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CAT/GMAT QA Test (6 questions - 12 minutes)

A test by Ravinder Kumar Mittal.

Test Questions
  1. Question
    It was vacation time, and so I decided to visit my cousin's home. What a grand time we had! In the mornings, we both would go for a jog. The evenings were spent on the tennis court. Tiring as these activities were, we could manage only one per day, i.e., either we went for a jog or played tennis each day. There were days when we felt lazy and stayed home all day long. Now, there were 15 mornings when we did nothing, 9 evenings when we stayed at home, and a total of 12 days when we jogged or played tennis. For how many days did I stay at my cousin's place?
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  2. Question
    If you were to construct a 7 × 7 checkered square (i.e., a 7 × 7 chess board), how many rectangles would there be in total? You need to include squares too because a square is a special kind of rectangle.
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  3. Question
    A block of wood in the form of a cuboid 4" × 10" × 13" has all its six faces painted pink. If the wooden block is cut into 520 cubes of 1" × 1" × 1", how many of these would have pink paint on them?
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  4. Question
    A tennis championship is played on a knock-out basis, i.e., a player is out of the tournament when he loses a match. How many players participate in the tournament if 127 matches are totally played?
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  5. Question
    • A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 3 hours to fill the tank with the large inlet pipe. On the other hand, it takes 4 hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in 7 hours. What fraction of the tank (initially empty) will be filled in 1.70 hours if all three pipes are in operation?
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  6. Question
    My Dad has a miniature Pyramid of Egypt. It is 3 inches in height. Dad was invited to display it at an exhibition. Dad felt it was too small and decided to build a scaled-up model of the Pyramid out of material whose density is (1 / 7) times the density of the material used for the miniature. He did a "back-of-the-envelope" calculation to check whether the model would be big enough. If the mass (or weight) of the miniature and the scaled-up model are to be the same, how many inches in height will be the scaled-up Pyramid?
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