Directions: Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer:
Important for :
1
A surveyor draw three parallel straight lines on a Paper for a land survey. Two points P1 and P2 are marked on the first straight line, points P3 and P4 are marked on the second straight line and points P5 and P6 are marked on the third straight line. Each of these six points can move to any positions on its respective straight line.

Statement I: The maximum number of triangle that can be drawn by joining these points  is 18.

Statement II: The minimum number of triangles that can be drawn by joining these points is zero.
» Explain it
B
The maximum triangles would be in case all these 6 points are non-collinear. In such a case the number
of triangles is 6C3

 = 6 × 5 × 4 = 20 1 × 2 × 3

Hence, statement I is incorrect.

In other case if surveyor take the position that P1 and P2 coincide on the first straight line, P3 and P4 coincide on the second straight line, P5 and P6 coincide on the third straight line and all these coincidences happen at 3 points which are on the same straight line in such a case there would be 0 triangles formed.

Hence, statement II is correct.

Therefore, option (B) is correct.

2
Prem and Ramesh started from two cities Patna and Allahabad respectively, traveling at constant speeds, to reach Allahabad and Patna respectively. At what time will they meet?

Statement I: The distance between Patna and Allahabad is 250 km. Prem travels at 50 km/hr and Ramesh travels at 25 km/hr

Statement II: Prem started from Patna at 5:00 a.m. and reached Allahabad at 11:00 a.m. Ramesh started from Allahabad at 7:00 a.m. and reached Patna at 3.00 p.m.
» Explain it
B
From statement I:

It is not given whether both start simultaneously or not.

Also no time is given which we can use as reference for finding the meeting point.

So, statement I alone is not sufficient to answer the question.

From statement II:

Prem and Ramesh take 6 hours and 8 hours respectively to cover Patna to Allahabad

(say ‘S’)

 So, Prem’s speed = S km/hr 6

 And, Ramesh’s speed = S km/hr 8

 By, 7:00 a.m. Prem would have covered S km 3

The time when both will meet
 S – S 3
hr =
 2 × S 3
=     = 2.285 hr
2 × 48
 S + S 6 8
14S 3 × 14
48
Hence, statement II alone is sufficient to answer the question.

Therefore, option (B) is correct.

3
Ganpat is a oil trader, he mixes two varieties of oil in the ratio of 1 : 4. By selling the mixture at 14.40 per kg he gets a profit of more than 20%. Is the cost of the dearer variety, which is mixed, more than 20 per kg?

Statement I: The cost of the cheaper variety of oil mixed is 10 per kg.

Statement II: For every 1 kg of the cheaper variety of oil he mixed 4 kg of the dearer variety of oil.
» Explain it
C
 The cost price of the mixture is less than 14.40 × 100 = Rs.12 Per Kg. 120

From Statement I:

The quantities of cheaper to dearer could be 1 : 4 or 4 : 1

Case I: Consider 1 : 4

So, x kg of the cheaper is mixed with 4x kg of the dearer.

Let the cost of the dearer variety be Rs. k per kg.

 Then, 10 x + 4kx < 12 x + 4x

⇒ 4k + 10 < 60

⇒ 4k < 50

⇒ k < 12.5

Case II: Consider 4 : 1,

So, 4x kg of the cheaper in mixed with x kg of the dearer
 kx + 40x < 12 x + 4x

⇒ k + 40 < 60

⇒ k < 20

So, in either case, the dearer variety costs less than Rs. 20 per kg.

Hence, statement I alone is sufficient to answer the question.

From statement II:

Let the cost of the cheaper variety be Rs. y and dearer variety be Rs. z per kg

Let the quantities of the cheaper and dearer varieties be x and 4x respectively

 Given, yx + 4zx < 12 5x

⇒ y + 4z < 60

Since, y > 0 ⇒ 4z < 60 ⇒ z < 15

So, the dearer variety costs less than Rs. 20 per kg.

Hence, statement II alone is sufficient to answer the question.

Therefore, option (C) is correct.

4
During a three-years period, viz. 2010, 2011 and 2012. The profits of Bharti Airtel changed by what percent from the 2011 to 2012?

Statement I: The increase in profits of Bharti Airtel from the year 2010 to the year 2011 was the same as the increase from the year 2010 to the year 2012.

Statement II: For Bharti Airtel the profits for the year 2010 were Rs. 13000 crore and the profits for the year 2012 were Rs. 14000 crore.
» Explain it
A
From Statement I:

The increase in profits was the same from year 2010 to 2011 as from year 2010 to 2012. This statement is a tricky statement that most people under-leverage. At first moment after watching, it appears insufficient but a careful analysis shows that this information proves that there was no change from year 2011 to year 2012. The only way that the change could be the same from year 2010 to the year 2011 as from year 2010 to year 2012 is with a zero percentage change from year 2011 to year 2012.
So, statement I alone is sufficient to answer the question.

From Statement II:

The profits in year 2010 were Rs. 13000 crore and in year 2012 were Rs. 14000 crore.

So, the increase in profits from year 2010 to 2012 = (14000 – 13000) = 1000 crore

We can calculate the percentage gain from year 2010 to year 2012.

But it is not possible to know how much of this increase occurred between year 2010 to 2011 versus year 2011 to 2012.

So, statement II alone is not sufficient to answer the question.

Hence, option (A) is correct.

5
Is Lionel Messi older than Luka Modric, if both of them are at least 1 year old?

Statement I:  Four times Lionel Messi’s age is 4 years less than thrice Luka Modric’s age.

Statement II:  Five times Lionel Messi’s age is one more than four times Luka Modric’s age.
» Explain it
C
Let Lionel Messi's age be A years and Luka Modric's age be B years.

Statement 1.

4A = 3B – 4

⇒ 4A + 4 = 3B

⇒ 4 (A + 1) = 3B

 ⇒ B = 4 (A + 1) 3

⇒ B > A (1) is sufficient

Statement2

5A = 4B + 1

⇒ A = 0.8B + 0.2

If B = 1 then A = 1 i.e., B = A. If B > 1 then A < B

∴ In either case, A is not greater than B   (2) is sufficient

Hence, option (C) is correct.