# Hard Level Data Sufficiency and Inequality in Quantitative Aptitude Section for IBPS/SBI Exams

Q1.

**Is the average of the largest and the smallest of four given numbers greater than the average of four numbers?**I. The difference between the largest and the second largest number is less than the difference between the second largest and the second smallest number.

II. The difference between the largest and the second largest number is greater than the difference between the second smallest and the smallest number

III. The difference between the largest and the second smallest number is greater than the difference between the second largest and the smallest number.

A. Only Statement I

B. Either II or III

C. I and Either II or III

D. Only Statement II

E. Cannot be determined

Q2.

**A, B, and C together start a business with a total investment of 15000. At the end of the year, the total profit is Rs.3000. What is A’s share in the profit?**I. A’s contribution is 3/2 times of B’s

II. B’s contribution is twice that of C.

III. A’s contribution is thrice that of C.

A. I and II

B. II and III

C. All I, II and III

D. Any two of the three

E. None of the Above

Q3.

**What is the monthly income of Mr. X?**I. Mr. X spends 85% of his income on various items and remaining amount is saved

II. Monthly savings of Mr. X are 4500

III. Out of the total money spent by Mr.X in a month, one-fifth is spent on food and remaining amount of Rs.20400 on other items.

A. Only II

B. Only III

C. All the given statements are Insufficient

D. Only either II or III

E. None of the Above

Q4.

**What was the profit earned on the CP by Ramesh by selling an article?**I. He got 15% concession on labelled price in buying that article

II. He sold it for Rs.3060

III. He earned a profit of 2% on he labelled price in buying that article.

A. Only I and II

B. Only II and III

C. Only either I or III and II together are required

D. All I, II and III together are required

E. None of the Above

Q5.

**An Express Train leaves Delhi at 4pm for Mumbai, At what time will it reach Mumbai?**I. It maintains the average speed of 110 kmph

II. It has four stoppages of 10 min each between Delhi and Mumbai

III. It covers 250km before each stoppage

A. Only II

B. Only II

C. Only III

D. All the given statements are Sufficient

E. All the given statements are Insufficient

**:**

__INEQUALITY__
Q6.

**Mr. Ramesh bought two watches which together cost him Rs.440. He sold one of the watches at a loss of 20% and the other one at a gain of 40%. The selling price of both watches are same.****Quantity I: SP and CP one of the watches sold at a loss of 20%**

**Quantity II: SP and CP one of the watches sold at a profit of 40%**

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 relation cannot be established

Q7.

**Ravi, Hari and Sanjay are three typists, who working simultaneously, can type 228 pages in four hours. In one hour, Sanjay can type as many pages more than Hari as Hari can type more than Ravi. During a period of five hours, Sanjay can type as many passages as Ravi can, during seven hours.****Quantity I: Number of pages typed by Ravi**

**Quantity II: Number of pages typed by Hari**

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 relation cannot be established

B. Quantity I < Quantity II

C. Quantity I ≥ Quantity II

D. Quantity I ≤ Quantity II

E. Quantity I = Quantity II or relation cannot be established

Q8.

**A Cistern has an inlet pipe and outlet pipe. The inlet pipe fills the cistern completely in 1 hour 20 minutes when the outlet pipe is plugged. The outlet pipe empties the tank completely in 6 hours when the inlet pipe is plugged.****Quantity I: X = Inlet Pipe Efficiency**

**Quantity II: Y = Outlet Pipe Efficiency**

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 relation cannot be established

Q9.

**A basket contains 6 White 4 Black 2 Pink and 3 Green balls. If four balls are picked at random,****Quantity I: Probability that at least one is Black.**

**Quantity II: Probability that all is Black.**

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 relation cannot be established

Q10.

**Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom of the tank it took 48 minutes’ excess time to fill the cistern.****Quantity I: Due to leakage, time taken to fill the tank**

**Quantity II: Time taken to empty the full cistern**

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 relation cannot be established

**Solution:**

**Q1. SOL: C**

From Statement I,

D – C < C – B

B + D < 2C ; From Statement II, D – C > B – A

A + D > B + C

A + D/2 > A + B + C + D / 4

From Statement III,

D – B > C – A

D + A > C + B

**Q2. SOL: D**

C = x

From I and II

C = x, B = 2x, A = (3/2 * 2x) => A = 3x

From II and III

C = x, B = 2x, A = 3x

From I and III

C = x, A = 3x, B = (2/3 * 3x) => B = 2x

A:B:C = 3:2:1, A’s share = (3000 * (3/6)) = 1500

Thus any two of the three statements, are sufficient to answer the question.

**Q3. SOL: E**

Let the income of Mr.X = y

From I and II

15% of y = 4500 => y = 30000

From II and III

4/5th of expenditure = 20400 => Expenditure = Rs. 25500, Savings = Rs.4500

Income = 25500 + 4500 = 30000

From I and III

4/5 of 85% of x = 20400

x = 30000

Thus any two of the three statements, are sufficient to answer the question.

From I and II

15% of y = 4500 => y = 30000

From II and III

4/5th of expenditure = 20400 => Expenditure = Rs. 25500, Savings = Rs.4500

Income = 25500 + 4500 = 30000

From I and III

4/5 of 85% of x = 20400

x = 30000

Thus any two of the three statements, are sufficient to answer the question.

**Q4. SOL: D**

From statement I, CP = 85% of x

From statement II and III, 2 = (3060 – x/ x)*100 x=3000

CP= 85% of 3000 = 2550

Thus All I, II and III together are required.

**Q5. SOL: D**

From statement I and II, Distance covered from Delhi to Mumbai Stoppage = 250*5 = 1250km

From Statement I, Time = Distance/speed = 1250/110

So all the three statements required to answer this question.

From Statement I, Time = Distance/speed = 1250/110

So all the three statements required to answer this question.

**:**

__INEQUALITY__**Q6. SOL: D**

80/100 * x = 140/100 * y

x = 7/4y

x + y = 440

7/4 y + y = 440

y = 160 ; x = 280

x = 7/4y

x + y = 440

7/4 y + y = 440

y = 160 ; x = 280

**Q7. SOL: B**

Let Ravi, Hari and Sanjay can type x, y, and z pages respectively in 1 h.

Therefore, they together can type 4(x + y + z) pages in 4 h

∴ 4(x + y + z) = 228

⇒ x + y + z = 57 …..(i)

Also, z – y = y – x

i.e., 2y = x + z ……(ii)

5z = 7x ……(iii)

From Eqs. (i) and (ii), we get

3y = 57

⇒ y = 19

From Eq. (ii), x + z = 38

x = 16 and z = 22

Therefore, they together can type 4(x + y + z) pages in 4 h

∴ 4(x + y + z) = 228

⇒ x + y + z = 57 …..(i)

Also, z – y = y – x

i.e., 2y = x + z ……(ii)

5z = 7x ……(iii)

From Eqs. (i) and (ii), we get

3y = 57

⇒ y = 19

From Eq. (ii), x + z = 38

x = 16 and z = 22

**Q8. SOL: A**

Outlet pipe Efficiency = 100/(6) = 16.66%

**Q.9 SOL: A**

Total Balls = 15

Probability = 11c4/15c4 = 22/91

One is black = 1 – 22/91 = 69/91

Probability = 11c4/15c4 = 22/91

One is black = 1 – 22/91 = 69/91

**Q10.SOL: B**

Work done by the two pipes in 1 hour = (1/12)+(1/18) = (15/108).

Time taken by these pipes to fill the tank = (108/15)hrs = 7 hours 12 min.

Due to leakage, time taken to fill the tank = 7 hours 12 min + 48 min = 8 hours

Work done by two pipes and leak in 1 hour = 1/8.

Work done by the leak in 1 hour =(15/108)-(1/8)=(1/72).

Leak will empty the full cistern in 72 hours.

Time taken by these pipes to fill the tank = (108/15)hrs = 7 hours 12 min.

Due to leakage, time taken to fill the tank = 7 hours 12 min + 48 min = 8 hours

Work done by two pipes and leak in 1 hour = 1/8.

Work done by the leak in 1 hour =(15/108)-(1/8)=(1/72).

Leak will empty the full cistern in 72 hours.

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