GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 17 Feb 2020, 01:59

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

### Show Tags

11 Sep 2008, 02:49
5
38
00:00

Difficulty:

95% (hard)

Question Stats:

39% (03:11) correct 61% (03:11) wrong based on 419 sessions

### HideShow timer Statistics

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 $$x\sqrt{2} - x$$ 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

### Show Tags

19 Nov 2013, 02:11
11
19
dancinggeometry 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 $$\sqrt{2}*x-x$$ 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 Note that we are not asked in how many days prices will cost the same. Let $$y$$ be the # of days when these two bushels will have the same price. First let's simplify the formula given for the rate of decrease of the price of wheat: $$\sqrt{2}*x-x=1.41x-x=0.41x$$, this means that the price of wheat decreases by $$0.41x$$ cents per day, in $$y$$ days it'll decrease by $$0.41xy$$ cents; As price of corn increases $$5x$$ cents per day, in $$y$$ days it'll will increase by $$5xy$$ cents; Set the equation: $$320+5xy=580-0.41xy$$, solve for $$xy$$ --> $$xy=48$$; The cost of a bushel of corn in $$y$$ days (the # of days when these two bushels will have the same price) will be $$320+5xy=320+5*48=560$$ or$5.6.

_________________
Intern
Joined: 03 Mar 2014
Posts: 6

### Show Tags

11 Sep 2008, 09:16
3
1
dancinggeometry 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 x(2^1/2) - 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 Lets y be the number of days until prices are equal. The end price of corn = 3.2 + 5xy The end price of wheat = 5.8 - x(1.4-1) = 5.8 - 0.4xy The two end prices are equal -> 3.2 +5xy = 5.8 - 0.4xy From here we get that 5.4xy = 2.6, or y = 2.6/5.4x or 26/54x Replace y in first equation and you get 3.2 + 5x(26/54x), cross the x and you get approximately 3.2 + 2.4 =$5.6
Check price for 2nd equation = 5.8 - 0.4x(26/54X), cros x and you get 5.8 - 0.2 = $5.6 I got to y = 2.6/5.4X via a number of simple methods and it took me 4-5 mins to realize this is all I needed:)) Math Expert Joined: 02 Sep 2009 Posts: 61202 Re: The price of a bushel of corn is currently$3.20, and the price of a  [#permalink]

### Show Tags

19 Mar 2015, 04:49
1
Bunnel,

320+5xy=580-0.41xy, solve for xy --> xy=48; (Especially the last step 260/5.41)

AM

320 + 5xy = 580 - 0.41xy;

5xy + 0.41xy = 580 - 320;

5.41xy = 260

541/100*xy = 260

xy = 260*100/541 = ~48.
_________________
Intern
Joined: 17 Apr 2012
Posts: 14
Location: United States
WE: Information Technology (Computer Software)

### Show Tags

18 Mar 2015, 04:59
Bunnel,

320+5xy=580-0.41xy, solve for xy --> xy=48; (Especially the last step 260/5.41)

AM
VP
Joined: 09 Mar 2016
Posts: 1221
Re: The price of a bushel of corn is currently $3.20, and the price of a [#permalink] ### Show Tags 06 Mar 2018, 09:58 dancinggeometry 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 x(2^1/2) - 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

hi Bunuel, niks18

i have no idea if approached the question correctly, but I got correct answer 9i decoded this info x(2^1/2) - x as 2^1/2 = $$\sqrt{2}$$ = 1.4 hence x(2^1/2) - x = 1.4x -1.4

$$3,20 + 1.6x = 5.80 -1.4x -1.4$$

$$1.6x + 1.4x = 5.80 - 3.20-1.4$$

$$3x = 1.2$$

$$x = 2.5$$

$$3.20+2.50 = 5.70$$

so i chose $$E$$
Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3552

### Show Tags

21 Jul 2018, 05:28
Bunuel I'm a little confused by this last line:

541/100*xy = 260

xy = 260*100/541 = ~48.

Did you just divide 26,000 by 541 in your head or something? I'm confused how people are getting that ballpark 48 number. Guess and check? Thanks!
Senior Manager
Status: Whatever it takes!
Joined: 10 Oct 2018
Posts: 381
GPA: 4

### Show Tags

10 Dec 2019, 10:08
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________