Directions (Q. 15): Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read the question and both the statements and 
Give answer (a) if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
Give answer (b) if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
Give answer (c) if the data either in statement I alone or in statement II alone are sufficient to answer the question.
Give answer (d) if the data even in both the statements I and II together are not sufficient to answer the question.
Give answer (e) if the data in both the statements I and II together are necessary to answer the question.
1.What is the two digit number where the digit at the unit place is smaller?I. The difference between the two digits is 5.
II. The sum of the two digits is 7.
Number = 10y + x
From statement I,
y – x = 5 ... (i)
From statement II,
y + x = 7 ... (ii)
From (i) and (ii), x, y can be calculated and two digit number can be found.
Answer is: E
2.Train 'A' running at a certain speed crosses another train 'B' running at a certain speed in the opposite direction in 12 seconds. What is the length of train 'B'?
I. The length of both the trains together is 450 metres.
II. Train 'A' is slower than train 'B'.
Time taken by both the trains in crossing each other
= 450/S1 + S2 = 12,
S1 + S2 = 37.5
S1 and S2 can have so many values. Both statement I and II are not sufficient to find speed of train B.
Answer is: D
3. Area of a rectangle is equal to the area of a right angled triangle. What is the length of the rectangle?
I. The base of the triangle is 40 cms.
II. The height of the triangle is 50 cms.
From the information given in both the statements, we can find area of triangle or area of rectangle. For finding length, breadth is required, which is not known.
Answer is: D
4.What is the speed of the boat in still water?
I. It takes 2 hours to cover distance between A and B downstream.
II. It takes 4 hours to cover distance between A and B upstream.
Again, let speed of boat in still water be x kmph and that of stream be y kmph.
Rate downstream = (x + y) kmph
Rate upstream = (x – y) kmph
From statement I,
z/ x + y = 2... (i)
From statement II,
= z/x – y =4 ... (ii)
We have two equations and three variables, therefore both equations are not sufficient.
Answer: D
5. What was the total compound interest on a sum after three years?
I. The interest after one year was Rs. 100/ and the sum was Rs. 1,000/.
II. The difference between simple and compound interest on a sum of Rs. 1,000/ at the end of two years was 10/.
r = 100 × 100/1000
= 10%
Thus we have,
P = 1000, r = 10%, t = 3 years
Hence, C.I. can be determined
From the statement II.
S.I. = 1000 × r × 2/100 = 20r
C.I.= 1000 [(1+r/100)^2 1]
C.I. – S.I. = 1000 [(200r+r^2)/10000] – 20r
200r + r^2 – 200r = 100
r = 10
Hence, C.I. can be determined.
Answer: C
Directions (Q. 610): In these questions, a question is given followed by information in three statements. You have to consider the information in all the three statements and decide the information in which of the statement(s) is not necessarily required to answer the question and therefore can be dispensed with. Indicate your answer accordingly.
6.What is Suchitra’s present age?
I. Suchitra’s present age is double the age of her son.
II. Ratio between present ages of Suchitra and her mother is 2 : 3 respectively.
III. Four years hence the ratio between Suchitra’s age and her son’s age will be 13 : 24 respectively.
Suchitra’s present age
= 2x years
After 4 years,
(2x+ 4)/(x+4) = 13/24
We can get the required answer by this relation.
So statement II is not required.
Answer: A
7.What is the labelled price of the article?
I. Cost price of the article is 500.
II. Selling price after offering 5% discount.
III. Profit earned would have been 28% if no discount was offered.
Marked price = 128 × 500/100
= 640
So statement I& III is sufficient to give the answer.
Answer: B
8.How many students from Institute ‘A’ got placement?
I. Number of students studying in Institutes A& B are in the ratio of 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.
Let the number of students in the institutes A and B be 3x and 4x respectively. However we get no conclusive answer by using data given in all the statements.
Answer: E
9. 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 saving of Mr. X are 4,500/.
III. Out of the total money spent by Mr. X in a month, onefifth is spent on food and remaining amount of 20, 400 on other items.
income = x. Then
15 × x/100 =4500
x = 4500 × 100/15
30000
From statements I and III,
X × 4/5 × 85/100
= 20400
X = 20400 × 5 × 100/4 × 85
X = 30000
Answer: C
10.What is Neeta’s share in the profit earned at the end of 2 years in a joint business run by Neeta, Seeta and Geeta?
I. Neeta invested 85,000/ to start the business.
II. Seeta and Geeta joined Neeta’s business after six months investing amounts in the ratio of 3 : 5 respectively.
III. Total amount invested by Seeta and Geeta is 2.3 lakhs
= 3/8 × 2.5 lakh
= 93750
Geeta’s investment
= 156250
Ratio of Neeta’s, Seeta’s and Geeta’s profit
= 85000 × 24 : 93750 × 18 : 156250 × 18
We can get the share of Neeta if total profit is given.
So data given in all three statements is required to answer the question.
Answer: D
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