Edition 23

Edition 15

1. Refrigerators come in cartons 40 inches deep × 48 inches wide × 60 inches high. They must stand upright when stored. If Jones has a storage room 45 feet across, 60 feet deep, and 8 feet high, what is the greatest number of refrigerators he can store there?

  • (A) 180
  • (B) 195
  • (C) 198
  • (D) 201
  • (E) 396

2. In triangle ABC, given that AB = AC and D is any point on BC. Length of BD if AB = 17 cm, AD = 15 cm and CD = 4 cm is

  • (A) 4 cm
  • (B) 12 cm
  • (C) 16 cm
  • (D) 4 cm
  • (E) 8 cm

3. Positive integers a and b, possibly equal, are chosen randomly from among the divisors of 400. The numbers a, b are chosen independently, each divisor being equally likely to be chosen. The probability that gcd(a, b) = 1 and lcm(a, b) = 400 is

  • (A) 4/25
  • (B) 2/25
  • (C) 4/215
  • (D) 4/225
  • (E) 2/215
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7 comments

  1. Problem #2) Solution :
    B D=x cm;;
    C o s
    Or (A B ^2+ B D ^2-A D ^2)/(2 * A B* B D)=(A C ^2+C D ^2-A D ^2)/(2* A C * C D);
    Or ( 1 7^2 +x ^2 -1 5 ^2/(2* 17 * x)=(1 7^2 + 4 ^2-1 5 ^2)/(2 * 17* 4);
    Or (64+ x^2)/x= (80)/4=20;
    Or 64+ x^2=20 *x; or x=4 or 16 ;
    Admissible value of x=16B D= x cm=16 cm

    Reply

    2. Solution of problem1.
      First we will measure 3 conis each side.
      Case1 – if balance is eqall we will measure two out of 3 coins putting one on each side, thus we will get the heavier one.
      Case 2 – if one side is heavier them we will take 2 coins of the heavier side and measure by putting one each side, thus we can find the heavier one.

      Reply

  2. Solution of problem1.
    First we will measure 3 conis each side.
    Case1 – if balance is eqall we will measure two out of 3 coins putting one on each side, thus we will get the heavier one.
    Case 2 – if one side is heavier them we will take 2 coins of the heavier side and measure by putting one each side, thus we can find the heavier one.

    Reply

  3. Question 1 solution :
    (c)
    As 10 houses have less than 6rooms, they are to be excluded.
    Given,
    4 houses have more than 8 rooms .
    Therefore, number of houses having either less than 6 or greater than 8 rooms = 10 + 4 = 14.
    The remaining houses, that is 11 houses fulfill the above mentioned criteria.

    Reply

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