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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## A grocery store sells apples by the pound. If the price per ##### This topic has 5 expert replies and 1 member reply ## A grocery store sells apples by the pound. If the price per 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?

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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 Answer: C Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### Top Member Legendary Member Joined 29 Oct 2017 Posted: 965 messages Followed by: 4 members 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!

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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.

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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.

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Save $100 off any live Veritas Prep GMAT Course Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15351 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 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.
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!

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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 canâ€™t be negative, p = 5.

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