   Directions: Each of the questions below consists of a question and May Four statements numbered I, II, III and IV given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer:
Important for :
1
The following information is given about a four sided polygon.

I.  The polygon is a rectangle
II.  The area of the polygon is given to be 100 m2.
III.  One side of the polygon is 8 m.
IV.  All the adjacent sides are at right angle to each other.

Which of the above facts are sufficient to determine the dimensions of the polygon?
» Explain it
B
From the statement IV, it is clear that the polygon is a rectangle. Thus, statements I and IV are similar.

Now, let the two adjacent sides of the polygon be x and y.

Then, from statements II and III,

xy = 100

 x = 100 (if y = 8) 8

⇒ x = 12.5

Thus, to find the dimensions of the polygon, either I, II and III or II, III and IV are sufficient.

Hence, option B is correct.

2
What is the capacity of the cylindrical tank?

I.  Radius of the base is half of its height.

II.  Area of the base is 462 sq m.

III.  Height of the cylinder is 14 m.
» Explain it
E
To know the capacity, we have to find the volume of the cylinder, i.e. πr2h. For this, any two of the three are enough, e.g.,

Take statements I and III,

 h = 14 m, then r = 14 = 7 m 2

 Then, πr2h = 22 × 7 × 7 × 14 = (22 × 7 × 14)m3 7

From statements II and III,

Area = πr2 = 462 sq m, h = 14 m

∵ Capacity = Area × h = πr2h = (462 × 14)m3

From statement I and II,
Capacity =  ( 462 × 2 ×
 462 π
) m3

Hence, any two of the three is sufficient to answer this question, option (E) is correct.

3
The compound interest on a sum of Rs. 4000 is Rs. 1324. Find the rate of interest.

I. The simple interest on the same sum at the same rate is Rs. 1200.
II. Compound interest is compounded every four months.
III. The sum doubles itself in 25 years at the rate of 4% per annum.
» Explain it
E
Statement (III) is not an informative statement because it is true in all case. In order to find out the rate of interest, we need the time for which the sum has been deposited. But this has not been provided either in (I) or in (II).

4
Is the sum of the costs of a Laptop and a Modem more than the sum of the costs of a Mobile and a Headphone?

I. 30% of the cost of the Laptop and 20% of the cost of the Modem is more than 40% of a cost of the Mobile and 60% of the cost of Headphone.

II. 20% of the cost of the Laptop and 30% of the cost of the Modem is less than 10% of the cost of the Mobile and 15% of the cost of the Headphone.
» Explain it
C
Let the cost of the Laptop be Rs. x, the cost of the Modem be Rs. y, the cost of the Mobile be Rs. P and the cost of the Headphone be Rs. q.

From Statement I:

0.3x + 0.2y > 0.4p + 0.6q

 ⇒ 3x + 2y > 4p + 6q  ⇒  x + 2 y > 4 p + 2q 3 3

So the sum of cost of the Laptop and 2/3 of cost of the Modem is more than the sum of the cost of 4/3 of the Mobile (4/3 implies more than 1 here) and twice of that headphone (twice implies 2 headphones). Evidently, the sum cost of the Laptop and that of the Modem must be more than the sum of the cost of the Mobile and that of the Headphone. So, statement I alone is sufficient.

From Statement II:

2x + 3y < p + 1.5q

Clearly, the sum of the cost of the Mobile and 1 and a half of the Headphone is more than the sum of the cost of the two Laptops and that of the three Modems.

So, statement II alone is also sufficient.

Hence, either of the statements is sufficient to reach the answer.

5
What is the curved surface area of cylinder?

I. The base area of the cylinder is half of the area of the region enclosed by 4 circles of equal radius of 14 cm, touching one another.

II. The volume of the cone that can be fit into the cylinder is 88 cubic units.
» Explain it
E
Curverd surface area of a cylinder is 2πrh.

From statement I: We can find the are enclosed by the four cicles because their radius is given and further we can find the area of the base of the cylinder as well but as we do not know height of the cylinder, so we can't answer the question.

From statement II: From this statement we can find the volume of the cylinder (πr2h) which will be thrice the volcume of the cone that fits in it. Using the radius of the base from statement I we can calculate the height of the cylinder as well.

Therefore, combining statements I and II, r and h can be found and thus we can answer the question.

Hence, option E is the correct choice.