224

If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

225

If [x] is the greatest integer less than or equal to x, what is the value of [1.6] +[3.4]+[2.7]?

226

In the first week of the year, Nancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that Nancy saved during the 52 weeks?

227

In a certain sequence, the term $${x}_{n}$$, is given by the formula $${x}_{n}={2}{x}_{n1}\frac{1}{2}({x}_{n2})$$ for all $${n}\geq{2}$$. If $${x}_{0}=3$$ and $${x}_{1}=2$$, what is the value of $${x}_{3}$$

228

During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine`s average speed for the entire trip?

229

If $${n}={33}^{43}+{43}^{33}$$, what is the units digit of n?

230

Team A and Team B are competing against each other in a game of tugofwar. Team A, consisting of 3 males and 3 females, decides to line up male, female, male, female, male, female. The lineup that Team A chooses will be one of how many different possible lineups?

231

A border of uniform width is placed around a rectangular photograph that measures 8 inches by 10 inches. If the area of the border is 144 square inches, what is the width of the border, in inches?

232

If $${d}=\frac{1}{{2}^{3}\times{5}^{7}}$$ is expressed as a terminating decimal, how many nonzero digits will d have?

233

For any positive integer n, the sum of the first n positive integers equals $$\frac{n(n+1)} 2$$. What is the sum of all the even integers between 99 and 301?

234

November 16, 2001, was a Friday. If each of the years 2004, 2008, and 2012 had 366 days, and the remaining years from 2001 through 2014 had 365 days, what day of the week was November 16, 2014?

235

How many prime numbers between 1 and 100 are factors of 7,150 ?

236

A sequence of numbers $${a}_{1}$$, $${a}_{2}$$, $${a}_{3}$$, ... is defined as follows:$${a}_{1}$$ = 3, $${a}_{2}$$ = 5, and every term in the sequence after $${a}_{2}$$ is the product of all terms in the sequence preceding it, e.g., $${a}_{3}$$ = ($${a}_{1}$$)($${a}_{2}$$) and $${a}_{4}$$ =($${a}_{1}$$)($${a}_{2}$$)($${a}_{3}$$). If $${a}_{n}$$ = t and n > 2, what is the value of $${a}_{n+2}$$ in terms of t?

237

Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?

238

Of the 300 subjects who participated in an experiment using virtualreality therapy to reduce their fear of heights, 40 percent experienced sweaty palms, 30 percent experienced vomiting, and 75 percent experienced dizziness. If all of the subjects experienced at least one of these effects and 35 percent of the subjects experienced exactly two of these effects, how many of the subjects experienced only one of these effects?

239

The outer dimensions of a closed rectangular cardboard box are 8 centimeters by 10 centimeters by 12 centimeters, and the six sides of the box are uniformly $$\frac{1}{2}$$ centimeter thick. A closed canister in the shape of a right circular cylinder is to be placed inside the box so that it stands upright when the box rests on one of its sides. Of all such canisters that would fit, what is the outer radius, in centimeters, of the canister that occupies the maximum volume?

240

if $${m}^{1}=\frac{1}{3}$$,then $${m}^{2}$$ is equal to

241

A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer`s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer`s initial cost for the 60 cameras?

242

Seven pieces of rope have an average (arithmetic mean) length of 68 centimeters and a median length of 84 centimeters. If the length of the longest piece of rope is 14 centimeters more than 4 times the length of the shortest piece of rope, what is the maximum possible length, in centimeters, of the longest piece of rope?

243

What is the difference between the sixth and the fifth terms of the sequence 2,4, 7,... whose $$n^{th}$$ term is $$n + {2}^{n1}$$?
