This month, a factory will produce a certain number of articles

Question

This month, a factory will produce a certain number of articles, a part of which will be sold. Next month the factory will produce only half the number of articles produced this month, but for each article that is unsold this month, k articles will be sold next month. Ignoring the production and sales of articles in all months prior to this month, in terms of k, what fraction of the number of articles produced this month should be sold this month so that the cumulative number of articles remaining unsold next month would be equal to 1/3 the number of articles sold this month?

(A) \(\frac{4 (2 − k)}{3 (1 − k)}\)

(B) \(\frac{2 (4 − 2k)}{3 (2 − 3k)}\)

(C) \(\frac{3 (4 − 3k)}{2 (3 − 2k)}\)

(D) \(\frac{(3 − 2k)}{(4 − 3k)}\)

(E) \(\frac{3 (3 − 2k)}{2 (4 − 3k)}\)

(A)  \frac{4 (2 − k)}{3 (1 − k)}

(B)  \frac{2 (4 − 2k)}{3 (2 − 3k)}

(C)  \frac{3 (4 − 3k)}{2 (3 − 2k)}

(D)  \frac{(3 − 2k)}{(4 − 3k)}

(E)  \frac{3 (3 − 2k)}{2 (4 − 3k)}

Kinshook · Answer

Given: This month, a factory will produce a certain number of articles, a part of which will be sold. Next month the factory will produce only half the number of articles produced this month, but for each article that is unsold this month, k articles will be sold next month.

Asked: Ignoring the production and sales of articles in all months prior to this month, in terms of k, what fraction of the number of articles produced this month should be sold this month so that the cumulative number of articles remaining unsold next month would be equal to 1/3 the number of articles sold this month?

This month:
Articles produced = 2x
Articles sold = 2mx
Articles unsold = 2x - 2mx

Next month:
Articles produced = x
Articles sold = k(2x - 2mx)
Articles unsold = x - k(2x-2mx)

Cumulative articles unsold = 2x - 2mx + x - k(2x-2mx) = 2mx/3

3 - 2m = 2k - 2mk + 2m/3
3 - 2k = 2m - 2mk + 2m/3 = 8m/3 - 2mk = m(8-6k)/3
 m = \frac{3(3-2k)}{2(4-3k)}

IMO E

Kushchokhani · Answer

Kinshook

I think there is a problem in your solution.
Next month:
Articles produced = x
Articles sold = k(2x - 2mx) --- Here it would be multiply rather than divide
Articles unsold = x - k(2x-2mx)

Cumulative articles unsold = 2x - 2mx + x - k(2x-2mx) = 2mx/3
x will now cancel out!

Further, I solved this ques in a bit different way:
Let 100 units produced this month. So, 50 units produced next month.
Let 90 units sold this month. So, 10 units unsold this month.
Let k=3, So, 30 units sold next month.
Cumulative unsold next month=10+20=30, which is equal to 1/3rd of units sold this month. This means that our assumptions are valid.
We want to determine what fraction of the number of articles produced this month should be sold this month i.e. 90/100=9/10
Now, substitute k=3 in each of the answer choices to get final answer as 9/10
Only choice E matches this.
Hence, IMO answer should be E.
However, OA given is C.  KarishmaB   chetan2u   Bunuel  what's your view on this?

chetan2u · Answer

Two ways

(1)  ALGEBRAIC  
Month……Produced…….Total………Sold……..Unsold
Present………..x………..……x…………..a…………..x-a
Next……………x/2……… (x-a)+\frac{x}{2} ….k(x-a)……  (x-a)+\frac{x}{2} - k(x-a)

Given:  (x-a)+\frac{x}{2} - k(x-a)=\frac{a}{3}

We are looking for the value of  \frac{a}{x}

(x-a)+\frac{x}{2} - k(x-a)=\frac{a}{3} 
 \frac{3x}{2}-a - kx+ak=\frac{a}{3} 
 \frac{(3-2k)x}{2}=\frac{3a(1-k)+a}{3}=\frac{a(4-3k)}{3} 
Divide the entire expression by x
 \frac{(3-2k)x}{x*2}=\frac{a(4-3k)}{3*x} 
 \frac{(3-2k)}{2}=\frac{a}{x}*\frac{(4-3k)}{3} 
 \frac{a}{x}=\frac{3(3-2k)}{2(4-3k)}

(2)  Substitution  as also shown by  Kushchokhani 
Month……Produced…….Total………Sold……..Unsold
Present……100………..…100…………..60…………..40
Next…………50…………….90………….40k…………..20
So, 90-40k=20 or k=7/4

K as 7/4 should give the answer as 60/100 or 3/5.
E gives the answer.

E

Ulfat · Answer

Is it really a GMAT relevant problem. Somehow, I doubt it, because it requires only lengthy and tedious calculations. Nothing else!

This month, a factory will produce a certain number of articles

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