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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, 03:30
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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 [Reveal] Spoiler: OA _________________ 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. Find a 10% off coupon code for GMAT Club members. “Receive 5 Math Questions & Solutions Daily” Unlimited Access to over 120 free video lessons - try it yourself See our Youtube demo Senior Manager Joined: 17 Oct 2016 Posts: 327 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 29 Jan 2018, 03:51 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. _________________ Help with kudos if u found the post useful. Thanks VP Joined: 22 May 2016 Posts: 1338 A grocery store sells apples by the pound. If the price per pound is i [#permalink] Show Tags 30 Jan 2018, 09:53 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) = .4 pounds
(2.4 - 2) = .4

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Formerly genxer123

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4897
GPA: 3.82
Re: A grocery store sells apples by the pound. If the price per pound is i [#permalink]

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31 Jan 2018, 01:51
=>

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.

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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.
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“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Re: A grocery store sells apples by the pound. If the price per pound is i   [#permalink] 31 Jan 2018, 01:51
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