apples and oranges

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pappueshwar: Master | Next Rank: 500 Posts; Posts: 234; Joined: Fri Oct 01, 2010 7:28 pmFollowed by: 4 members; Location: chennai; Thanked: 5 times

by pappueshwar » Thu Mar 01, 2012 7:18 am

At a certain food stand, the price of each apple is $40 and the price of each orange is $60. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is $56. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is $52?

A. 1 B. 2 C. 3 D. 4 E. 5

pls assist

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Source: Beat The GMAT — Problem Solving | Thu Mar 01, 2012 7:18 am

Jim@StratusPrep: MBA Admissions Consultant; Posts: 2279; Joined: Fri Nov 11, 2011 7:51 amFollowed by: 266 members; Location: New York; Thanked: 660 times; GMAT Score:770

by Jim@StratusPrep » Thu Mar 01, 2012 7:50 am

First, 40(x)/10 + 60(y)/10 = 56 or 4x + 6y = 56 and x + y = 10, solving for y you can get 2y = 16 or y = 8, which means x = 2. We will use this information to get a new equation:

40(2)/(2+z) + 60(z)/(2+z) = 52
80 + 60z = 104 + 52z
8z = 24
z=3

This means you only need 3 oranges so she has to put back 5 (8-3)

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krusta80: Master | Next Rank: 500 Posts; Posts: 143; Joined: Mon Mar 14, 2011 3:13 amFollowed by: 5 members; Thanked: 34 times

by krusta80 » Thu Mar 01, 2012 8:05 am

pappueshwar wrote:At a certain food stand, the price of each apple is $40 and the price of each orange is $60. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is $56. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is $52?

A. 1 B. 2 C. 3 D. 4 E. 5

pls assist

Let x represent the number of apples and 10-x the number of oranges...

[40x + 60(10-x)]/10 = 56

(40x+600-60x)/10 = 56
-2x+60 = 56
x=2 apples and therefore 8 oranges

Double checking...

We get 2*40+8*60 = 560 -> average is 56 GOOD

Now, for the second part of the problem...

Let x denote the number of apples put back
Let y denote the number of oranges put back.

They DO tell us the final average, so let's use that to come up with one formula or x and y:

52 = (560-40x-60y)/(10-x-y)
520-52x-52y = 560-40x-60y
8y-12x = 40
2y-3x = 10

y = (10+3x)/2

The question asks how many oranges need to be put back, so we can assume that there are NO apples put back, which means that x = 0. This allows us to quickly solve for y.

y = 5, so choice E

Now, let's assume that the question read: "How many pieces of fruit did she put back?" In other words, if they don't specify apples or organges. Well, it turns out that we can still narrow it down, based on the choices.

In this case, since we can't really come up with another formula for x and y now, let's work with our tighest constraint. Since we only have 2 apples to start with, there are only three posible values for x (or how many apples we can put back): 0, 1, and 2. Let's plug in these values to see what we get:

a.) x = 0
y = 5, this is a choice so we're done (but I'll do the other two for completeness)

b.) x = 1
y=6.5, which doesn't work because we can't split fruit in half

c.) x = 2
y = 8, which brings the total to 10 pieces, which is NOT a choice

Again, the answer is E

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Mar 01, 2012 9:38 am

pappueshwar wrote:At a certain food stand, the price of each apple is $40 and the price of each orange is $60. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is $56. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is $52?

A. 1 B. 2 C. 3 D. 4 E. 5

pls assist

ALWAYS LOOK AT THE ANSWER CHOICES.

After the oranges are put back, the average price per piece of fruit is 52.
Since the cost of each piece of fruit is 40 or 60, the total cost is a multiple of 10.
Thus, the number of pieces of fruit must be a multiple of 5 or 10.
Since the original number of pieces is 10, the only viable answer choice is E:
10-5 = 5 pieces of fruit, so that -- after the oranges are put back -- the total cost = 5*52 = 260.

The correct answer is E.

P.S. Remind me NEVER to shop at this food stand. $40 for an apple and $60 for an orange?

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kul512: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Thu Sep 29, 2011 5:15 amFollowed by: 1 member; Thanked: 7 times; GMAT Score:740

by kul512 » Fri Mar 02, 2012 6:46 am

suppose she puts back a oranges-

so
after putting oranges total price=52(10-a)
price of total oranges she put back=60a
Summation of these two must be equal to total price of 10 items=56X10=560

so 52(10-a)+60a=560
-->8a=40
-->a=5

So she put back 5 oranges.

Sometimes there is very fine line between right and wrong: perspective.

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