Directions (Q.1-5): Each of the questions below is followed by two statements I and II. You are to determine whether the data given in the statement are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose between the possible answers.
Give answer
(a) Statement I alone is sufficient to answer the question but the statement II alone is not sufficient
(b) Statement II alone is sufficient to answer the question but the statement II alone is not sufficient
(c) Both the statements I and II together are needed to answer the question
(d) Either the statement I alone or statement II alone is sufficient to answer the question
Q1. The ages of Anand and Sujeet are in the ratio of 6 : 5. What is the age of Anand?
I. The ages of Anand and Sandeep are in the ratio fo 10 : 7.
II. After 5 yr, the ratio of Anand’s and Sujeet’s ages will be 7 : 6.
Q2. What is the three-digit number?
I. Three-fifth of that number is less than that number by 90.
II. One-fourth of that number is 25% of that number.
Q3. In how many days 14 men can complete a piece of work?
I. If 18 women can complete the same piece of work in 24 days.
II. If 28 children can complete the same piece of work in 56 days.
Q4. What is the salary of A, in a group of A, B, C, D, and E whose average salary is Rs. 65780?
I. Total of the salaries of B and C is Rs. 88545.
II. Total of the salaries of D and E is Rs. 59020.
Q5. What is the profit earned by selling a watch for Rs. 15675?
I. Total cost price of 5 such watches is equal to selling price of 4 such watches.
II. 25% profit is earned by selling each watch.
Directions (Q6-10): In these questions, a question is given followed by information in three statements. You are to consider the information in all the three statements and decide the information in which of the statements is not necessarily required to answer the question and therefore can be dispensed with. Indicate your answer accordingly.
Q6. How many students from institute A got placement?
I. Number of students studying in institutes A and B are in the ratio of 3 : 4.
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) Only I
(b) Only II
(c) Anyone of three
(d) Data is insufficient
(e) None of these
Q7. What is the monthly income of Mr. X?
I. Mr. X spends 85% of his income on various items and saves the remaining amount.
II. Monthly saving of Mr. X is 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) Either II and III
(d) Data is insufficient
(e) None of these
Q8. What is Suchitra’s present age?
I. Suchitra’s present age is double the age of her son.
II. Ratio of present age of Suchitra to that of her mother is 2 : 3.
III. 4 yr hence the ratio between Suchitra’s age and her son’s age will be 13 : 11.
(a) Only II
(b) Only III
(c) Either I or II
(d) Either II or III
(e) None of these
Q9. What is Neeta’s share in the profit earned at the end of 2 yr in a joint business run by Neeta, Seeta and Geeta?
I. Neeta invested Rs. 85000 to start the business.
II. Seeta and Geeta joined Neeta’s business after six months investing amount in the ratio of 3 : 5.
III. Total amount investing by Seeta and Geeta is Rs. 2.5 lakh.
(a) Only II
(b) Only III
(c) Either II and III
(d) All of these
(e) None of these
Q10. What is the labeled price of the article?
I. Cost price of the article is Rs. 500.
II. Selling price after offering 5% discount on the labeled price is Rs. 608.
III. Profit earned would have been 28% if not discount was offered.
(a) Only I
(b) Only II
(c) II and III
(d) I and III
(e) I and II
Answers:
Q1. The ages of Anand and Sujeet are in the ratio of 6 : 5. What is the age of Anand?
I. The ages of Anand and Sandeep are in the ratio fo 10 : 7.
II. After 5 yr, the ratio of Anand’s and Sujeet’s ages will be 7 : 6.
1. Ans.(b)
Sol.
From statement II,
(6x + 5)/(5x + 5)=7/6
⇒36x + 30 = 35x + 35
⇒36x - 35x = 35 - 30 ⇒x=5
∴ Age of Anand = 6 × 5 = 30 yr
So, statement II is alone sufficient.
Q2. What is the three-digit number?
I. Three-fifth of that number is less than that number by 90.
II. One-fourth of that number is 25% of that number.
2. Ans.(a)
Sol. From statement I,
Suppose, the number be x.
x - 3/5 x = 90 ⇒2/5 x=90
x = 225
From statement II,
x×1/4 = 25/100 x ⇒x/4=x/4
So, statement I is sufficient
Q3. In how many days 14 men can complete a piece of work?
I. If 18 women can complete the same piece of work in 24 days.
II. If 28 children can complete the same piece of work in 56 days.
3. Ans.(e)
Sol. More data are required.
Q4. What is the salary of A, in a group of A, B, C, D, and E whose average salary is Rs. 65780?
I. Total of the salaries of B and C is Rs. 88545.
II. Total of the salaries of D and E is Rs. 59020.
4. Ans.(c)
Sol.
From the statement I and II,
Salary of A = 5 × 65780 – (88545 + 59020)
= 328900 – 147565 = Rs. 181335
Both statements are required.
Q5. What is the profit earned by selling a watch for Rs. 15675?
I. Total cost price of 5 such watches is equal to selling price of 4 such watches.
II. 25% profit is earned by selling each watch.
5. Ans.(d)
Sol. From statement I,
Selling price of the watch = Rs. 15675
And the cost price of watch =15675×4/5= Rs. 12540
∴ Profit =15675-12540= Rs. 3135
From statement II,
Cost price of watch =15675/(100 + 25)×100= Rs. 12540
∴ Profit = 15675 – 12540 = Rs. 3135
Directions (Q6-10): In these questions, a question is given followed by information in three statements. You are to consider the information in all the three statements and decide the information in which of the statements is not necessarily required to answer the question and therefore can be dispensed with. Indicate your answer accordingly.
Q6. How many students from institute A got placement?
I. Number of students studying in institutes A and B are in the ratio of 3 : 4.
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) Only I
(b) Only II
(c) Anyone of three
(d) Data is insufficient
(e) None of these
6. Ans.(d)
Sol. From statement I,
Suppose, in institutions A and B, total number of students studying by 3x and 4x. Answer cannot be determined by all statements because data is insufficient.
Q7. What is the monthly income of Mr. X?
I. Mr. X spends 85% of his income on various items and saves the remaining amount.
II.Monthly saving of Mr. X is 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) Either II and III
(d) Data is insufficient
(e) None of these
7. Ans.(c)
Sol. From statements I and II,
If the monthly income of Mr. X is Rs. X then
(15 × x)/100=4500⇒x=(4500 × 100)/15= Rs. 30000
From statements I and III,
x × 4/5 × 85/100 = 20400
x = (20400 × 5 × 100)/(4 × 85) = Rs. 30000
Income can be determined from Either I and II or I and III
Q8. What is Suchitra’s present age?
I. Suchitra’s present age is double the age of her son.
II. Ratio of present age of Suchitra to that of her mother is 2 : 3.
III. 4 yr hence the ratio between Suchitra’s age and her son’s age will be 13 : 11.
(a) Only II
(b) Only III
(c) Either I or II
(d) Either II or III
(e) None of these
8. Ans.(a)
Sol. From statements I and III,
Suppose, the present age of Suchitra’s son = x yr
Present age of Suchitra’s = 2x yr
After 4 yr, (2x + 4)/(x + 4)=13/11
x = 8/9
Required answer can be find with the help of it.
Here, Statement II is not necessary.
Q9. What is Neeta’s share in the profit earned at the end of 2 yr in a joint business run by Neeta, Seeta and Geeta?
I. Neeta invested Rs. 85000 to start the business.
II. Seeta and Geeta joined Neeta’s business after six months investing amount in the ratio of 3 : 5.
III. Total amount investing by Seeta and Geeta is Rs. 2.5 lakh.
(a) Only II
(b) Only III
(c) Either II and III
(d) All of these
(e) None of these
9. Ans.(e)
Sol. From all three statements
Investment of Seeta =(3/8×2.5)lakh = Rs. 93750
Investment of Geeta =(5/8×2.5)lakh = Rs. 156250
Ratio of profits of Neeta, Seeta and Geeta
= 85000 × 24 : 93750 × 18 : 156250 × 18
= 272 : 225 : 375
Hence, we can find the share of profit of Neeta if the amount of profit is given.
Q10. What is the labeled price of the article?
I. Cost price of the article is Rs. 500.
II. Selling price after offering 5% discount on the labeled price is Rs. 608.
III. Profit earned would have been 28% if not discount was offered.
(a) Only I
(b) Only II
(c) II and III
(d) I and III
(e) I and II
10. Ans.(d)
Sol.
Suppose labeled price of goods be Rs. x
From statements II,
(95 × x )/100=608 ⇒x=(608 × 100)/95= Rs. 640
So, we can find the answer without statements I and III also.
