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Math Expert V
Joined: 02 Sep 2009
Posts: 58381
The numbers of nuts stored by two squirrels, Burl and Shirl, at the be  [#permalink]

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16 00:00

Difficulty:   95% (hard)

Question Stats: 55% (03:21) correct 45% (03:00) wrong based on 235 sessions

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The numbers of nuts stored by two squirrels, Burl and Shirl, at the beginning of September were in the ratio A : B. At the end of September, the numbers of nuts stored by Burl and Shirl were in the ratio C : D. If Burl had n times as many nuts at the end of September as at the beginning of September, then by what percent did the number of nuts stored by Shirl increase during September?

(A) $$\frac{100nAD}{(BC)}$$

(B) $$\frac{100n(AD - B)}{(BC)}$$

(C) $$\frac{100(D}{(BC)}*(n + A) - 1)$$

(D) $$\frac{100D(n + A)}{(BC)}$$

(E) $$100(\frac{nAD}{(BC)} - 1)$$

Kudos for a correct solution.

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Re: The numbers of nuts stored by two squirrels, Burl and Shirl, at the be  [#permalink]

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2
Let's denote the percent change in Shirl's nuts as x.

Ratio at the beginning: A : B
Ratio at the end: An : B+Bx/100 or C : D

An/(B+Bx/100)=C/D Hence x=(AnD-BC)/BC * 100

This can be simplified as x=100(AnD/BC - 1)

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Manager  Joined: 10 Aug 2015
Posts: 103
Re: The numbers of nuts stored by two squirrels, Burl and Shirl, at the be  [#permalink]

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Solution:

At the end of september, let the no. of nuts with sherl be B#
$$\frac{C}{D} = \frac{An}{B#}$$
$$B# = \frac{nAD}{C}$$

Change in % = [(B#-B)/B]* 100

Option E
EMPOWERgmat Instructor V
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The numbers of nuts stored by two squirrels, Burl and Shirl, at the be  [#permalink]

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Hi All,

I received a PM about this question. In answer to that PM - YES, you can answer this question by TESTing VALUES. There's actually a great built-in 'shortcut' too: since we're never told that Shirl actually collected more nuts, we can say that she did NOT collect more nuts - so we can make B and D the SAME VALUE and the answer to the question (by what percent did the number of Shirl's nuts increase?) will be 0%.

With that solution (0), you'll find that you can avoid much of the 'math' in the answer choices, since the only way to get to 0 while doing lots of multiplication is if one of the 'pieces' is 0.

In my approach, I used the following VALUES:
A = 5
B = 2
C = 10
D = 2
N = 2

Using these values, you'll find that just one solution matches (as it provides the '0' that we're looking for)...

GMAT assassins aren't born, they're made,
Rich
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Joined: 02 Sep 2009
Posts: 58381
Re: The numbers of nuts stored by two squirrels, Burl and Shirl, at the be  [#permalink]

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Bunuel wrote:
The numbers of nuts stored by two squirrels, Burl and Shirl, at the beginning of September were in the ratio A : B. At the end of September, the numbers of nuts stored by Burl and Shirl were in the ratio C : D. If Burl had n times as many nuts at the end of September as at the beginning of September, then by what percent did the number of nuts stored by Shirl increase during September?

(B) 100n(AD - B)/(BC)
(C) 100(D/(BC)*(n + A) - 1)
(D) 100D(n + A)/(BC)
(E) 100(nAD/(BC) - 1)

Kudos for a correct solution.

Because no actual quantities are given, the problem technically requires at least one unknown multiplier: for instance, using the unknown multiplier x, you could define the numbers of nuts at the beginning of September as Ax and Bx. However, the answer choices contain only the quantities defined in the problem statement, so you must be able to answer the question using only those quantities. Therefore, without loss of generality, you can let Burl’s and Shirl’s nut collections be just A and B, respectively, at the beginning of September. Because Burl had n times as many nuts at the end of September as at the beginning, Burl must have had nA nuts at the end of September.

Make a table: The ratio of the two quantities in the second row is C : D, so set up a proportion to solve for the unknown quantity:

nA/[unknown] = C/D

Solve for the unknown by cross-multiplication:

C × [unknown] = nAD

Finally, find the desired percentage change, which is the percent change from an initial value of B to a final value of nAD/C:

Percent change = $$100(\frac{\frac{nAD}{C}-B}{B})$$

Since this is a complex fraction, multiply through by the common denominator of the inside terms (which, in this case, is C, the only denominator appearing on the inside at all):

Percent change = $$100(\frac{nAD-BC}{BC})$$

$$= 100(\frac{nAD}{BC}-1)$$

The correct answer is E.

Attachment: 2015-09-13_2053.png [ 6.24 KiB | Viewed 3391 times ]

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Re: The numbers of nuts stored by two squirrels, Burl and Shirl, at the be  [#permalink]

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EMPOWERgmatRichC wrote:
Hi All,

I received a PM about this question. In answer to that PM - YES, you can answer this question by TESTing VALUES. There's actually a great built-in 'shortcut' too: since we're never told that Shirl actually collected more nuts, we can say that she did NOT collect more nuts - so we can make B and D the SAME VALUE and the answer to the question (by what percent did the number of Shirl's nuts increase?) will be 0%.

With that solution (0), you'll find that you can avoid much of the 'math' in the answer choices, since the only way to get to 0 while doing lots of multiplication is if one of the 'pieces' is 0.

In my approach, I used the following VALUES:
A = 5
B = 2
C = 10
D = 2
N = 2

Using these values, you'll find that just one solution matches (as it provides the '0' that we're looking for)...

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

i did not get the 0 % part. it should be 100% right??
EMPOWERgmat Instructor V
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The numbers of nuts stored by two squirrels, Burl and Shirl, at the be  [#permalink]

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Hi arnabs,

The question asks for the PERCENT INCREASE in the number of Shirl's nuts. By making the number of nuts the SAME (in my example, the variables "B" and "D" are both 2), then the percent increase is 0%.

GMAT assassins aren't born, they're made,
Rich
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Re: The numbers of nuts stored by two squirrels, Burl and Shirl, at the be  [#permalink]

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EMPOWERgmatRichC wrote:
Hi arnabs,

The question asks for the PERCENT INCREASE in the number of Shirl's nuts. By making the number of nuts the SAME (in my example, the variables "B" and "D" are both 2), then the percent increase is 0%.

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

i might sound really silly here, but can you please help me solve as to you how did you get 0 as an answer. i would be really obliged.  EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The numbers of nuts stored by two squirrels, Burl and Shirl, at the be  [#permalink]

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1
Hi arnabs,

Based on the starting ratio of nuts (A:B = 5:2) and the ending ratio of nuts (C:D = 10:2), I chose the following values for the ACTUAL number of nuts....

Beginning of month:
Burl = A = 5 nuts
Shirl = B = 2 nuts

End of the month:
Burl = C = 10 nuts
Shirl = D = 2 nuts

As you can see, Burl's number of nuts DOUBLED, while Shirl's number was the SAME.

We're told that Burl had "N times" as many nuts at the end of the month as he did at the beginning, so....
N = 2

We're asked for the PERCENT INCREASE in the number of Shirl's nuts. Since her total did NOT increase, the percentage change is 0. Using the above values for A, B, C, D and N, there is only one answer that gives us a total of 0...

One of the other great 'shortcuts' in this question is that you really don't have to check all of the answer choices. Each of the 5 variables I chose is a POSITIVE number, so two of the answers can be eliminated immediately (since they're adding, multiplying and/or dividing POSITIVE numbers - and doing just those tasks will NEVER lead to 0).

GMAT assassins aren't born, they're made,
Rich
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Joined: 06 Aug 2013
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Re: The numbers of nuts stored by two squirrels, Burl and Shirl, at the be  [#permalink]

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EMPOWERgmatRichC wrote:
Hi arnabs,

Based on the starting ratio of nuts (A:B = 5:2) and the ending ratio of nuts (C:D = 10:2), I chose the following values for the ACTUAL number of nuts....

Beginning of month:
Burl = A = 5 nuts
Shirl = B = 2 nuts

End of the month:
Burl = C = 10 nuts
Shirl = D = 2 nuts

As you can see, Burl's number of nuts DOUBLED, while Shirl's number was the SAME.

We're told that Burl had "N times" as many nuts at the end of the month as he did at the beginning, so....
N = 2

We're asked for the PERCENT INCREASE in the number of Shirl's nuts. Since her total did NOT increase, the percentage change is 0. Using the above values for A, B, C, D and N, there is only one answer that gives us a total of 0...

One of the other great 'shortcuts' in this question is that you really don't have to check all of the answer choices. Each of the 5 variables I chose is a POSITIVE number, so two of the answers can be eliminated immediately (since they're adding, multiplying and/or dividing POSITIVE numbers - and doing just those tasks will NEVER lead to 0).

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

you know what Rich, this is practically so stupid of me. i was calculating the percentage change for Burl's nuts all this while, not shirl's. this is probably the dumbest thing i've ever done. a kudos to you for all the pain you took in explaining an idiot of his idiocy, wish i could give you more. EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The numbers of nuts stored by two squirrels, Burl and Shirl, at the be  [#permalink]

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Hi arnabs,

You should expect to make some mistakes during your practice, so don't worry about that. Instead, use each experience as a way to hone your skills and improve.

When dealing with questions of any type (but especially the tougher/wordier prompts), note-taking is essential - including writing down the specific question that is asked. By quickly jotting down "percent change in number of Shirl's nuts" on the pad (which takes all of 3 seconds), you'll have a reference point for all of the work that you'll end up doing later. Over time, these extra steps will help speed you up and make you a far more accurate and efficient Test Taker.

GMAT assassins aren't born, they're made,
Rich
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Joined: 06 Aug 2013
Posts: 65
Re: The numbers of nuts stored by two squirrels, Burl and Shirl, at the be  [#permalink]

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EMPOWERgmatRichC wrote:
Hi arnabs,

You should expect to make some mistakes during your practice, so don't worry about that. Instead, use each experience as a way to hone your skills and improve.

When dealing with questions of any type (but especially the tougher/wordier prompts), note-taking is essential - including writing down the specific question that is asked. By quickly jotting down "percent change in number of Shirl's nuts" on the pad (which takes all of 3 seconds), you'll have a reference point for all of the work that you'll end up doing later. Over time, these extra steps will help speed you up and make you a far more accurate and efficient Test Taker.

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

completely agree, thanks again for the valuable tips and suggestions.
Intern  Joined: 22 Jul 2015
Posts: 5
GRE 1: Q780 V560 Re: The numbers of nuts stored by two squirrels, Burl and Shirl, at the be  [#permalink]

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Bunuel wrote:
The numbers of nuts stored by two squirrels, Burl and Shirl, at the beginning of September were in the ratio A : B. At the end of September, the numbers of nuts stored by Burl and Shirl were in the ratio C : D. If Burl had n times as many nuts at the end of September as at the beginning of September, then by what percent did the number of nuts stored by Shirl increase during September?

(B) 100n(AD - B)/(BC)
(C) 100(D/(BC)*(n + A) - 1)
(D) 100D(n + A)/(BC)
(E) 100(nAD/(BC) - 1)

Kudos for a correct solution.

Another approach is to think of how the answer should look like. Since I am calculating a % change I should see a Sum or Subtraction somewhere, also the outcome should be a pure number, meaning that number of nuts in numerator and denominator should cancel out.
A simple ratio, no sum or sub
B nB does not cancel out with BC
C nD does not cancel out with BC
D nD does not cancel out with BC
E only answers that make sense

Let me know your thoughts.
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Re: The numbers of nuts stored by two squirrels, Burl and Shirl, at the be  [#permalink]

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_________________ Re: The numbers of nuts stored by two squirrels, Burl and Shirl, at the be   [#permalink] 12 Oct 2018, 00:28
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