Here are some questions on Data Sufficiency. Try to solve these and share your marks in comments box.

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**QUESTIONS **

Each of the following questions is followed by three statements. You have to study the question and all the three statements. You have to study the question and all the three statements given and decide

whether any information provided in the statement(s) is redundant and can be dispensed with while answering the questions.

whether any information provided in the statement(s) is redundant and can be dispensed with while answering the questions.

**Ques 1) A 25 m long wire is cut into 3 pieces. How long is the longest piece?**

I. Two pieces are each 1 m shorter than the longest piece.

II. Two pieces of the wire are of the same length.

III. The longest piece of the wire is 12.5% more than the smallest piece.

(a) Only 1

(b) Either I alone or II and III together

(c) Only II and III together

(d) II and either I and III

(e) None of the above

**Ques 2. Is the average of the largest and the smallest of four given numbers greater than the average of the 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 smallest number is greater than the difference between the second largest and the smallest number.

(a) Only I

(b) Either II or III

(c) I and either II or III

(d) Any two of them

(e) None of these

**Ques 3. Rajdhani Express leaves Delhi at 4pm for Mumbai. At what time will it reach Mumbai?**

I. It maintains the average speed of 110 km/h.

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

III. It covers 250 km before each stoppage.

(a) Only II

(b)Any two of the three

(c)Any one of the three

(d)All of them

(e)Question cannot be answered even with the information in all the three statements.

**Ques 4.**How many students from institute A got placement?

I. Number of students studying in institutes A and B are in the ratio 3:4 respectively.

II. Number of students who got placement from institute B is 120% of the number of students who got placement from institute A.

III. 80% of the students studying in institute B got placement.

(a) None of the statements can be dispensed with

(b) Only I

(c) Only II

(d) Any of the three

(e) Question cannot be answered even with the information in all the three statements.

**Ques 5. What is the monthly income of Mr X?**

I. Mr X spends 85% of his income on various items and remaining speed amount is saved.

II. Monthly savings of Mr. X are Rs. 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) Only either II or III

(d) Question cannot be answered even with the information in all the three statements.

(e) None of the above

**Ques 6. What is Meetu’s present age?**

I. Meetu’s present age is double than the age of her son.

II. Ratio between present age of Meetu and her mother is 2:3, respectively.

III. 4 year hence the ratio between Meetu’s age and her son’s age will 24:13, respectively.

(a) Only II

(b) Only III

(c) Either I or II only

(d) Either II or III only

(e) None of these

**Ques 7. What is Neetu’s share in the profit earned at the end of 2 year in a joint business run by Neetu, Meetu and Geetu?**

I. Neetu invested Rs. 85000 to start the business.

II. Meetu and Geetu joined Neetu’s business after six months investing amount in the ratio of 3:5, respectively.

III. Total amount invested by Meetu and Geetu in Rs. 2.5 lakhs.

(a) Only II

(b) Only III

(c) Either II or III

(d) Information in all the statements is required for answering the question

(e) Question cannot be answered even with the information in all the three statements.

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**ANSWERS**

**1)**Option - b; Either I alone or II and III together

**2)**Option - c; I and either II or III

**3)**Option - e; Question cannot be answered even with the information in all the three statements.

**4)**Option - e; Question cannot be answered even with the information in all the three statements.

**5)**Option - e; None of the above

**6)**Option - a; Only II

**7)**Option - e; Question cannot be answered even with the information in all the three statements.

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**SOLUTIONS**

**1)**Let, Each of two shorter piece = x m

Longer piece = (x+1) m

=> x + x + (x+1) = 25

=> x =8

From statements II and III together, we can find that the two pieces of same length are greater or shorter than the third piece but we don’t know the exact condition.

Hence, the statement II and III together can be dispensed with.

**2)**Let four number in ascending order be A, B, C and D.

From Statement I,

D – C < C – B

B + D < 2C

From Statement II,

D – C > B – A

=> A + D > B + C

=> A + D + A + D > A + D + B + C

=> A+D/2 > (A + B + C + D)/4

Thus, average of the largest and the smallest of four numbers greater than the average of the four numbers.

From Statement III,

D – B > C - A

=> D + A > C + B

It’s the same result as found in statement II.

Hence, I and either II or III are redundant.

**3)**From Statement III,

Distance covered from Delhi to stoppage D

= 250 × 4 = 1000 km

But

**we can’t find the distance between Stoppage D and Mumbai**.
Thus, answer can’t be determined.

**4)**Number of students who got placement from institute A can’t be determined even using all the three given statements.

**5)**Let X’s Income = Rs x

From Statement I and II,

15% of x = 4500

=> x = 4500 × 100/15 = Rs. 30000

From Statement I and III,

4/5 of 85% of x = 20400

X = 30000

From Statement II and III,

4/5

^{th}of expenditure = 20400
Expenditure = 20400 × 5/4 = Rs 25500

And savings = Rs. 4500

=> Total monthly income = Expenditure + Savings

= 25500 + 4500 = Rs 30000

Hence, any of the statements can be dispensed with.

**6)**From Statement I,

Meetu’s Son’s Age = x

And Meetu’s Age = 2x

From Statement III,

(2x + 4)/(x+4) = 24/13

By solving this, we can find the Meetu's age = 44 years and her son's age = 22 years.

Hence, Statement II is redundant.

**7)**From Statement II and III,

Meetu’s Investment = 3/8 ×2.5 lakh = Rs. 939750

Geetu’s Investment = 5/8 × 2.5 lakh = Rs. 156250

Now using I,

Ratio of profits earned at the end of 2 year by Neetu, Meetu and Geetu

= 85000 × 24: 93750 × 18:156250 × 18

Even, then we can find only ratio of profits not their actual profits. Hence, we can’t find the answer even with the information in all the three statements.