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

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Math Revolution GMAT Instructor
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A grocery store sells apples by the pound. If the price per pound is i  [#permalink]

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29 Jan 2018, 04:30
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35% (medium)

Question Stats:

77% (02:05) correct 23% (01:58) wrong based on 83 sessions

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[GMAT math practice question]

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
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Re: A grocery store sells apples by the pound. If the price per pound is i  [#permalink]

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29 Jan 2018, 04:51
C

lets 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 new cost is A+1. no of pounds that can be bought with when the cost is 'A+1' for$12 = 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. As the cost is positive A=5.
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A grocery store sells apples by the pound. If the price per pound is i  [#permalink]

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30 Jan 2018, 10:53
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MathRevolution wrote:
[GMAT math practice question]

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 Using answer choices Start with Answer C to get a benchmark. At$5 per pound, the number of pounds that can be purchased for $12 is $$\frac{12}{5}= 2.4$$ pounds Price per pound increases by$1, to $6 per pound. At$6 per pound, the number of pounds that can be purchased for $12 is $$\frac{12}{6}= 2$$ pounds (Original number of pounds) - (more expensive number of pounds) = .4 pounds (2.4 - 2) = .4 Answer C _________________ In the depths of winter, I finally learned that within me there lay an invincible summer. -- Albert Camus, "Return to Tipasa" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6038 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: A grocery store sells apples by the pound. If the price per pound is i [#permalink] ### Show Tags 31 Jan 2018, 02:51 => Suppose p is the current price of apples at the grocery store. Then $$\frac{12}{p} – \frac{12}{(p+1)} = 0.4$$ $$⇔ 12(p+1) – 12p = 0.4p(p+1)$$ if we multiply both sides by p(p+1) $$⇔ 12 = 0.4(p^2+p)$$ $$⇔ 30 = p^2+p$$ after multiplying by $$2.5$$ $$⇔ p^2+p-30 = 0$$ $$⇔ (p-5)(p+6) = 0$$ $$⟹ p = 5$$, since prices cannot be negative. Therefore, the answer is C. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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A grocery store sells apples by the pound. If the price per pound is i  [#permalink]

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13 Mar 2018, 05:50
Let x be the original price and p the number of pounds

Before the price increase: $12=xp.......(1) ==> p=12/x .......(2) After the price increase:$12=(x+1)(p-0.4)=xp-0.4x+p-0.4 .......(3)

By substituting (1)&(2)in (3)

$$12=12-0.4x+(12/x)-0.4$$
$$0.4x-(12/x)=-0.4$$
$$4x^2-120=(-0.4)(10x)$$ (divided by 4)
$$x^2+x-30=0$$

By Backsolving (choice c; x=5)

25+5-30=0
Choice c is the right answer
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Re: A grocery store sells apples by the pound. If the price per pound is i  [#permalink]

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13 Mar 2018, 08:12
Top Contributor
MathRevolution wrote:
[GMAT math practice question]

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: 0.4C² + 12.4C - 12 = 12C Rearrange: 0.4C² + 0.4C - 12 = 0 Multiply both sides by 10 to get: 4C² + 4C - 120 = 0 Divide both sides by 4 to get: C² + 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 RELATED VIDEO FROM OUR COURSE _________________ Brent Hanneson – Founder of gmatprepnow.com VP Joined: 07 Dec 2014 Posts: 1069 Re: A grocery store sells apples by the pound. If the price per pound is i [#permalink] ### Show Tags 13 Mar 2018, 22:19 MathRevolution wrote: [GMAT math practice question] 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 p=current price per pound
w=weight in pounds
pw=$12 w=12/p substituting, p*(12/p)=(p+1)*[(12/p)-.4] ➡p^2+p-30=0 ➡(p+6)*(p-5)=0 p=$5
C
Re: A grocery store sells apples by the pound. If the price per pound is i &nbs [#permalink] 13 Mar 2018, 22:19
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