1. A store labels its products with three digits codes composed entirely of letters of the alphabet arranged alphabetically. How many such codes can be created?

 
 
 
 
 

2. As a result of this experience, he wrote a best-seller describing the harrowing life of the inmates, which later becomes a movie, winning accolades from both the public and from national and international critics.

 
 
 
 
 

3. Susie can buy apples from two stores: a supermarket that sells apples only in bundles of 4, and a convenience store that sells single, unbundled apples. If Susie wants to ensure that the total number of apples she buys is a multiple of 5, what is the minimum number of apples she must buy from the convenience store?

 
 
 
 
 

4. Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she saved at the end of the year was 3 times the amount of her take-home pay that she didn’t save. If all money she saved last year was from her take-home pay, what fraction of her pay did she save each month?

 
 
 
 
 

5. Is positive integer z greater than 275?

(1) z is a multiple of 21

(2) z is a multiple of 39

 
 
 
 
 

6. Rates for having a manuscript typed at a certain typing service are $5 per page for the first time a page is typed and $3 per page each time a page is revised. If a certain manuscript has 100 pages, of which 40 were revised only once, 10 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed?

 
 
 
 
 

7. Birds have been said to be descended from certain birdlike dinosaur species with which they share distinctive structural features. The fossil record, however, shows that this cannot be so, since there are bird fossils much older than the earliest birdlike dinosaur fossils that have been found.

Which of the following is an assumption on which the argument relies?

 
 
 
 
 

8. Is b an even integer?

(1) The product of b and integer c is even.
(2) b is divisible by 4.

 
 
 
 
 

9. Overuse of antibiotics often leads to a reduction in the effectiveness of the drugs; this theory has recently been bolstered by observations that people who regularly take antibiotics have fewer disease-fighting organisms in their bodies than do people who rarely take antibiotics.

 
 
 
 
 

10. Lightbox, Inc., owns almost all of the movie theaters in Washington County and has announced plans to double the number of movie screens it has in the county within five years. Yet attendance at Lightbox’s theaters is only just large enough for profitability now and the county’s population is not expected to increase over the next ten years. Clearly, therefore, if there is indeed no increase in population, Lightbox’s new screens are unlikely to prove profitable.

Which of the following, if true about Washington County, most seriously weakens the argument?

 
 
 
 
 

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