Problem Solving

alanforde800Maximus wrote:Aunt Maura spends $12 on mangoes at a local merchant. If Aunt Maura bought the mangoes at a shopping center instead, she could purchase an extra pound of mangoes for the same amount of money. The mangoes are $1 cheaper per pound at the shopping center than at the local merchant. What is the price per pound of mangoes at the local merchant?

a) $3
b) $4
c) $5
d) $6
e) $7

Please assist with above problem.

Say Aunt Maura buys x pounds of mangoes from the local merchant.

=> Price per pound = 12/x at the local merchant

Since she can buy one more pound from the shopping center, she buys (x+1) pounds for $12.

=> Price per pound = 12/(x+1) at the shopping center

Given that the mangoes are $1 cheaper per pound at the shopping center than at the local merchant:

=> 12/x - 12/(x+1) = 1

=> [12{(x+1) - x}]/[x(x+1)] = 1

=> 12 = x(x+1)

We see that 12 is a product of two consecutive integers, thus x = 3 pounds

=> Price per pound = 12/x = 12/3 = $4 at the local merchant

OA: B

-Jay

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alanforde800Maximus wrote:Aunt Maura spends $12 on mangoes at a local merchant. If Aunt Maura bought the mangoes at a shopping center instead, she could purchase an extra pound of mangoes for the same amount of money. The mangoes are $1 cheaper per pound at the shopping center than at the local merchant. What is the price per pound of mangoes at the local merchant?

a) $3
b) $4
c) $5
d) $6
e) $7

We are given that Aunt Maura spends $12 on mangoes at a local merchant and that if Aunt Maura bought the mangoes at a shopping center instead, she could purchase an extra pound of mangoes for the same amount of money. We are also given that the price per pound of mangoes at the shopping center is $1 cheaper than the price at the local merchant.

We can let p = the price per pound of mangoes at the local merchant and q = the number of pounds of mangoes purchased at the local merchant.

Thus, the number of pounds of mangoes purchased at the shopping center = q + 1 and the price per pound at the shopping center = p - 1.

Thus, we have two equations:

pq = 12

AND

(p - 1)(q + 1) = 12

pq - q + p - 1 = 12

Since 12/p = q, we can substitute 12/p for q in the equation pq - q + p - 1 = 12 and have:

p(12/p) - 12/p + p = 13

12 - 12/p + p = 13

Multiplying the entire equation by p gives us:

12p - 12 + p^2 = 13p

p^2 - p - 12 = 0

(p - 4)(p + 3) = 0

p = 4 or p = -3

Since p must be positive, p = 4.

Answer: B

Hi alanforde800Maximus,

This question has a number of built-in patterns that you can take advantage of. First, the answer choices are small integers, so you can TEST THE ANSWERS. Second, the numbers involved are also all integers... Maura bought $12 worth of mangoes at a merchant, but the mangos are $1 cheaper per pound at the shopping center - and at that price she could purchase 1 extra pound of mangos for $12..

From the answer choices, we can see that the total cost per pound at the merchant must ALSO be an integer... almost certainly one that divides evenly into $12. So we need two integers, one for each of the two prices... that BOTH divide into $12 AND that differ by $1. That can ONLY be $3 and $4. Now we just have to double-check to make sure that we're answering the question that is asked...

$12 spent at the merchant (where mangoes are $4 a pound) = 3 pounds
$12 spent at the center (where mangoes are $3 a pound) = 4 pounds

This matches perfectly. The question asks for the price per pound at the merchant....

Final Answer: B

GMAT assassins aren't born, they're made,
Rich