## A grocery store sells apples by the pound. If the price per

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### A grocery store sells apples by the pound. If the price per

by BTGmoderatorAT » Tue Mar 13, 2018 6:42 am
A grocery store sells apples by the pound. If the price per pound is increased by $1,$12 will buy 0.4 pounds less of apples than if the price remains at the current level. What is the current price per pound of apples at the grocery store?

A. $4 B.$4.5
C. $5 D.$5.5
E. $6 I'm confused how to set up the formulas here. Can any experts help? ### GMAT/MBA Expert GMAT Instructor Posts: 15795 Joined: 08 Dec 2008 Location: Vancouver, BC Thanked: 5254 times Followed by:1267 members GMAT Score:770 by [email protected] » Tue Mar 13, 2018 7:08 am ardz24 wrote:A grocery store sells apples by the pound. If the price per pound is increased by$1, $12 will buy 0.4 pounds less of apples than if the price remains at the current level. What is the current price per pound of apples at the grocery store? A.$4
B. $4.5 C.$5
D. $5.5 E.$6
let C = CURRENT price per pound
So, C - 1 = INCREASED price per pound

If the price per pound is increased by $1,$12 will buy 0.4 pounds less of apples than if the price remains at the current level.
Let's first turn this statement into a word equation
We can write: pounds of apples that can be purchased with $12 at CURRENT price - 0.4 = pounds of apples that can be purchased with$12 at INCREASED price
Convert to algebraic expression: 12/C - 0.4 = 12/(C - 1)
Rewrite as: 12/C - 0.4C/C = 12/(C - 1)
Combine terms: (12 - 0.4C)/C = 12/(C - 1)
Cross multiply: (12 - 0.4C)(C - 1) = (12)(C)
Expand and simplify: 0.4CÂ² + 12.4C - 12 = 12C
Rearrange: 0.4CÂ² + 0.4C - 12 = 0
Multiply both sides by 10 to get: 4CÂ² + 4C - 120 = 0
Divide both sides by 4 to get: CÂ² + C - 30 = 0
Factor: (C - 5)(C + 6) = 0
So, EITHER C = 5 OR C = -6
Since C cannot have a NEGATIVE value, we can be certain that C = 5

Cheers,
Brent

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by swerve » Tue Mar 13, 2018 9:26 am
Hi ardz24, you can try as follow,

Let's say the current cost of the apple be A.

No of pounds that can be bought with when the cost is A for $12 = 12/A. Now, the new cost is A+1. No of pounds that can be bought with when the cost is A+1 = 12/(A+1). Per question stem, we have current pound when cost is A - pound when cost is A+1 = 0.4. (12/A) - (12/(A+1)) = 0.4. Solving gives a quadratic equation with A = -6.5 and A = 5. As the cost is positive, then A = 5. Option C. Regards! Legendary Member Posts: 2663 Joined: 14 Jan 2015 Location: Boston, MA Thanked: 1153 times Followed by:128 members GMAT Score:770 by [email protected] » Tue Mar 13, 2018 9:54 am ardz24 wrote:A grocery store sells apples by the pound. If the price per pound is increased by$1, $12 will buy 0.4 pounds less of apples than if the price remains at the current level. What is the current price per pound of apples at the grocery store? A.$4
B. $4.5 C.$5
D. $5.5 E.$6

I'm confused how to set up the formulas here. Can any experts help?
You could also back-solve. Typically, you want to test B, C, or D first, and then adjust accordingly. Because C is the only integer of the bunch, it would make sense to start there.

If the price/pound = $5, then$12 would buy 12/5 = 2.4 pounds of apples.
If the price/pound increased by $1, it would be$6. Now $12 would buy 12/6 = 2 pounds of apples. Thus the weight of apples you could purchase would have decreased by 2.4 - 2 = .4 pounds. That's what we want! C is the answer. Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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by [email protected] » Tue Mar 13, 2018 9:56 am
[email protected] wrote:
ardz24 wrote:A grocery store sells apples by the pound. If the price per pound is increased by $1,$12 will buy 0.4 pounds less of apples than if the price remains at the current level. What is the current price per pound of apples at the grocery store?

A. $4 B.$4.5
C. $5 D.$5.5
E. $6 I'm confused how to set up the formulas here. Can any experts help? You could also back-solve. Typically, you want to test B, C, or D first, and then adjust accordingly. Because C is the only integer of the bunch, it would make sense to start there. If the price/pound =$5, then $12 would buy 12/5 = 2.4 pounds of apples. If the price/pound increased by$1, it would be $6. Now$12 would buy 12/6 = 2 pounds of apples. Thus the weight of apples you could purchase would have decreased by 2.4 - 2 = .4 pounds. That's what we want! C is the answer.
And as a public service announcement, if you are in a grocery store that's charging $5/pound for apples, you should leave this store at once. Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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by GMATGuruNY » Tue Mar 13, 2018 10:18 am
ardz24 wrote:A grocery store sells apples by the pound. If the price per pound is increased by $1,$12 will buy 0.4 pounds less of apples than if the price remains at the current level. What is the current price per pound of apples at the grocery store?

A. $4 B.$4.5
C. $5 D.$5.5
E. $6 We can PLUG IN THE ANSWERS, which represent the current price per pound. When the current price per pound increases by$1, the number of pounds that can be purchased with $12 decreases by 0.4 -- implying that the number of pounds that can be purchased with$120 must decrease by 4.
The reasoning behind the statement in blue:
If the amount of money spent increases by a factor of 10 to $120, then the decrease in weight must also increase by a factor of 10 to 4 pounds. Since the weight decrease for$120 is an INTEGER VALUE, the correct answer is almost certain to be a factor of $120. Thus, the correct answer is likely to be A, C, or E. Start with option in the middle: C. When the correct answer is increased by$1, $120 must buy 4 fewer pounds. C:$5 per pound
At a price $5 per pound, the number of pounds that can be purchased with$120 = 120/5 = 24.
After the price increases by $1 to$6 per pound, the number of pounds that can be purchased with $120 = 120/6 = 20. Weight decrease = 24-20 = 4. Success! The correct answer is C. Mitch Hunt Private Tutor for the GMAT and GRE [email protected] If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at [email protected]. Student Review #1 Student Review #2 Student Review #3 ### GMAT/MBA Expert GMAT Instructor Posts: 6362 Joined: 25 Apr 2015 Location: Los Angeles, CA Thanked: 43 times Followed by:26 members by [email protected] » Wed Mar 14, 2018 3:27 pm ardz24 wrote:A grocery store sells apples by the pound. If the price per pound is increased by$1, $12 will buy 0.4 pounds less of apples than if the price remains at the current level. What is the current price per pound of apples at the grocery store? A.$4
B. $4.5 C.$5
D. $5.5 E.$6
We can let p = the current price per pound and a = the current number of pounds of apples that can be bought with \$12 and create the equations:

pa = 12

a = 12/p

and

(p + 1)(a - 0.4) = 12

pa + a - 0.4p - 0.4 = 12

Substituting, we have:

12 + 12/p - 0.4p - 0.4 = 12

12/p - 0.4p - 0.4 = 0

Multiplying by p, we have:

12 - 0.4p^2 - 0.4p = 0

0.4p^2 + 0.4p - 12 = 0

Dividing by 0.4, we have:

p^2 + p - 30 = 0

(p + 6)(p - 5) = 0

p = -6 or p = 5

Since p can't be negative, p = 5.