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

by Max@Math Revolution » Mon Jan 29, 2018 3:27 am
[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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by Scott@TargetTestPrep » Tue Jan 30, 2018 10:34 am
Max@Math Revolution 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
We can let p = the current price and a = the current number of pounds of apples can be bought with $12and 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 can't be negative, p = 5.

Answer: C

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by Max@Math Revolution » Wed Jan 31, 2018 1:46 am
=>

Suppose p is the current price of apples at the grocery store. Then
12/p - 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(p2+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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grocery

by GMATGuruNY » Wed Jan 31, 2018 3:57 am
Max@Math Revolution 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
We can PLUG IN THE ANSWERS, which represent the current price per pound.
When the correct answer is plugged in, a $1 increase in the price will decrease the amount that can purchased by 2/5 of a pound.
Notice the following:
The amount that can purchased with $12 = 12/(price per pound).
The fraction in blue has a DENOMINATOR OF 5.
Thus, the correct answer is probably C (which indicates a current price of $5 per pound) or A (which will yield a price of $5 per pound after the $1 increase).

C: $5 per pound
At a current price of $5 per pound, the amount that be purchased with $12 = 12/5 pounds.
If the price increases by $1 to $6 per pound, the amount that can purchased with $12 = 12/6 = 2 pounds.
Difference between the two amounts = 12/5 - 2 = 12/5 - 10/5 = 2/5.
Success!

The correct answer is C.
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