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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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New post 29 Jan 2018, 04:30
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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
E. $6

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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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New post 29 Jan 2018, 04:51
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.
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A grocery store sells apples by the pound. If the price per pound is i  [#permalink]

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

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New post 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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New post 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

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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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New post 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
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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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