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A total of s oranges

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by rsarashi » Thu Jan 26, 2017 9:14 am

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Answers

A

B

C

D

E

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Difficulty—

A total of s oranges are to be packaged in boxes that will hold r oranges each, with no oranges left over. When n of these boxes have been completely filled, what is the number of boxes that remain to be filled?

A) s-nr

B) s-(n/r)

C) rs-n

D) (s/n)-r

E) (s/r)-n

OAE
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by [email protected] » Thu Jan 26, 2017 9:27 am
Hi rsarashi,

This question can be solved by TESTing VALUES.

IF....
S = 6
R = 2

Then we're packing 6 oranges into boxes that will hold 2 oranges each... which means that there will be 3 boxes.

N = 1

So after 1 (of the 3) boxes is filled, there will be 2 boxes left. Thus, we're looking for an answer that equals 2 when we test the above three values.

Answer A: 6 - 2 = 4 NOT a match
Answer B: 6 - 1/2 = 5.5 NOT a match
Answer C: 12 - 1 = 11 NOT a match
Answer D: 6 - 2 = 4 NOT a match
Answer E: 3 - 1 = 2 This IS a match

Final Answer: E

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by DavidG@VeritasPrep » Thu Jan 26, 2017 10:45 am
rsarashi wrote:A total of s oranges are to be packaged in boxes that will hold r oranges each, with no oranges left over. When n of these boxes have been completely filled, what is the number of boxes that remain to be filled?

A) s-nr

B) s-(n/r)

C) rs-n

D) (s/n)-r

E) (s/r)-n

OAE
Algebraically:

If there are s oranges total and r oranges are packed into each crate, then the total number of crates required is s/r.
If n crates have been packed, then there are still (s/r) - n left to pack. The answer is E
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by Jay@ManhattanReview » Thu Jan 26, 2017 9:15 pm
rsarashi wrote:A total of s oranges are to be packaged in boxes that will hold r oranges each, with no oranges left over. When n of these boxes have been completely filled, what is the number of boxes that remain to be filled?

A) s-nr

B) s-(n/r)

C) rs-n

D) (s/n)-r

E) (s/r)-n

OAE
Hi rsarashi,

The challenge with Word Problems is that one must comprehend what the prompt states, and then transform the textual information into mathematical expression(s) or/and workable equation(s). Sometimes the usage of variables can make things look weird. With regards to this question, it's an easy question. Had the question been like this, it may have been easier for you.

A total of 100 oranges are to be packaged in boxes that will hold 10 oranges each, with no oranges left over. When 6 of these boxes have been completely filled, what is the number of boxes that remain to be filled?

Solution:

We need to accommodate 100 oranges in 10 boxes. This needs 100/10 = 10 boxes. Once 6 boxes are filled, 10 - 6 = 4 boxes remain to be filled.

The original question is identical to this one.

Number of remaining boxes to be filled =[spoiler] (s/r) - n.[/spoiler]

Answer: E

Hope this helps!

-Jay
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by Scott@TargetTestPrep » Mon Jan 30, 2017 4:41 pm
rsarashi wrote:A total of s oranges are to be packaged in boxes that will hold r oranges each, with no oranges left over. When n of these boxes have been completely filled, what is the number of boxes that remain to be filled?

A) s-nr

B) s-(n/r)

C) rs-n

D) (s/n)-r

E) (s/r)-n
Since there are a total of s oranges and they are going into n boxes that hold r oranges each, the number of oranges that can be put into these n boxes is rn. The number of oranges left to be put into boxes is s - rn. Finally, the number of boxes that are left to be filled is:

(s - rn)/r = s/r - (rn/r) = s/r - n

Answer: E

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by Matt@VeritasPrep » Wed Feb 01, 2017 6:39 pm
If we think about it conceptually we know that we've got n boxes, each with r oranges, giving us a total of n*r oranges already in boxes. That means we've still got s - nr oranges left. From here

Oranges left / Oranges per box =

(s - nr) / r =

s/r - n
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by rsarashi » Sat Feb 04, 2017 8:32 pm
Then we're packing 6 oranges into boxes that will hold 2 oranges each... which means that there will be 3 boxes.

N = 1
Hi Rich ,

If we have 6 oranges and each boxes hold 2 oranges, so that means n will be 3. So how come N=1?

Also in E option, we have to put n=3, so why did you put n=1?

Please explain.

Thansk
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by [email protected] » Sun Feb 05, 2017 10:52 am
Hi rsarashi,

This question includes 3 variables: S, R and N. When I decided to TEST VALUES, I chose the following variables:

S = 6
R = 2
N = 1

The values for S and R are used to determine the total number of boxes. Based on how the question is worded, N has to be less than, or equal to, the total number of boxes.

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by rsarashi » Sun Feb 05, 2017 8:33 pm

This question includes 3 variables: S, R and N. When I decided to TEST VALUES, I chose the following variables:

S = 6
R = 2
N = 1

The values for S and R are used to determine the total number of boxes. Based on how the question is worded, N has to be less than, or equal to, the total number of boxes.
Hi Rich ,

Thank you so much for your reply, but sill I really want to know that how come N=1, because here N = S/R so if we choose S=6 and R=2, then N will be 3 right?

Please explain, where I am getting wrong?

Thanks
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by [email protected] » Mon Feb 06, 2017 10:09 am
Hi rsarashi,

The prompt does NOT equate N to either of the other two variables. We're asked... after N of the boxes are filled, what is the number of boxes that REMAIN to be filled. This means that N <= (S/R). In my example, S/R = 6/2 = 3, so N would have to be 0, 1, 2 or 3. I chose N=1 because I thought that would be easy to deal with.

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by rsarashi » Tue Feb 07, 2017 8:26 am

The prompt does NOT equate N to either of the other two variables. We're asked... after N of the boxes are filled, what is the number of boxes that REMAIN to be filled. This means that N <= (S/R). In my example, S/R = 6/2 = 3, so N would have to be 0, 1, 2 or 3. I chose N=1 because I thought that would be easy to deal with.
Hi Rich ,

Thank you so much for your explanation. All clear.
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Re: A total of s oranges

by AdityaBir » Sun Jan 26, 2020 12:13 am
rsarashi wrote: ↑
Thu Jan 26, 2017 9:14 am
 A total of s oranges are to be packaged in boxes that will hold r oranges each, with no oranges left over. When n of these boxes have been completely filled, what is the number of boxes that remain to be filled?

A) s-nr

B) s-(n/r)

C) rs-n

D) (s/n)-r

E) (s/r)-n

OAE
Total oranges = s
Oranges per box = r
Boxes filled = n
Total oranges currently in boxes = nr
Oranges left outside boxes = total oranges - oranges in boxes = s-nr
boxes required to pack remaining oranges = (oranges left outside boxes)/box capacity = (s-nr)/r = s/r -n
Hence option E is correct.
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