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Last year 12.6 percent of the total value of all merchandise sold by

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Last year 12.6 percent of the total value of all merchandise sold by [#permalink] New post   25 Nov 2023, 13:17
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Last year 12.6 percent of the total value of all merchandise sold by a certain department store was from the store's brand. If the revenue from the sale of the store's brand of merchandise last year was $7.2 million, approximately how many million dollars of revenue did the store earn from the sale of merchandise that was not the store's brand?

(A) 1
(B) 6
(C) 36
(D) 50
(E) 58
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D
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Re: Last year 12.6 percent of the total value of all merchandise sold by [#permalink] New post   25 Nov 2023, 14:30
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Arghi wrote:
Last year 12.6 percent of the total value of all merchandise sold by a certain department store was from the store's brand. If the revenue from the sale of the store's brand of merchandise last year was $7.2 million, approximately how many million dollars of revenue did the store earn from the sale of merchandise that was not the store's brand?

(A) 1
(B) 6
(C) 36
(D) 50
(E) 58


The total value of all merchandise sold = \($x\)

\(12.6\)% \(* x = 7.2*10^{6}\)

\(\frac{12.6}{100}*x = 7.2*10^{6}\)

\(x = \frac{7.2*10^{6}*100}{12.6}\)

\(x = \frac{72*10^{6}*10}{12.6}\)

\(x \approx 60*10^6\)

Percentage of merchandise that was not from the store's brand = 100% - 12.6% = 87.4%

Revenue from the sale of 87.4% of merchandise \(\approx 87.4\)% of \(60*10^6\)

\(\approx 87\)% of \(60*10^6\)

\(\approx \frac{87}{100}*60*10^6\)

\(\approx 52.2*10^6\)

The closest option is 50

Option D
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Re: Last year 12.6 percent of the total value of all merchandise sold by [#permalink] New post   26 Nov 2023, 10:18
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Simple Approach

First thing to ask yourself; 7.2m is 12.6% of what number (x)? Since the question says approximate, let us round the numbers to 7m & 13%.

So, back to our Q --> 7=13/100(x) --> x≈53.

We already know 7 of that 53 is the stores own brand, the question asks for the rest of the amount excluding the stores brand.

So, 53-7 = 46

The closest option to 46 is 50, answer D.
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Re: Last year 12.6 percent of the total value of all merchandise sold by [#permalink] New post   14 Jan 2024, 12:41
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It should be noticed that 12.6 percent is roughly 1/8, meaning total value of all merchandise can be approximated by multiplying 8 by 7.2 million, which is 57.6 million. So, if we subtract store's brand revenue of 7.2 million from the total of 57.6 million, we get an approximate value close to 50 million. The answer is D.
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Re: Last year 12.6 percent of the total value of all merchandise sold by [#permalink]
14 Jan 2024, 12:41
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