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# A store's monthly sales total declined j percent from October to Novem

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Math Expert
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A store's monthly sales total declined j percent from October to Novem  [#permalink]

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18 Jun 2019, 00:43
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Difficulty:

55% (hard)

Question Stats:

64% (02:49) correct 36% (01:56) wrong based on 25 sessions

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A store's monthly sales total declined j percent from October to November. If the store's total sales in December were equal to its total sales in October, by what percent, in terms of j, did the store's sales increase from November to December?

A. j

B. $$\frac{100j}{100+j}$$

C. $$\frac{10,000j}{100-j}$$

D. $$\frac{100j}{100-j}$$

E. $$\frac{j}{1-j}$$

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Re: A store's monthly sales total declined j percent from October to Novem  [#permalink]

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18 Jun 2019, 02:06
First method (plug-in)

S=100 fall=20% so increase is 25% (20*100/80). Only Option E gives 25%

Second method

N=S*(1-J) D=S; Increase is S-S*(1-J)=S-S+SJ=SJ; % Increase = SJ/S*(1-J); S is eliminated to get J/(1-J) IMO E
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Re: A store's monthly sales total declined j percent from October to Novem  [#permalink]

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18 Jun 2019, 10:40
Bunuel wrote:
A store's monthly sales total declined j percent from October to November. If the store's total sales in December were equal to its total sales in October, by what percent, in terms of j, did the store's sales increase from November to December?

A. j

B. $$\frac{100j}{100+j}$$

C. $$\frac{10,000j}{100-j}$$

D. $$\frac{100j}{100-j}$$

E. $$\frac{j}{1-j}$$

let october sale 10 and nov = 8 so drop by 20%=j
and Decemer = 10 so increase by 25%
find answer which gives j=.2 as 25%
IMO E $$\frac{j}{1-j}$$[/quote]
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Re: A store's monthly sales total declined j percent from October to Novem  [#permalink]

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18 Jun 2019, 11:53
Bunuel wrote:
A store's monthly sales total declined j percent from October to November. If the store's total sales in December were equal to its total sales in October, by what percent, in terms of j, did the store's sales increase from November to December?

A. j

B. $$\frac{100j}{100+j}$$

C. $$\frac{10,000j}{100-j}$$

D. $$\frac{100j}{100-j}$$

E. $$\frac{j}{1-j}$$

Let the sales in October = 100

Sales decreased by j % in November
—> Sales in November = 100 - j

Sales in December should be 100 (as of October)
—> % increase = (Final - Initial)/Initial*100
= (100 - (100 - j))/(100 - j)*100
= j/(100 - j)*100
= 100j/(100 - j)

IMO Option D

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Re: A store's monthly sales total declined j percent from October to Novem  [#permalink]

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21 Jun 2019, 16:34
Bunuel wrote:
A store's monthly sales total declined j percent from October to November. If the store's total sales in December were equal to its total sales in October, by what percent, in terms of j, did the store's sales increase from November to December?

A. j

B. $$\frac{100j}{100+j}$$

C. $$\frac{10,000j}{100-j}$$

D. $$\frac{100j}{100-j}$$

E. $$\frac{j}{1-j}$$

We can let sales in October = C, so sales in November are C(100 - j)/100.

We can let n = the percent increase and create the equation:

C(100 - j)/100 x (100 + n)/100 = C

(100 - j)/100 x (100 + n)/100 = 1

(100 - j)(100 + n) = 10,000

10,000 - 100j + 100n - jn = 10,000

100n - jn = 100j

n(100 - j) = 100j

n = 100j/(100 - j)

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Re: A store's monthly sales total declined j percent from October to Novem   [#permalink] 21 Jun 2019, 16:34
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