Analytical

Analytical

Data Sufficiency Hard 3

⏱ 10:00

600%
  • Hard 3 - 6 In the figure above, what is the value of x + y? (i) x = 70 (ii) ABC and ADC are both isosceles triangles.
  • Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal ? (i) s = 4 (ii) 90<r<100
  • When a player in a certain game tossed a coin a number of times, 4 more heads than tails resulted. Heads or tails resulted each time the player tossed the coin. How many times did heads result? (i) The player tossed the coin 24 times. (ii) The player received 3 points each time heads resulted and 1 point each time tails resulted, for a total of 52 points.
  • Are all of the numbers in a certain list of 15 numbers equal? (i) The sum of all the numbers in the list is 60. (ii) The sum of any 3 numbers in the list is 12.
  • If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75 ? (i) None of the six numbers is less than 75. (ii) None of the six numbers is greater than 75.
  • What was the total amount of revenue that a theater received from the sale of 400 tickets, some of which were sold at x percent of full price and the rest of which were sold at full price? (i) x = 50 (ii) Full-price tickets sold for $20 each.
  • What amount did Jean earn from the commission on her sales in the first half of 1988 ? (i) In 1988 Jean’s commission was 5 percent of the total amount of her sales. (ii) The amount of Jean’s sales in the second half of 1988 averaged $10,000 per month more than in the first half.
  • If Sara’s age is exactly twice Bill’s age, what is Sara’s age? (i) Four years ago, Sara’s age was exactly 3 times Bill’s age. (ii) Eight years from now, Sara’s age will be exactly 1.5 times Bill’s age.
  • If the measures of' the three interior angles of a triangle are y°, 15x°, and 18x°, what is the value of y ? (i) x =5 (ii) 15x + y = 90
  • If n is a positive integer, is n divisible by at least six positive integers? (i) n is the product of three different prime numbers. (ii) n = 30
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