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Quantitative Aptitude Test - 1

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Quantitative Aptitude Test - 1
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Weekly Quiz Competition
  • Question 1
    4 / -1

    A necklace must be made using 32 beads and a gold pendant which looks different from both the sides. There are 7 beads of red colour, 6 of green, 8 of yellow and 11 of blue. In how many ways can the necklace be made, so that the two beads, one on either side of the pendant are red?

    Solution

     

  • Question 2
    4 / -1

    In how many different ways can the letters of the word '\(APPLE\)' be arranged?

    Solution

    We can solve by the permutation method,

    \(APPLE\) contains \(1 {A}, 2 {P}, 1 {L}\) and \(1 {E}\).

    We know that,

    \(P(n, r)=\frac{n !}{(n-r) !}\)

    Required number \(r=\frac{5 !}{2 !}=\frac{(5 \times 4 \times 3 \times 2 \times 1)}{2}=60\)

  • Question 3
    4 / -1

    The profit margin on readymade shirts is 20%. If there is a defect, they are disposed off at Rs.100 per shirt. It costs Rs.120 to make a shirt, and 5 shirts out of 100 are defective. The profit realized on 100 shirts coming out of the tailoring unit is:

    Solution

     

  • Question 4
    4 / -1

    In an election, the votes cast for two candidates are in the ratio 3 : 10. If all votes are valid votes and if the successful candidates received 156200 votes, then the total votes polled are:

    Solution

    Given:

    Votes received by two candidates in terms of ratio = 3 : 10

    Total votes received = 156200

    Let the votes got by two candidates be 3x & 10x.

    10x = 156200

    ⇒ x = 15620

    Total votes polled,

    3x + 10x = 13 × 15620 = 203060

    ∴ The total votes polled are 203060.

    Hence, thr correct option is (D).

  • Question 5
    4 / -1

    A truck is carrying a pile of cubical cartons of side 1 unit. The height of the cuboidal pile is 10 units, its length is 10 units and its breadth is 12 units. The truck meets with an accident and 90% boxes from the top layer of the pile fall. This percentage goes on reducing by 10 for each successive layer from the top to the bottom. The boxes that fall get dirty. The driver repiles all the boxes. On reaching the destination, a box is picked up at random for inspection. Find the probability of the box being dirty.

    Solution

     

  • Question 6
    4 / -1

    Two boys start moving together along a circular track at speeds of 1 kmph. and 1.5 kmph. respectively. One of them takes half an hour more than the other to traverse it. The radius of the circular track is:

    Solution

     

  • Question 7
    4 / -1

    12 caps are kept on a table out of which four are red, four are white and four are green. In how many ways can a person choose 5 caps such that he should have at least one cap of each colour?

    Solution

     

  • Question 8
    4 / -1

    What is the probability that a five-digit number has at least one zero in it?

    Solution

    There are 90000 five digit numbers.

    With one zero there are \(4 \mathrm{Cl}^{*} 9000=36000\) numbers.

    With two zeros there are \(4 \mathrm{C} 2^{*} 900=5400\) numbers.

    With three zeros there are \(4 \mathrm{C} 3^{*} \mathrm{~g} 0=360\) numbers.

    With four zeros there are \(4 \mathrm{C} 4^{\star} \mathrm{g}=9\) numbers.

    Adding up there are 41769 five digit numbers with atleast one zero in it.

    Therefore the probability that a five-digit number has at least one zero in it is \(0.4641 .\)

    Cheers

  • Question 9
    4 / -1

    If prices are reduced by 25% and the sales volume increased by 20%, then what is the net effect on the revenue?

    Solution

     

  • Question 10
    4 / -1

    A train approaches a tunnel PQ which is 16 m long. Two rabbits A and B are located at points which are 12 m and 8 m inside the tunnel with respect to entrance P. When the train is 'x' m away from P, A start’s running towards P and B towards Q. Difference between the ratio of the speed of A to that of the train and the ratio of the speed of B to that of the train is 1/8 How much can the distance 'x' be if both A & B get caught by the train at the ends of the tunnel?

    Solution

     

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