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277
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For all z, [z] denotes the least integer greater than or equal to z. Is [x] = 0?(1) - 1 < x < - 0.01(2) [x + 0.5] = 1
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278
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 The circular base of an above-ground swimming pool lies in a level yard and just touches two straight sides of a fence at points A and B, as shown in the figure above. Point C is on the ground where the two sides of the fence meet. How far from the center of the pool's base is point A ? (1) The base has area 250 square feet.(2) The centre of the base is 20 feet from point C.
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279
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If xy = -6, what is the value of xy (x +y )?(1) x - y = 5 (2) $${x}{y}^{2}={18}$$
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280
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[y] denotes the greatest integer less than or equal to y. Is d < 1?(1) d = y - [y](2) [d] = 0
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281
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If N is a positive odd integer, is N prime?(1) $$N = 2^{k} + 1$$ for some positive integer k.(2) N + 2 and N + 4 are both prime.
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282
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If m is a positive integer, then $${M}^{3}$$ has how many digits?(1) M has 3 digits.(2) $${M}^{2}$$ has 5 digits
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283
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What is the value of $$x^{2} - y^{2}$$?(1) $$({x - y})^{2} = 9$$(2) x + y = 6
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284
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For each landscaping job that takes more than 4 hours, a certain contractor charges a total of r dollars for the first 4 hours plus 0.2r dollars for each additional hour or fraction of an hour, where r＞100. Did a particular landscaping job take more than 10 hours?(1) The contractor charged a total of $288 for the job.(2) The contractor charged a total of 2.4r dollars for the job.
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285
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If $$x^{2} = 2^{x}$$, what is the value of x?(1) $$2x = ({\frac{x}{2}})^{3}$$(2) $$x = {2}^{x -2}$$
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286
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The sequence $$s_{1}$$, $$s_{2}$$, $$s_{3}$$, ...$$s_{n}$$,... is such that $$s_{n} = \frac{1}{n} - \frac{1}{n +1}$$ for all integers $$n\ge 1$$. If k is a positive integer, is the sum of the first k terms of the sequence greater than $$\frac{9}{10}$$?(1) k > 10(2) k < 19
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287
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In the sequence S of numbers, each term after the first two terms is the sum of the two immediately preceding terms. What is the 5th term of S?(1) The 6th term of S minus the 4th term equals 5.(2) The 6th term of S plus the 7th term equals 21.
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288
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If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?(1) 60 percent of the guests who ordered dessert also ordered coffee.(2) 90 percent of the guests who ordered coffee also ordered dessert.
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289
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A tank containing water started to leak. Did the tank contain more than 30 gallons of water when it started to leak?(Note :1 gallon = 128 ounces ) (1) The water leaked from the tank at a constant rate of 6.4 ounces per minute.(2) The tank became empty less than 12 hours after it started to leak.
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290
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In the xy-plane, lines k and $$\ell$$ intersect at the point (1,1) . Is the y-intercept of k greater than the y-intercept of $$\ell$$?(1) The slope of k is less than the slope of $$\ell$$.(2) The slope of $$\ell$$ is positive.
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291
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A triangle has side lengths of a, b, and c centimeters. Does each angle in the triangle measure less than 90 degrees?(1) The 3 semicircles whose diameters are the sides of the triangle have areas that are equal to 3 $$cm^{2}$$, 4$$cm^{2}$$, and 6 $$cm^{2}$$, respectively.(2) c < a + b < c + 2
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292
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Each of the 45 books on a shelf is written either in English or in Spanish, and each of the books is either a hardcover book or a paperback. If a book is to be selected at random from the books on the shelf, is the probability less than $$\frac{1}{2} $$that the books selected will be a paperback written in Spanish?(1) Of the books on the shelf, 30 are paperbacks.(2) Of the books on the shelf, 15 are written in Spanish.
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293
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A small school has three foreign language classes, one in French, one in Spanish, and one in German. How many of the 34 students enrolled in the Spanish class are also enrolled in the French class?(1) There are 27 students enrolled in the French class, and 49 students enrolled in either the French class, the Spanish class, or both of these classes.(2) One - half of the students enrolled in the Spanish class are enrolled in more than one foreign language class.
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294
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If S is a set of four numbers w, x, y, and z, is the range of the numbers in S greater than 2?(1) w - z >2(2) z is a the least number in S.
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295
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Last year $$\frac{3}{5}$$of the number of a certain club were males. This year the members of the club include all the members from last year plus some new members. Is the fraction of the members of the club who are males greater this year than last year?(1) More than half of the new members are male.(2) The number of members of the club this year is $$\frac{6}{5}$$ the number of members last year.
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296
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If a , b, and c are consecutive integers and 0 < a < b < c, is the product abc a multiple of 8?(1) The product ac is even.(2) The product bc is a multiple of 4.
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