**Q1. PBA and PDC are two secants. AD is the diameter of the circle with centre at O. ∠A= 40°, ∠P = 20°**

**Quantity 1:** ∠DBC

**Quantity 2:** ∠ADB

(a) Quantity I > Quantity II

(b) Quantity I < Quantity II

(c) Quantity I ≥ Quantity II

(d) Quantity I ≤ Quantity II

(e) Quantity I = Quantity II or No relation

**Q2. Quantity 1:** Height of the tank if the volume of cylindrical tank is 12320 cubic cm. Its radius and height are in the ratio of 7 : 10 respectively.

**Quantity 2:** Level kerosene in the jar. A conical vessel of base radius 2 cm and height 3 cm is filled with kerosene. This liquid leaks through a hole in the bottom and collects in a cylindrical jar of radius 2 cm.

(a) Quantity I > Quantity II

(b) Quantity I < Quantity II

(c) Quantity I ≥ Quantity II

(d) Quantity I ≤ Quantity II

(e) Quantity I = Quantity II or No relation

**Q3.** I. P²-18p+77=0

II. 3q²-25q+28=0

**Quantity 1:** Value of P

**Quantity 2 :** Value of q

(a) Quantity I > Quantity II

(b) Quantity I < Quantity II

(c) Quantity I ≥ Quantity II

(d) Quantity I ≤ Quantity II

(e) Quantity I = Quantity II or No relation

**Q4. A man who swim 48m/minute in still water, swims 200m against the current and 200m with the current. The difference between the time taken by him against the stream and with the stream is 10 minutes. **

**Quantity 1:** speed of current.

**Quantity 2:** Speed of a man who completes 3 rounds of a circular path of radius 49 m in 14 minutes.

(b) Quantity I < Quantity II

(c) Quantity I ≥ Quantity II

(d) Quantity I ≤ Quantity II

(e) Quantity I = Quantity II or No relation

**Directions (5-8): The following questions are accompanied by two statements I and II. You have to determine which statements(s) is/are sufficient/necessary to answer the questions.**

**Q5. Find the sum of present age of X & Z? **

I. Four years ago, average age of X, Y and Z was 16 years while age of X, Y and Z is in arithmetic progression.

II. Average of present age of X and Z is same as present age of Y while Y is four years younger than Z.

(a) Statement I alone is sufficient to answer the question but statement II alone is not sufficient to answer the question.

(b) Statement II alone is sufficient to answer the question but statement I alone is not sufficient to answer the question.

(c) Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question.

(d) Either statement I or statement II by itself is sufficient to answer the question.

(e) Statements I and II taken together are not sufficient to answer the question.

**Q6. Is Rahul meet Prabhat at half of the distance on a circular track (48km) if they both started to move at same time in same direction? **

I. Speed of Prabhat is 24km/hr more than speed of Rahul.

II. Prabhat’s speed is 200% more than that of Rahul

(a) Statement I alone is sufficient to answer the question but statement II alone is not sufficient to answer the question.

(b) Either statement I or statement II by itself is sufficient to answer the question.

(c) Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question.

(d) Statement II alone is sufficient to answer the question but statement I alone is not sufficient to answer the question.

(e) Statements I and II taken together are not sufficient to answer the question.

**Q7. Find number of yellow balls in a box which contains 3 black balls and 7 red and yellow balls. **

I. Probability of selecting two yellow balls from the box is 2/15

II. Probability of selecting one red and black ball is 1/5.

(a) Statement I alone is sufficient to answer the question but statement II alone is not sufficient to answer the question.

(b) Statement II alone is sufficient to answer the question but statement I alone is not sufficient to answer the question.

(c) Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question.

(d) Either statement I or statement II by itself is sufficient to answer the question.

(e) Statements I and II taken together are not sufficient to answer the question.

**Q8. Find number of pens sold by retailer if he earns total 37.5% profit on selling some pens and some pencils. **

I. Ratio between pen sold to pencil sold is 2 : 3 while ratio between cost price of pen to pencil is 3 : 2.

II. On selling a pen and a pencil, he earns 25% and 50% profit respectively.

(a) Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question.

(b) Statements I and II taken together are not sufficient to answer the question.

(c) Statement II alone is sufficient to answer the question but statement I alone is not sufficient to answer the question.

(d) Statement I alone is sufficient to answer the question but statement II alone is not sufficient to answer the question.

(e) Either statement I or statement II by itself is sufficient to answer the question.

**Q9. Veer, Satish and Neeraj started a business together. They invested in the ratio 2 : 3 : 4. Neeraj left the business after working for 6 months. Veer and Satish worked for ‘x’ and ‘y’ months respectively.**

**Quantity I:.** Value of ‘x’, If profit share of all three is equal.

**Quantity II:** Value of ‘y’, if profit share of Veer, Satish and Neeraj is in the ratio 2 : 3 : 2

(a) Quantity I > Quantity II

(b) Quantity I < Quantity II

(c) Quantity I ≥ Quantity II

(d) Quantity I ≤ Quantity II

(e) Quantity I = Quantity II

**Q10. ABCD is a square inscribed in a circle. BF is a tangent on circle, DF = 6 and Area of ∆ BDF = 12 cm²**

**Quantity I:** Area of shaded region

**Quantity II:** [3π-6]
(a) Quantity I ≤ Quantity II

(b) Quantity I < Quantity II

(c) Quantity I > Quantity II

(d) Quantity I ≥ Quantity II

(e) Quantity I = Quantity II

**Solutions**