The total cost to pick apples at a certain orchard consists of a fixed

Question

The total cost to pick apples at a certain orchard consists of a fixed charge plus an additional charge per pound of apples picked. What is the total cost to pick 15 pounds of apples at this orchard?

(1) The total cost to pick 8 pounds of apples at this orchard is 1.50$ more than the total cost to pick 5 pounds
(2) The total cost to pick 10 pounds of apples at this orchard is 1.00$ more than the total cost to pick 8 pounds

Sol>

let T be the total cost/pound which includes fixed+additional charge

st1>

8T=5T+1.5
therefore T=0.5 
sufficient

st2>
like st1, st2 is sufficient

but I am wrong?

Am I missing something?

Ravi

chetan2u · Accepted Answer

Hi,

this Q tells you that the total consist of two items 
1) Fixed charge , say F
2) variable charge per pound say x per pound..

lets see the statements 
1> The total cost to pick 8 pounds of apples at this orchard is 1.50$ more than the total cost to pick 5 pounds
 here you can easily see that 3 pounds cost 1.5 or x is 1.5/3 = $0.5 per pound
F not known 
Insuff

2> The total cost to pick 10 pounds of apples at this orchard is 1.00$ more than the total cost to pick 8 pounds
 Again we can just say that 10-8 =2 pound cost $1 or x = 1/2 = $0.5..
F not known
Insuff

where you are going wrong is that you are not realizing that when you subtract TOTAL cost of two different quantities, ONLY variable is left .FIXED charge gets cancelled out .. 
 
E

chetan2u · Answer

hi,
the T for 8 pounds = F + 8X 
and for 5 pounds = F + 5x..
as per st 1
F +8x = F+5x+1.5..
3x = 1.5..
Hope you have understood

email2vm · Answer

Chetan,

Isn't the questions saying:

T=F+x

The  total cost  to pick 8 pounds of apples at this orchard is 1.50$ more than the  total cost  (and not the x (variable)) to pick 5 pounds

St1> 8T =5T+1.5?

and the question is asking for

The  total cost  to pick apples at a certain orchard consists of a fixed charge plus an additional charge per pound of apples picked.
What is the  total cost  to pick 15 pounds of apples at this orchard?

mzuberi · Answer

You are able to determine the price per pound of apple from both statement 1 and statement 2 ($0.5/pound). However, in order to calculate the total cost to pick 15 pounds, you will also need to know the fixed cost, which is still unknown. Therefore the answer is E.

alandizzle · Answer

Please correct me if I'm wrong, but can't you use the value of the cost of pounds per apple to plug back into the formula to determine F? Or would that be incorrect?

Thanks!

ajay2121988 · Answer

Even if you plug it back, it will cancel out.

Let f= fixed cost ; a= additional cost per pound

By st1. f+8a = f+5a + 1.05

a= (1.05/3) = 0.35

Now even if you plug this back, you cannot get 'f' because it gets cancelled out.

Hope it's clear.

Cez005 · Answer

Taking 1):

f = fixed charge, p=price per pound

f+8p=f+5p+1.5
3p=1.5
p=0.5

But, f is still needed. Putting p=0.5 back into the equation:
f+4=f+4, so we still don't know what the fixed price is.

Same for 2), and combining 1) and 2) does not provide additional info.

Kudos if you agree! Comment if you have a better method.

Chets25 · Answer

Hi Chetan,

Can you clarify one point for me:

In this case in each of the statements we are able to figure out cost per pound of apples is 0.5.

Therefore, for 5 pounds of apples, it should be 2.50. The remaining 2.50 should be the fixed cost!!!
Similarly, 8 pounds of apple - 8*0.5+2.50=6.50, which is 1.50 as per the stem.

What m i missing out here

rbramkumar · Answer

Remaining 2.50? Remaining from what?

From what I see in the question, it is not mentioned anywhere that 5 pounds cost $5.

5 pounds could cost $10, and the fixed price can be $7.50
5 pounds could cost $100, and the fixed price can be $97.50

Assuming that the total cost/pound is the same for both 8 pounds and 5 pounds is incorrect in this case, because the total consists of 2 parts: a fixed and a variable. Your equation should be: 8(T1) = 5(T2) + 1.5

Tpral · Answer

chetan2u  ,

From (1) and (2) can we say:

(2) is 10p = 1 +8p

we replace 8p in the above by (1) and we have (1) + (2): 10p = 1 + 1,5 + 5p = 2,5 + 5p

If we multiply each side of the previous by 3:

3 x (10p) = 3 x (2,5 + 5p)
so: 30p = 7,5 +15p

Thus, 30p-15p = 7,5 => 15p = 7,5

I don't see where I can be wrong here,

Thanks in advance for your help,

nhatanh811 · Answer

Bunuel , please add the tag Gmatprep in this question. Thanks!

Bunuel · Answer

__________________________
Added the tag. Thank you!

ccoinflip · Answer

What is the quickest way to do these questions usually? Is it simply based on shortcuts like here or just raw logical algebra that gives us the answer 100% of time?

bumpbot · Answer

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The total cost to pick apples at a certain orchard consists of a fixed

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