Directions (1-5): **The following questions are accompanied by two statements (A) and (B). You have to determine which statement(s) is/are sufficient /necessary to answer the questions**

**Q1. Find the value of 8y² (y + 3x) + 8x² (x + 3y)**

A) Product of x and y is equal to 6

B) Sum of inverse of x and y is equals to ⅚

(a) if the Statement ‘A’ alone is sufficient to answer the question but the Statement ‘B’ alone is not sufficient

(b) if the Statement ‘B’ alone is sufficient to answer the question but the Statement ‘A’ alone is not sufficient

(c) if both Statement ‘A’ and ‘B’ together are needed to answer the question

(d) if either the Statement ‘A’ alone or Statement ‘B’ alone is sufficient to answer the question

(e) if you cannot get the answer from both the Statements together

**Q2. If X, Y and Z together can complete the work in 8 days, find in how many days Y alone can complete the work?**

A) X and Y together can complete the work in 12 days while Z is 25% less efficient than ‘X’.

B) Z is 50% more efficient than ‘Y’ who is 100% less efficient than ‘X’.

(a) if the Statement ‘A’ alone is sufficient to answer the question but the Statement ‘B’ alone is not sufficient

(b) if the Statement ‘B’ alone is sufficient to answer the question but the Statement ‘A’ alone is not sufficient

(c) if both Statement ‘A’ and ‘B’ together are needed to answer the question

(d) if either the Statement ‘A’ alone or Statement ‘B’ alone is sufficient to answer the question

(e) if you cannot get the answer from both the Statements together

**Q3. What will be the speed of boat if A is the starting point and B is the destination point?**

A) Man go to a point B and come back to initial point A in total 12 hours while the ratio of speed of boat to speed of stream is 3 : 2.

B) Man reached at mid-point of A and B in 5 hour and then go to point B and come back to mid-point of A and B in total 6 hours while speed of stream is 10 km/hr.

(a) if the Statement ‘A’ alone is sufficient to answer the question but the Statement ‘B’ alone is not sufficient

(b) if the Statement ‘B’ alone is sufficient to answer the question but the Statement ‘A’ alone is not sufficient

(c) if both Statement ‘A’ and ‘B’ together are needed to answer the question

(d) if either the Statement ‘A’ alone or Statement ‘B’ alone is sufficient to answer the question

(e) if you cannot get the answer from both the Statements together

**Q4. Three numbers are co-prime to each other. Find the sum of these numbers?**

A) Product of first two number is 286 while the product of last two numbers is 470.

B) Sum of first two number is 35 while the sum of last two number is 57.

(a) if the Statement ‘A’ alone is sufficient to answer the question but the Statement ‘B’ alone is not sufficient

(b) if the Statement ‘B’ alone is sufficient to answer the question but the Statement ‘A’ alone is not sufficient

(c) if both Statement ‘A’ and ‘B’ together are needed to answer the question

(d) if either the Statement ‘A’ alone or Statement ‘B’ alone is sufficient to answer the question

(e) if you cannot get the answer from both the Statements together

**Q5. Find the sum of digits of given two-digit number?**

A) If we interchange the numbers then the new number formed is greater than the original number by 9.

B) If we interchange the number then product of new number and original number is 1462.

(a) if the Statement ‘A’ alone is sufficient to answer the question but the Statement ‘B’ alone is not sufficient

(b) if the Statement ‘B’ alone is sufficient to answer the question but the Statement ‘A’ alone is not sufficient

(c) if both Statement ‘A’ and ‘B’ together are needed to answer the question

(d) if either the Statement ‘A’ alone or Statement ‘B’ alone is sufficient to answer the question

(e) if you cannot get the answer from both the Statements together

Directions (6-10): **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.**

**Q6. If there are only three friends (Shivam, Ayush and Veer) in a group, then find the age of Ayush?**

I. If average of present age of all 3 friends is 42 years and ratio of Veer’s age 6 years ago to Shivam’s present age is 2 : 3.

II. If average age of Ayush and Veer 5 years hence is 41 years and ratio of present age of Veer to that of Shivam is 7 : 9. Ayush’s age 8 years hence is 10 years less than Shivam’s age 6 years ago.

(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 question, 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.

**Q7. Two persons A and B started a business by investing some amounts. Find investment period of B.**

I. A and B together invested Rs.50,000 in the business and ratio of period of investment of A to that of B is 1 : 2.

II. If at the end of the year, profit sharing ratio of A to that of B is 9 : 7.

(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 question, 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. A train travels from Delhi to Jaipur and back from Jaipur to Delhi. Find speed of the train during its journey from Delhi to Jaipur, if distance between Delhi to Jaipur is 540 km.**

I. If the train takes total of 11 hours and 15 minutes for the whole journey.

II. If ratio of speed of train when it travels from Delhi to Jaipur and when it travels from Jaipur to Delhi is 3 : 2.

(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 question, 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.

**Q9. A person invested equal amount across two schemes – A & B. Both schemes offer same rate of interest and scheme – A offers SI and scheme – B offers CI. Find rate of interest.**

I. If total interest received from both schemes after 2 years is Rs.12450.

II. If interest received from scheme – B after 2 years is 7.5% more than interest received from scheme – A after 2 years.

(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 question, 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.

**Q10. Bag – A contains three colored balls (red, yellow and black). Then, find total number of balls in bag – A.**

I. Number of yellow balls in bag – A is half of number of black balls in bag – A.

II. If two balls are selected randomly from the bag-A, then the probability of 1 ball being red and 1 ball being yellow is 8/25.

(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 question, 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.

**Solutions**