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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7585
GMAT 1: 760 Q51 V42 GPA: 3.82
A grocery store sells apples by the pound. If the price per pound is i  [#permalink]

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14 00:00

Difficulty:   45% (medium)

Question Stats: 71% (02:31) correct 29% (02:43) wrong based on 96 sessions

### HideShow timer Statistics [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 _________________ Senior Manager  G Joined: 17 Oct 2016 Posts: 317 Location: India Concentration: Operations, Strategy GPA: 3.73 WE: Design (Real Estate) Re: A grocery store sells apples by the pound. If the price per pound is i [#permalink] ### Show Tags 1 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. _________________ Help with kudos if u found the post useful. Thanks Senior SC Moderator V Joined: 22 May 2016 Posts: 3063 A grocery store sells apples by the pound. If the price per pound is i [#permalink] ### Show Tags 3 1 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

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) = 0.4 pounds
(2.4 - 2.0) = 0.4

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7585
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]

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=>

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.

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

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

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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 + 11.6C + 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 _________________ Originally posted by GMATPrepNow on 13 Mar 2018, 08:12. Last edited by GMATPrepNow on 07 Mar 2019, 12:24, edited 1 time in total. VP  P Joined: 07 Dec 2014 Posts: 1206 Re: A grocery store sells apples by the pound. If the price per pound is i [#permalink] ### Show Tags 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
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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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