Analytical

Analytical

Data Sufficiency Hard 1

⏱ 10:00

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  • Hard 1 - 6 If arc PQR above is a semicircle, what is the length of diameter PR? (i) a=4 (ii) b=1
  • If d is a positive integer, is an integer? (i) d is the square of an integer. (ii) √d is the square of an integer.
  • The length of the edging that surrounds circular garden K is 1/2 the length of the edging that surrounds circular garden G. What is the area of garden K ? (Assume that the edging has negligible width.) (i) The area of G is 25π square meters. (ii) The edging around G is 10π meters long.
  • The range of the numbers in set S is x, and the range of the numbers in set T is y. If all of the numbers in set T are also in set S, is x greater than y ? (i) Set S consists of 7 numbers. (ii) Set T consists of 6 numbers.
  • The hypotenuse of a right triangle is 10 cm. What is the perimeter, in centimeters, of the triangle? (i) The area of the triangle is 25 square centimeters. (ii) The 2 legs of the triangle are of equal length.
  • What was the revenue that a theater received from the sale of 400 tickets, some of which were sold at the full price and the remainder of which were sold at a reduced price? (i) The number of tickets sold at the full price was 1/4 of the total number of tickets sold. (ii) The full price of a ticket was $25.
  • A box contains only red chips, white chips, and blue chips. If a chip is randomly selected from the box, what is the probability that the chip will be either white or blue? (i) The probability that the chip will be blue is 1/5. (ii) The probability that the chip will be red is 1/3.
  • If Q is an integer between 10 and 100, what is the value of Q? (i) One of Q’s digits is 3 more than the other, and the sum of its digits is 9. (ii) Q < 50
  • How many of the boys in a group of 100 children have brown hair? (i) Of the children in the group, 60 percent have brown hair. (ii) Of the children in the group, 40 are boys.
  • The annual rent collected by a corporation from a certain building was x percent more in 1998 than in 1997 and y percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997 ? (i) x>y (ii) (xy/100)< (x – y)
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