Six shipments of machine parts were shipped from a factory on two trucks, with each shipment entirely on one of the trucks. Each shipment was labeled either S1, S2, S3, S4, S5, or S6. The table shows the value of each shipment as a fraction of the total value of the six shipments. If the shipments on the first truck had a value greater than of the total value of the six shipments, was S3 shipped on the first truck?

（1） S2 and S4 were shipped on the first truck.

（1） S1 and S6 were shipped on the second truck.

If the positive integer b is 5% greater than the positive integer a, which of the following expressions must be equal to an integer?

I.
II.
III.

­If a, b, and c are positive constants, how many different numbers y are there such that a∗y+b=c?

For the numbers on the number line above, which of the following statements is true?

All the T-shirts a clothing store stocks are plain, and they are all in one of exactly four colors: blue, green, red, and yellow. On any given day, the store sells about twice as many blue T-shirts as it does green T-shirts. Last week, did the store sell more blue T-shirts than red T-shirts?

（1）Last week, the store sold fewer blue T-shirts than red T-shirts and green T-shirts combined.

（2）Last week, the store sold more blue T-shirts than half the total number of red T-shirts and yellow T-shirts combined.

Find the value of y given that and y<|y|

A primary concern among manufacturers polled in a 1998 survey was the inefficiency of trade promotions- inducements offered by manufacturers to retailers to encourage them to reduce retail prices temporarily so as to boost sales volume. Such inducements may include temporarily reduced costs of goods, free goods, or display allowances (fees manufacturers pay retailers to encourage them to allocate premium shelf space to a product). At the heart of manufacturers' dissatisfaction lies concern regarding widespread retailer opportunism. Although consumers know from experience the approximate frequency of promotional pricing, they do not typically have complete information about ongoing trade promotions in a given period, so retailers can profit by sometimes choosing not to pass along their own savings to their customers. Inefficient use of trade promotion dollars has prompted several large manufacturers to adopt an "everyday low price" policy for their goods, but at least one diaper manufacturer found it had to revert to its former pricing strategies in the face of increasing promotional competition from other brands. Adopting an alternative approach, some manufacturers have themselves advertised ongoing promotions. By informing at least some customers about promotions, manufacturers believe they can regulate retailer opportunism by increasing customers' propensity to search for discounted prices.

An investor will use $2,000 to purchase 10 shares of a certain stock at $200 per share. At the same time, she will invest another sum of money in a certificate of deposit (CD) that earns 2% simple interest annually. The investor would like to know how much money she should invest in the CD to meet her goal of net earnings (before any taxes or other fees) of $360 from the two investments at the end of one year.

In the table, select for CD assuming 10% gain the amount the investor should invest in the CD to meet her goal under the assumption that the stock price will have increased by 10% at the end of one year, and select for CD assuming 5% loss the amount she should invest in the CD to meet her goal under the assumption that the stock price will have decreased by 5% at the end of one year. Make only two selections, one in each column.

Tom and Harry started running around a circular track of length 400 meters at the same time from diametrically opposite points. Tom ran clockwise while Harry ran anti-clockwise. If they kept running continuously at their own uniform speeds till they met for the second time, after how much time did they meet for the second time?

(1) Ratio of speeds of Tom and Harry is 3:2.

(2) Tom is 50% faster than Harry.

Key industry analysts have recommended that grocery retailers lower operating costs by adopting a strategy of efficient assortment, whereby stock - keeping units (SKUs, or product lines) that sell poorly are eliminated. But grocers have resisted the suggested cutback, on the basis of research showing that assortment perceptions (perceptions by shoppers of wideness in selection of items in a merchandise category—e.g., laundry detergent) are positively related to consumer attitudes toward a given store. Retailers worry that shoppers will notice that offerings have been reduced, lower their assortment perceptions, and thereby shop less frequently in the retailers’ stores.

However, results from a recent study suggest that this risk is smaller than retailers have assumed. The study found that consumer assortment perceptions are significantly affected by the simple cues of availability of a favorite item (the favorite - available cue) and amount of space devoted to a category of SKUs (the category - space cue). If the number of SKUs is decreased while category space is held constant and favorite items remain available, the threshold for perceiving a reduction in items tends to be somewhere between 25 and 50 percent. Therefore, a 25 percent reduction in SKUs within most merchandise categories should not adversely affect consumers' assortment perceptions or store choice.

Moreover, the study found that a 25 percent SKU reduction can increase consumer assortment perceptions when low - preference SKUs are removed and replaced with duplicate facings of the most popular SKUs from the same category, perhaps because it is thereby easier for consumers using the favorite - available cue to find the desired products.

With the recent proliferation of SKUs, there may be considerable latitude for retailers to reduce their SKU numbers while maintaining availability of favorite products for majorities of consumers. Furthermore, even if a few consumers perceive marginal reductions in assortment, the increased profitability due to lower inventory and restocking costs, along with fewer out - of - stock products, still makes assortment reductions worthwhile.

Finally, more - sophisticated guidelines for SKU elimination, factoring in similarities in behavior within identifiable groups of consumers, could allow greater reductions of SKU numbers without negatively affecting perceptions of availability, though retailers need also to carefully consider the category - space cue when making assortment decisions.