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# A total of s oranges are to be packaged in boxes that will hold r oran

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Re: A total of s oranges are to be packaged in boxes that will hold r oran [#permalink]
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AbdurRakib 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–($$\frac{n}{r}$$)

C) rs–n

D) ($$\frac{s}{n}$$)–r

E) ($$\frac{s}{r}$$)–n

OG 2017 New Question

No of boxes required = $$\frac{s}{r}$$

n boxes have been filled , so no of boxes left is -

($$\frac{s}{r}$$)–n

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Re: A total of s oranges are to be packaged in boxes that will hold r oran [#permalink]
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AbdurRakib 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–($$\frac{n}{r}$$)

C) rs–n

D) ($$\frac{s}{n}$$)–r

E) ($$\frac{s}{r}$$)–n

OG 2017 New Question

well this can be solved by plugging in numbers.
Let the total number of oranges= s= 100
Let the number of oranges per box= r= 10
let the number of boxes already filled= n=8
Now substitute these values and find out which of the options give you the answer 2.
(s/r)-n = (100/10)-8= 2
E
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Re: A total of s oranges are to be packaged in boxes that will hold r oran [#permalink]
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AbdurRakib 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–($$\frac{n}{r}$$)

C) rs–n

D) ($$\frac{s}{n}$$)–r

E) ($$\frac{s}{r}$$)–n

Since s oranges are to be packaged in boxes that will hold r oranges each, the total number of boxes to be packed is s/r. Thus, after n boxes have been filled, the number of boxes left to be filled is (s/r) - n.

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Re: A total of s oranges are to be packaged in boxes that will hold r oran [#permalink]
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Hi All,

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

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Re: A total of s oranges are to be packaged in boxes that will hold r oran [#permalink]
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Total Oranges = S
Total Boxes Filled = n, No of oranges per box = r, so Total Oranges boxed = n*r
Thus, Oranges left = S-nr

Now, we need to find the number of boxes to pack these leftover oranges ( 1 Box = r oranges)
=> (S-nr)/r = (s/r)-n

Option E
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A total of s oranges are to be packaged in boxes that will hold r oran [#permalink]
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Re: A total of s oranges are to be packaged in boxes that will hold r oran [#permalink]
AbdurRakib 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–($$\frac{n}{r}$$)

C) rs–n

D) ($$\frac{s}{n}$$)–r

E) ($$\frac{s}{r}$$)–n

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Re: A total of s oranges are to be packaged in boxes that will hold r oran [#permalink]
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Video solution from Quant Reasoning:
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Re: A total of s oranges are to be packaged in boxes that will hold r oran [#permalink]
If 'S' oranges are packed 'R' oranges to a box with no
oranges left over, then the number of boxes that
will be filled is S/R.
If 'N' of these boxes are already
filled, then S/R -n boxes remain to be filled.
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Re: A total of s oranges are to be packaged in boxes that will hold r oran [#permalink]
Just to note that if you choose numbers that leave you with zero remainder, three of the answers choices will give you the correct answer
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Re: A total of s oranges are to be packaged in boxes that will hold r oran [#permalink]
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BrentGMATPrepNow wrote:
AbdurRakib 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–($$\frac{n}{r}$$)

C) rs–n

D) ($$\frac{s}{n}$$)–r

E) ($$\frac{s}{r}$$)–n

OG 2017 New Question

One approach is to use the INPUT-OUTPUT approach.
Choose some INPUT values of s, r and n and see what the answer is OUTPUT is. Then check the answer choices to see which one yields the matching OUTPUT.

So, let's say there are 12 oranges (s = 12) and each box holds 3 oranges (r = 3).
Let's also say that we pack 2 of the boxes (n = 2)

Question: What is the number of boxes that remain to be filled?
If each box holds 3 oranges, then we'll need a total of 4 boxes to hold all 12 oranges.
So, if we pack 2 boxes, there will be 2 boxes remaining to be filled.

So, when we INPUT s = 12, r = 3 and n = 2 into the answer choices, the correct answer choice will be the one that yields an OUTPUT of 2

A) 12 - (2)(3) = 6 We want 2. ELIMINATE

B) 122/3 = 11 1/3 We want 2. ELIMINATE

C) (3)(12) – 2 = 34 We want 2. ELIMINATE

D) 12/2 - 3 = 3 We want 2. ELIMINATE

E) 12/32 = 2 BINGO!

Here's a video with some tips to consifer when using the INPUT-OUTPUT approach:

Cheers,
Brent

To confirm Brent, when you were choosing the numbers, you had to be mindful of choosing n=2 right because it could not be greater than 4? So technically, you have to be strategic about your smart numbers in the case, correct? Many thanks
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Re: A total of s oranges are to be packaged in boxes that will hold r oran [#permalink]
Stop plug in numbers all the time. If you are trying 700 or more, the author will turn the hard arithmetic questions impossible to you apply this technique.
Use simple algebra concepts in your study.
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Re: A total of s oranges are to be packaged in boxes that will hold r oran [#permalink]
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Quote:
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–($$\frac{n}{r}$$)

C) rs–n

D) ($$\frac{s}{n}$$)–r

E) ($$\frac{s}{r}$$)–n

A student of mine brought the above question to my attention. One approach I do not see outlined above, which can be useful on word problems that involve real-world measurements, is to translate the algebraic expressions into language to ensure that the answer you select will be sensible. Consider the first option, for example:

(A) s - nr

If we substitute the word or phrase for its algebraic stand-in, we get the following:

(oranges) - [(boxes of oranges)(oranges/box)]

Ask yourself what sort of unit that bracketed multiplication would produce. The boxes would cancel out and you would be left with oranges. It should be clear that we cannot answer a question that asks us to count boxes by subtracting oranges from oranges. (A) cannot be the answer. Now, consider the other options in a similar fashion:

(B) s - (n/r)

(oranges) - [(boxes of oranges)/(oranges/box)]

Even without doing the math, it is obvious that we cannot subtract anything from oranges to get boxes, since the units would not match. Get rid of (B).

(C) rs - n

[(oranges/box)(oranges)] - (boxes of oranges)

What sort of a unit is oranges squared? Again, it should be clear that you cannot derive boxes from this made-up unit. Nix (C).

(D) (s/n) - r

[(oranges)/(boxes of oranges)] - (oranges/box)

We cannot get boxes by subtracting a "rate" of oranges per box. Get rid of (D).

(E) (s/r) - n

[(oranges)/(oranges/box)] - (boxes of oranges)

What do you do when you divide by a fraction? You invert the divisor and multiply, of course, and here, we will finally derive a sensible unit that will help to answer the question:

[(oranges) * (box/oranges)] - (boxes of oranges)

[(box)] - (boxes of oranges)

And it is perfectly reasonable to count boxes by subtracting a set of boxes from other boxes. (E) must be the answer. Nothing more than a basic understanding of units and mathematics is necessary, and the question can be answered quickly and confidently.

See if you can apply the same logic to other word problems that use measurements and list algebraic answers. You may surprise yourself how handy the process of elimination outlined above may prove.

- Andrew
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Re: A total of s oranges are to be packaged in boxes that will hold r oran [#permalink]
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