## Problem Set #1

*The following table gives information about the ratio of functioning electronics to non-functioning electronics sold by companies A, B, C, D, and E, as well as the percentage of faulty products by type for each company.*

Company | Ratio of Functioning to Non-Functioning Electronics Sold in 2017 | Percentage of Faulty Goods Sold by Product | |||||
---|---|---|---|---|---|---|---|

Mobile Phone | CD Player | DVD Player | Computer | Printer | Television |
||

A | 49:1 | 2.4% | 4.1% | 2.6% | 1.9% | 3.2% | 1.8% |

B | 73:1 | 0.8% | 3.0% | N/A | 1.4% | 2.8% | 1.4% |

C | 55:2 | N/A | 3.6% | 1.8% | 5.4$ | 3.2% | 4.0% |

D | 31:2 | 9.7% | 2.3% | 3.0% | 10.0% | 6.5% | N/A |

E | 89:3 | 1.8% | 3.4% | 1.7% | 5.1% | 5.2% | 3.4% |

- Approximately how many functional (i.e. non-faulty) mobile phones did Company B sell in 2017 if the company sold two million units that year?
A. 1.84 million

B. 1.94 million

C. 1.98 million

D. 1.95 million - If Company C sells twice as many printers as Company A, approximately how many faulty printers did Company C sell in 2017 if Company A sold 3,000 faulty printers that year?
A. 6,000

B. 3,000

C. 1,500

D. 13,000 - Company D sells 2.4 million total products in 2017 and the ratio of products it sells to those that Company E sells is 3:2, what is the approximate ratio of faulty CD players sold by Companies D and E in 2017?
A. 15:10

B. 5:7

C. 24:17

D. Cannot be determined from the information provided. - For which companies and for what product was the difference in percentages of faulty goods the greatest between the company with the highest percentage of faulty products and the company with the lowest percentage of faulty products?
A. Company B and Company D, mobile phones

B. Company B and Company D, computers

C. Company A and Company C, printers

D. Company C and Company D, mobile phones **Answer: C.**Note: On the official exam, you will not see lettered answer choices. However, I am using them here for clarity’s sake.First, evaluate what data you have. The table gives us the percentage, rather than the number, of

*faulty*goods: 2.4%. We also have Company B’s total mobile phone sales for 2017: two million units.Next, you could approach this problem one of two ways. First, you could multiply two million (total units sold) by the percentage of faulty phones (0.8%), and then subtract your answer from two million (total – faulty = non-faulty units.) Secondly, and more easily, you could subtract the percentage of faulty phones from 100 (100%), then multiply that number, which represents the non-faulty phones, by two million (again, total units sold).

Using the second process, we can see that the percentage of non-faulty phones sold by Company B was 99.2%. Multiplying by two million, we end up with 1,984,000, or 1.98 million (it’s okay to round because the question stem gives us the word “approximately”: (C).

**Answer: A.**Identify the information you have: the number of Company A’s faulty printer sales (3,000, given in the question stem), the percentage of sales that those faulty printers comprise for Company A (3.2% of all sales, from the table), the fact that Company C’s printer sales are twice Company A’s (given in the question stem), and the percentage of sales that those faulty printers comprise for Company C (also 3.2%, from the table).Next, you could set up your calculations. To do this, you would set 3,000 faulty printers = 3.2/100 (

*x*), with*x*being Company A’s total printer sales. You’d arrive at 93,750 total printer sales for Company A. After that, double these printer sales for Company C: 187,500. Finally, calculate 3.2% of Company C’s total printer sales: 6,000. This is the number of faulty printers Company C sold.**But there’s a better way.**If you consider the information in the first paragraph carefully, you’ll realize that the companies sold the*same*percentage of faulty printers. With that in mind, all we have to do is double Company A’s faulty printer sales to find Company C’s, since the question stem tells us that Company C’s sales are twice Company A’s. 3,000 x 2 = 6,000, Answer (A).(B) is what you would get if you put in the information about Company A’s faulty printers from the question stem, or if you subtracted Company A’s faulty sales from Company C’s. (C) is what happens if you divided, rather than multiplied, by two. (D) is the approximate result you’d get if you accidentally used Company D’s information (6.5% faulty printers) rather than Company C’s.

**Answer: D.**State the information that you have: We know the number of total products that Company D sold (2.4 million), the ratio of products sold between Company D and Company E (3:2), the percentage of Company D’s CD players that were faulty (2.3%), and the percentage of Company E’s faulty CD players (3.4%).

Notice what information we DON’T have in all this info overload: we have no idea what percentage of total goods that CD players make up for either company. Maybe 90% of their products are CD players; maybe 2% are. Maybe it’s 90% for Company D and 2% for Company E—we have no way of knowing!(A) is what you’ll arrive at if you’re looking for an answer equivalent to the ratio given in the problem (3:2). (B) is approximately what you’ll get if you change the percentages of faulty CD players (2.3% and 3.4%) to a ratio. (C) is the answer you get if you make the faulty assumption that Company D sold 2.4 million CD players (rather than total products) and go on to calculate the ratio of faulty products between the two companies.

**Answer: A.**In this case, the complicated wording of the question makes it necessary to rephrase before moving on. Reading carefully, the question is asking us to find where the biggest difference in the percentage of faulty products occurs—for a single given product (though this last bit may not be clear from the question stem, looking at the answer choices clarifies it).To answer this problem, scan the table’s faulty product percentage columns for really big numbers and really small numbers in the same column. Doing this, you’ll see that one company had a high percentage of mobile phones faults (Company D, 9.7%) and one had a really small percentage (Company B, 0.8%), a difference of 8.9%.

(A) is the answer you’ll get if you don’t look closely enough. The only column that approaches the right answer is computers, where Company D had a 10% failure rate and Company B had a 1.4% failure rate–but that’s only a difference of 8.6%. Mobile phones still has a greater difference. (C) is the answer you’ll get if you accidently solve for the companies with the

*least*difference in failure rates. (D) is what you’ll get if you misunderstand that N/A means “not applicable”—i.e. Company C either did not produce mobile phones, none of them failed, or for whatever reason, we don’t have this information. It doesn’t mean for sure that none of them failed (though it could, we don’t know this from the information provided).

## Answers and Explanations

(A) represents what you’d get if you misread 0.8% as 8%. (B) is what you would get if you used Company B’s CD sales instead of mobile phone sales. Finally, (D) is what you would get if you mixed up your rows and performed the calculation for Company A instead of Company B.

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