

Please make argument if you need to suggest me.

Thanks
Sarwan

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Asif: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Thu May 20, 2010 5:08 amFollowed by: 1 member; Location: Dhaka

by Asif » Sun Aug 15, 2010 8:34 pm

Thanks Aarati.

Please note that the question asks to find out the price at which both corn and wheat will be same and you have one variable "x" which is common. As the days after which both the prices will be same we don't need to insert a second variable for "days", which is already denoted by "x" here. Therefore,

$ 3.2 + 5x = $ 5.8 - {Sqrt (2)x - x}

320 + 5x = 580 - (1.41x - x)

320 + 5x = 580 - .41x , now solve it for x which is 48 approx.

put the value of x, you will get $ 5.6

Asif.

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Asif: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Thu May 20, 2010 5:08 amFollowed by: 1 member; Location: Dhaka

by Asif » Sun Aug 15, 2010 8:49 pm

Thanks Sarwan.

I think we don't need to insert one/two other variables to find out "days". The question asked for the price when they will be same. And definitely the price has to be same after the same number of days since the increasing and decreasing is taking place at constant rate. Thats the clue. Therefore, if we just solve for "x" which is common in both sides we shall get the number of days.

Thanks.

Asif.

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Thu Aug 26, 2010 7:28 pm

Asif wrote:Thanks Aarati.

Please note that the question asks to find out the price at which both corn and wheat will be same and you have one variable "x" which is common. As the days after which both the prices will be same we don't need to insert a second variable for "days", which is already denoted by "x" here. Therefore,

$ 3.2 + 5x = $ 5.8 - {Sqrt (2)x - x}

320 + 5x = 580 - (1.41x - x)

320 + 5x = 580 - .41x , now solve it for x which is 48 approx.

put the value of x, you will get $ 5.6

Asif.

holdon a minute!
how come you guys count to get the number 1.41x because sqrt(2x)=1,41sqrtx, how come it could be 1.41x?
can you explain?

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Asif: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Thu May 20, 2010 5:08 amFollowed by: 1 member; Location: Dhaka

by Asif » Sat Aug 28, 2010 7:45 pm

Thats why I said ealier that questions needs to be modified to sqrt(2)x instead of Sqrt(2x). Pls. see the earlier posts.

Thanks.

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Sat Sep 18, 2010 12:42 pm

sarwan wrote: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 {sqrt(2x)- x} 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

Ans: E

Pls explain the reason.

ohhh my damn goodness!!!! i didnt understand anything even how the way you solved and got the answer 5.6 until i searched the source and it IS (xsqurt2)-x or x1.4-x
ohh my god, next time, please please please write down correct number and problem....
it wasted me 10 mins because of this!!!
jesus christ!!!!

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