Quantitative Ability (Part 6 of 9)

Directions: Answer these questions on the basis ofthe information given below:

Each question is followed by two statements I and II. Indicate your responses based on the directives given in choices:

  1. The average weight of a class of 100 students is 45 kg. The class consists of two sections, I and II, each with 50 students. The average weight, WI, of Section I is smaller than the average weight, WII of Section II. If the heaviest student, say Deepak, of Section II is moved to Section I, and the lightest student, say Poonam, of Section I is moved to Section II, then the average weights of the two sections are switched, i.e.. the average weight of Section I becomes WII and that of Section II becomes WI. What is the weight of Poonam?

    • Statement 1: I: WII-WI = 1.0.
    • Statement 2: II: Moving Deepak from Section II to I (without any move from I to II) makes the average weights of the two sections equal.
    1. question can be answered using I alone but not using B alone.

    2. question can be answered using II alone but not using A alone.

    3. question can be answered using I and II together, but not using either I or II alone.

    4. question cannot be answered even using I and II together.

    Answer: c

  2. Consider integers x, y and z. What is the minimum possible value of x2 + y2 + z2?

    • Statement 1: I: x + y + z = 89.
    • Statement 2: II: Among x, y, z two are equal.
    1. question can be answered using I alone but not using B alone.

    2. question can be answered using II alone but not using A alone.

    3. question can be answered using I and II together, but not using either I or II alone.

    4. question cannot be answered even using I and II together.

    Answer: a

  3. Rahim plans to draw a square JKLM with a point a on the side JK but is not successful. Why is Rahim unable to draw the square?

    • Statement 1: I: The length of OM is twice that of OL.
    • Statement 2: II: The length of OM is 4 cm
    1. question can be answered using I alone but not using B alone.

    2. question can be answered using II alone but not using A alone.

    3. question can be answered using I and II together, but not using either I or II alone.

    4. question cannot be answered even using I and II together.

    Answer: b

  4. ABC Corporation is required to maintain at least 400 Kilolitres of water at all times in its factory, in order to meet safety and regulatory requirements. ABC is considering the suitability of a spherical tank with uniform wall thickness for the purpose. The outer diameter of the tank is 10 meters. Is the tank capacity adequate to meet ABC's requirements?

    • Statement 1: I: The inner diameter of the tank is at least 8 meters.
    • Statement 2: II: The tank weights 30, 000 kg when empty, and is made of a material with density of 3gm/cc.
    1. question can be answered using I alone but not using B alone.

    2. question can be answered using II alone but not using A alone.

    3. question can be answered using I and II together, but not using either I or II alone.

    4. question cannot be answered even using I and II together.

    Answer: b

  5. Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and 50 Misos. In how many ways can you pay a bill of 107 Misos?

    1. 19

    2. 17

    3. 16

    4. 18

    5. 15

    Answer: d

  6. How many pairs of positive integers m, n satisfy 1/m + 4/n = 1/12 where n is an odd integer less than 60?

    1. 3

    2. 6

    3. 4

    4. 7

    5. 5

    Answer: a

  7. A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja, giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise, Shailaja noticed that she was left with exactly three times as much as the amount on the cheque. Which of the following is a valid statement about the cheque amount?

    1. Over Rupees 4 but less than Rupees 5

    2. Over Rupees 13 but less than Rupees 14

    3. Over Rupees 7 but less than Rupees 8

    4. Over Rupees 22 but less than Rupees 23

    5. Over Rupees 18 but less than Rupees 19

    Answer: e

  8. Consider the set S = {2, 3, 4, … 2n + I}, where n is a positive integer larger than 2007. Define X as the average of the odd integers in S and Y as the average of the even integers in S. What is the value of X-Y?

    1. 2008

    2. 0

    3. I

    4. 1/2n

    5. n + 1/2n

    Answer: c

  9. Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight-member joint family is nearest to

    1. 24 years

    2. 23 years

    3. 22 years

    4. 21 years

    5. 25 years

    Answer: a

  10. A function f (x) satisfies f (l) = 3600 and f (l) + f (2) + … + f (n) = n2 f (n), for all positive integers n > 1. What is the value of f (9)?

    1. 120

    2. 80

    3. 240

    4. 200

    5. 100

    Answer: b

  11. If mxm-nxn = 0, then what is the value of 1/xm + xn + 1/xm-xn in terms of xn?

    1. 2mn/xn (n2 − m2)

    2. 2mn/xn (n2 + m2)

    3. 2mn/xn (m2 − n2)

    4. 2mn/xn (m2 + n2)

    Answer: a

  12. In a certain zoo, there are 42 animals in one sector, 34 in the second sector and 20 in the third sector. Out of this, 24 graze in sector one-and also in sector two. 10 graze in sector two and sector three, 12 graze in sector one and sector three. These figures also include four animals grazing in all the three seotors are now transported to another zoo, find the total number of animals.

    1. 38

    2. 56

    3. 54

    4. None of the above

    Answer: c

  13. The ratio of the roots of bx2 + nx + n = 0 is p: q, then

    1. vq/p + vp/q + vl/n = 0

    2. vp/q + vq/p + vn/l = 0

    3. vq/p + vp/q + vl/n = 0

    4. vp/q + vq/p + vn/l = 0

    Answer: b