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**Data sufficiency **

**Directions (1-5): In each of the following questions, a question is followed by three statements I, II and III. Read all the statements to find the answer for given questions and then answer accordingly that which statement can give the answer alone/together.**

**1) ****Find the difference between CI on the sum at 2% per annum after 2 years and SI on that sum at 4% per annum after 4 years.**

**I: **Difference between CI and SI on that sum at 3% per annum after two years is Rs.22.5.

**II: **SI on that sum at 5% per annum after 5 years is Rs.6250.

**III:** The sum amounts to Rs.27040 on CI at 4% per annum after 2 years.

A) Only III

B) Only II

C) Only I

D) Both I and II

E) Anyone of the three

**2) ****How many men alone can complete a piece of work in 8 days?**

**I: **4 men, 6 women and 16 children can complete a piece of work in 12 days.

**II: **A man does the double the work a woman does and a child does half the work a man does.

**III: **6 men can complete the same piece of work in 12 days.

A) Only I

B) Only II

C) Only III

D) All the three

E) None of these

**3) ****Find the total number of students in a college?**

**I: **The average yearly fees per head of the entire students of the college consisting of two different departments ECE and CSE is Rs.23850.

**II: **The average yearly fee per head of ECE students is Rs.38000 and that of CSE students is Rs.21800.

**III: **The number of ECE students is 82.

A) Only I

B) Only II

C) Only III

D) I, II and III together

E) Both I and II

**4) ****What is the capacity of the cylindrical tank?**

**I: **The area of the base is 15400 sq.cm.

**II: **The height of the tank is 2 times the radius.

**III: **Circumference of base is 440cm.

A) Only I

B) Only II

C) Both I and II

D) Both I and II and Both II and III

E) None of these

**5) ****What will be the ratio between ages of Savithri and Abi after 3 years?**

**I: **Savithri’s present age is more than Abi’s present age by 15 years.

**II: **Abi’s present age is 27 years.

**III: **The ratio of Abi’s present age to Savithri’s present age is 9: 14.

A) Only I

B) Only II

C) Only III

D) Both I and II

E) Any two of I, II and III

**Application sums**

**6) ****A shopkeeper sold a toy for Rs.980 after giving 30% discount on the labelled price. Had he not given the discount, he would have earned a profit of 25% on the cost price, what was the cost price of the toy?**

A) Rs.1000

B) Rs.1120

C) Rs.1300

D) Rs.1450

E) None of these

**7) ****Navin can do a certain work in 5 days while Babu can do the same work in 3 days. Both of them complete the work together and get Rs.840, what is the share of Navin?**

A) Rs.205

B) Rs.310

C) Rs.315

D) Rs.380

E) None of these

**8)****Three persons attended an interview whose chances of being selected are 1/3, ¼ and ½ respectively. What is the probability that all are selected?**

A) 2/5

B) 1/3

C) 3/2

D) 3/4

E) None of these

**9) ****A student’s marks were wrongly entered as 62 instead of 42. Due to this, the average marks of the class got increased by half. What is the number of students in the class?**

A) 20

B) 40

C) 30

D) 35

E) None of these

**10) ****Naren got married 4 years ago. His present age is 8/7 times his age at the time of his marriage. Naren’s sister was 6 years younger to him at the time of his marriage. What is the difference in age of Naren’s sister and Naren’s wife who is 4 years younger than him?**

A) 1 year

B) 2 years

C) 3 years

D) 4 years

E) None of these

**Answers :**

**Directions (1-5) :**

**1) Answer: E**

CI – SI = Pr^{2}/100^{2}

From I => 22.5 = P * (3/100)^{2}

=> P = Rs.25000

CI = P(1 + r/100)^{2} – P

= 25000 * (1 + 2/100)^{2} – 25000 = Rs.1010

SI = Pnr/100 = 25000 * 4 * 4/100 = Rs.4000

Required difference = 4000 – 1010 = 2990

This statement alone is sufficient to answer the question.

From II => SI = Pnr/100

=> 6250 = P * 5 * 5/100

=> P = Rs.25000

CI = P(1 + r/100)^{2} – P

= 25000 * (1 + 2/100)^{2} – 25000 = Rs.1010

Required SI = Pnr/100 = 25000 * 4 * 4/100 = Rs.4000

Required difference = 4000 – 1010 = 2990

This statement alone is sufficient to answer the question.

From III =>

Amount = P(1 + r/100)^{t}

=> 27040 = P * (1 + 4/100)^{2}

=> P = Rs.25000

CI = P(1 + r/100)^{2} – P

= 25000 * (1 + 2/100)^{2} – 25000 = Rs.1010

Required SI = Pnr/100 = 25000 * 4 * 4/100 = Rs.4000

Required difference = 4000 – 1010 = 2990

This statement alone is sufficient to answer the question.

**2) Answer: E**

From I=> 4m + 6w + 16c complete the work in 12 days.

This statement is not sufficient to answer the question.

From II =>A man does the double the work a woman does and a child does half the work a man does.

This statement is not sufficient to answer the question.

From III => M_{1} * D_{1} = M_{2} * D_{2}

=> 6 * 12 = x * 8

=> x = 9 men

This statement is sufficient to answer the question.

From I and II =>

6 women = 3 men

16 children = 8 men

4m + 6w + 16c = 4m + 3m + 8m = 15m

M_{1} * D_{1} = M_{2} * D_{2}

=> 15 * 16 = x * 8

=> x = 30 men.

Both statements I and II together are necessary to answer the question.

Hence either statement III alone or statement I and II together is sufficient to answer the question.

**3) Answer: D**

From I, II and III =>

Ratio = 2050: 14150 = 41: 283

41 = 82 students in ECE

From the above, 1’s = 2’s

Total students (41 + 283)’s = 2 * (41 + 283) = 648

All the statements together are necessary to answer the question.

**4) Answer: D**

Capacity = ∏ * r^{2} * h

From I =>

∏ * r^{2} = 15400 => r = 70cm

This statement is not sufficient to answer the question.

From II => h = 2r

This statement is not sufficient to answer the question.

From III => 2 * ∏ * r = 440 => r = 70cm

This statement is not sufficient to answer the question.

From I and II => we get r = 70cm and h = 140cm

Capacity = ∏ * r^{2} * h = 2156 * 10^{3}

Both statement I and II is necessary to answer the question.

From II and III =>we get r = 70cm and h = 140cm

Capacity = ∏ * r^{2} * h = 2156 * 10^{3}

Both statement II and III is necessary to answer the question.

**5) Answer: E**

From I =>Savithri = Abi + 15

This statement is not sufficient to answer the question.

From II =>Abi = 27

This statement is not sufficient to answer the question.

From III =>Abi: Savithri = 9: 14

This statement is not sufficient to answer the question.

From I and II =>Savithri = 27 + 15 = 42 years

Required ratio = (42 + 3): (27 + 3) = 3: 2

Both statement I and II is necessary to answer the question.

From II and III =>

27: Savithri = 9: 14

=>Savithri = 42 years

Required ratio = (42 + 3): (27 + 3) = 3: 2

Both statement II and III is necessary to answer the question.

From I and III =>

14x-9x=15

5x=15

x=3

Abi: Savithri = 27: 42

Required ratio = (42 + 3): (27 + 3) = 3: 2

Both statement I and III is necessary to answer the question.

**Directions (6-10) :**

**6) Answer: B**

Let MP = x

SP of each toy = 70x/100 = 980 => x = Rs.1400

CP = 1400 * 100/125 = Rs.1120

**7) Answer: C**

Navin’s 1 day’s work = 1/5

Babu’s 1 day’s work = 1/3

Navin’s salary: Babu’s salary = 1/5: 1/3 = 3: 5

Navin’s share = 3/8 * 840 = Rs.315

**8) Answer: D**

P(Three persons selected) = 1 – P(none of them selected)

P(none of them selected) = (1 – 1/3) * (1 – 1/4 ) * (1 – ½) = ¼

Required probability = 1 – ¼ = ¾

**9) Answer: B**

Total no. of students = x and Average marks of all students = y

(xy – 42 + 62)/x = y + 0.5

=> x = 40

**10) Answer: B**

Naren’s age at the time of his marriage = x

x + 4 = 8x/7

=> x = 28 years. His present age = 28 + 4 = 32 years

Naren’s sister = 32 – 6 = 26 years

Naren’s wife = 32 – 4 = 28 years

Required difference = 28 – 26 = 2 years

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