During a sale, a store sells 20 percent of its remaining stock each

Let's pick a smart number for the initial amount. The store sold 20 percent each day, hmm, after looking at the answer choices 625 is used pretty often, so let's pick it.
1st day: 125 items sold, 500 left
2nd day: 100 items sold, 400 left
3rd day: 80 sold, 320 left
4th day: 64 sold, 256 left
\(Sum of the sold items = 125+100+80+64=369 --> \frac{369}{625}\), Answer E

Hi All,

This question can be solved by TESTing VALUES (the approach that BrainLab used). I'd like to add a particular point as to WHY it's so useful to use the number 625 - it's not just that it shows up in 3 of the 5 answer choices... ALL 5 answer choices can be written as 'fractions out of 625', it's just that 2 of the answers have been reduced.

Once you have that starting value, you can work through the individual calculations as shown. It's important to note what the question specifically ASKS FOR though. One of the wrong choices answers the question "what fraction of its stock does it have left?' (Answer B).

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

The store keeps selling 20% or 1/5 of its stock daily, without replacing. So at the end of the day, the stock that remains is 4/5 of the original stock. We have to find the fraction after four days, which means we have to multiply the original value four times by 4/5.

So lets start with a number '625' which represents the original stock. (because 625 = 5^4)
Thus, stock after 4 days = 625 * 4/5 * 4/5 * 4/5 * 4/5 = 256.
Stock remaining = 625-256 = 369

So the required fraction = 369/625

Hence E is answer

We can let the initial stock = x.

After day 1:

0.2x is sold and 0.8x is left over.

After day 2:

0.2(0.8x) = 0.16x is sold and 0.8(0.8x) = 0.64x is left over.

After day 3:

(0.2)(0.64x) = 0.128x is sold and 0.8(0.64x) = 0.512x is left over.

After day 4:

0.2(0.512x) = 0.1024x is sold and 0.8(0.512x) = 0.4096x is left over.

Since 0.4096x is left over at the end of 4 days, 1 - 0.4096 = 0.5904, or 59.04%, of the initial stock was sold. We re-express 0.5904 as a fraction: 0.5904 = 5904/10,000 = 738/1250 = 369/625 of the original stock was sold.

Answer: E
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Most easiest option i guess is use fraction i.e. first day 1/5 of X is sold and next day 4/5 of the stock remained.

\(20\) % = \(\frac{1}{5}\)

Thus, there is a reduction in stock by the fraction of \(\frac{1}{5}^{th}\)

Let, The total stock be 625 Units....

Day 1 : Stock in Hand = 625, Sold = 125, Remaining = 500
Day 2 : Stock in Hand = 500, Sold = 100, Remaining = 400
Day 3 : Stock in Hand = 400, Sold = 80, Remaining = 320
Day 4 : Stock in Hand = 320, Sold = 64, Remaining = 256

Total Quantity of Stock sold is 625 - 256 = 369 Units...



So, fraction of Original Stock he has is \(\frac{369}{625}\)

Thus, Answer must be (C) \(\frac{369}{625}\)
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I guess the easiest approach is to subtract the remaining stock from the original:

\(1-(\frac{4}{5})^4\)
\(=\frac{625}{625}-\frac{256}{625}\)
\(=\frac{369}{625}\)

I chose my smart number as 625. Why? because it's in answer choices.

In the end just build a quick calculation matrix of day/inventory/sold and work your way through 4 days. It took me less than 2 minutes to calculate.

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