1. What is the area of a right-angled triangle ABC, right angled at A?
Statement I: The circum radius of the triangle is 6 cm.
Statement II: Angle ABC = 60 degrees

A. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C. Either Statement I or Statement II alone is sufficient to answer the question. D. The data in both the statements I and II is not sufficient to answer the question. E. The data in both the statements I and II together is necessary to answer the question.

Answer: Option E
Explanation: If circum radius in the statement I is given then hypotenuse will be double of the circum radius. From the statement II, one angle is 60 degrees then other will be 30 degrees. Here we know all the angles and by combining with the statement I, we can conclude one side that is hypotenuse By using sin60 = [latex]\frac{height}{hypotenuse}[/latex] we can conclude the other side then after we can easily conclude the area of the triangle.
2. After 5 years, what will the sum of the age of Moni and Soni?
Statement I: 5 years before, Moni was 5 years older than Soni.
Statement II: At present, the ratio of their ages is 5 : 6.

A. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C. Either Statement I or Statement II alone is sufficient to answer the question. D. The data in both the statements I and II is not sufficient to answer the question. E. The data in both the statements I and II together is necessary to answer the question.

Answer: Option E
Explanation: From statement I,5 years before, let the age of moni = x then the age of soni = x – 5 At present, their age will be, Moni = x + 5 years, Soni = x – 5 + 5 = x years From statement II, the ratio of x + 5 and x are given, therefore, by combining both the statement, we can conclude our answer.
3. Two trains, running in the opposite direction cross each other in 18 sec. What is the difference between their lengths?
Statement I: The difference between their speeds is 12 m/sec
Statement II: The sum of their speeds is 36 meters per second.

A. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C. Either Statement I or Statement II alone is sufficient to answer the question. D. The data in both the statements I and II is not sufficient to answer the question. E. The data in both the statements I and II together is necessary to answer the question.

Answer: Option D
Explanation: If we combine both the statement, then we can conclude their speed as 24 m/sec and 12 m/sec Now we can conclude the sum of their length but the difference of their lengths is not possible to get. Therefore, the data in both the statements I and II are not sufficient to answer the question.
4. What is the value of three digits number, the unit digit of which is 3 and divisible by 7?
Statement I: The three digits number is divisible by 9.
Statement II: The three-digit number is divisible by 21.

A. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C. Either Statement I or Statement II alone is sufficient to answer the question. D. The data in both the statements I and II is not sufficient to answer the question. E. The data in both the statements I and II together is necessary to answer the question.

Answer: Option A
Explanation: From the question, the unit digit of the three-digit number is 3, and it is divisible by 7. From statement I, the number is divisible by 9 LCM of 9 and 7 = 63 The only number which is multiple of 63 and the unit digit of which is 3, is 63 × 11 = 693 Therefore, we can conclude our answer by this statement From statement II, the number is divisible by 21 therefore, LCM of 21 and 7 = 21 There are many numbers like, 273, 483 ------ which is divisible by 21 and 7, and the unit digit of which is 3 Therefore, we could not get a unique answer by this statement. Therefore, the data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
5. In a school, 60% of the girls aged 14 and above play football then how many of girls play football?
Statement I: In the school, there are no girls below 14 years who play football.
Statement II: In the school, girls comprise 60% of the total number of students who play football.

A. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C. Either Statement I or Statement II alone is sufficient to answer the question. D. The data in both the statements I and II is not sufficient to answer the question. E. The data in both the statements I and II together is necessary to answer the question.

Answer: Option D
Explanation: In none of the statement or in question, it is given any information about number therefore by using only percentage, we could not conclude our answer.

1. Find the distance traveled by Rajdhani express in two hours if it travels with its original speed?
Statement I: The train started from the origin station 20.25 hours later than the scheduled time towards its destination which is 750 km away from the origin.
Statement II: To reach the destination station in the scheduled time the loco – piolet of the train increases the speed of the train to 125% of the original speed.

A. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C. Either Statement I or Statement II alone is sufficient to answer the question. D. The data in both the statements I and II is not sufficient to answer the question. E. The data in both the statements I and II together is necessary to answer the question.

Answer: Option E
Explanation: From I and II: Let the original speed of the train is ‘100x’ km/h Increased speed = 125% of 100x = 125x km/h According to a question- ⇒ 750 – 750 = 20.25 100x 125x ⇒ x = 2 3 Original speed of the train = 100x = 100 × 2 = 200 km 3 3 Hence the distance traveled by train in 2 hours = 2 × 200 = 400 km 3 3 Hence statements I and II together are sufficient.
2. What should be the selling price of washing machine so as to make a profit of 25%?
Statement I: An electronic shop dealer marks washing machine 80% above the cost price and after allowing a discount of 25% he claims a profit of Rs. 3500.
Statement II: A shopkeeper sold the same washing machine for Rs. 15000 on the condition that shopkeeper will pay the transportation cost of Rs 2000 and he gets a profit of 25%.

A. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C. Either Statement I or Statement II alone is sufficient to answer the question. D. The data in both the statements I and II is not sufficient to answer the question. E. The data in both the statements I and II together is necessary to answer the question.

Answer: Option C
Explanation: From Statement I: Let the cost price of the working machine be x. then the marked price of washing machine = x + 80 × x = 1.8x 100 Selling price = 1.8x × 100 – 25 = 1.35x 100 Now, profit = 1.35x – x Profit = 0.35 x but 0.35x = 3500 ∴ x = 10,000 So, the cost price of the washing is Rs. 10000. Selling price in order to earn 25% profit = 125 × 10000 = 12,500 100 Hence, the statement I alone is sufficient From Statement II: Let the cost price of the washing machine be x then, Cost price after paying transportation = x + 2000 then ⇒ x + 2000 = 100 15000 125 ⇒ x + 2000 = 12000 ⇒ x = 10000 Cost price is Rs. 10000 Selling price in order to earn 25% profit = 125 × 10000= Rs. 125000 100 Hence, statement II alone is also sufficient. Here, Statement I or II alone is sufficient.
3. How many years old will Anuj be p years from now?
Statement I: Ankur is 14 years older than Anuj.
Statement II: The sum of the ages of Ankur and Anuj is p years.

A. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C. Either Statement I or Statement II alone is sufficient to answer the question. D. The data in both the statements I and II is not sufficient to answer the question. E. The data in both the statements I and II together is necessary to answer the question.

Answer: Option C
Explanation: From Statement I: Using the information given in above statement. Anuj + 14 = Ankur Here, we have no information about p and the actual age of Anuj. So, we cannot find the answer. Hence, the statement I alone is not sufficient. From Statement II: Using the information given in the above statement, we can say that Anuj + ankur = p Here, we have no information about the present age of Anuj So, we cannot find the answer. Both Statement I and II: From statement I: Anuj + 14 = Ankur From Statement II: Anuj + Ankur = p 2 Anuj + 14 = p Here, cannot find the actual age of Anuj and the real value of p. So, we cannot find the answer. Hence, Both statement I and II together are not sufficient.
4. If a rope is cut into three pieces of unequal length, what is the length of the shortest of these pieces of rope?
Statement I: The combined length of the longer two pieces of rope is 17 meters.
Statement II: The combined length of the shorter two pieces of rope is 15 meters.

A. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C. Either Statement I or Statement II alone is sufficient to answer the question. D. The data in both the statements I and II is not sufficient to answer the question. E. The data in both the statements I and II together is necessary to answer the question.

Answer: Option D
Explanation: Let the length of layer piece, middle piece and shorter piece be l, m and s respectively. From Statement I: Using the information given in above statement. l + m = 17 Here, we have no information about the total length of the rope or the length of the shorter piece. So, we cannot find the answer. Hence, the statement I alone is not sufficient. From Statement II: Using the information given in above statement, s + m = 19 Here, we have no other information about the length of these pieces. So, we cannot find the answer. Hence, statement II alone is not sufficient. Both Statement I and II:– From statement I : l + m = 17 From Statement II : s + m = 15 Combining both statements I and II we get l – s = 2 At this point, we have no information about the total length or the length of any of these pieces of the rop.e So, we cannot find the answer. Hence, Both statement I and II together are not sufficient.
5. At present, the age of A is [latex]\frac{1}{3}[/latex][latex]^{rd}[/latex] of the age of B then what are their ages?
Statement I: After 10 years, the ratio of their ages will become 5 : 11.
Statement II: 5 years age, the age of A was 25% of the age of B.

A. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C. Either Statement I or Statement II alone is sufficient to answer the question. D. The data in both the statements I and II is not sufficient to answer the question. E. The data in both the statements I and II together is necessary to answer the question.

Answer: Option C
Explanation: From the question, A : B = 1 : 3 Statement I: after 10 years, the ratio will become 5 : 11 Statement II: 5 years ago, the ratio was 1 : 4 Therefore, a statement I or Statement II alone is sufficient to get our answer, and their ages will be 15 years and 45 years respectively

1. At present, the age of A to B is in the ratio of 7 : 9. B is how many years older than A?
Statement I: 5 years before, the ratio of the age of A to C was 4 : 5.
Statement II: After 5 years, the ratio of the age of A to D will become 6 : 7.

A. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C. Either Statement I or Statement II alone is sufficient to answer the question. D. The data in both the statements I and II is not sufficient to answer the question. E. The data in both the statements I and II together is necessary to answer the question.

Answer: Option D
Explanation: A : B = 7 : 9 Let us assume it 7x and 9x From statement I: A’s age = 4y = 7x – 5 From statement II: A’s age = 6z = 7x + 5 If we combine both the statement, we could not find three variables Therefore, the data in both the statements I and II is not sufficient to answer the question.
2. Is x greater than y?
Statement I: [latex]\frac{1}{x}[/latex] is greater than 1.
Statement II: [latex]\frac{1}{x}[/latex] is less than [latex]\frac{1}{y}[/latex].

A. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C. Either Statement I or Statement II alone is sufficient to answer the question. D. The data in both the statements I and II is not sufficient to answer the question. E. The data in both the statements I and II together is necessary to answer the question.

Answer: Option E
Explanation: From statement I, [latex]\frac{1}{x}[/latex] is greater than 1 it means x is less than 1. We could not conclude if x is greater than or less than y From statement II, [latex]\frac{1}{x}[/latex] is less than [latex]\frac{1}{y}[/latex] 1 < 1 x y If x and y both are positive then This will be only possible if x is greater than y. But, if x is negative i.e. – 2 and y is positive i.e. 2 then x < y 1 = – 0.5 and 1 = 0.5 x y Here, 1 is also less than 1 x y From statement I, x is less than 1 Therefore, if we combined both the statement then we can conclude that x is less than y
3. What is the area of a triangle ABC of base 12 cm?
Statement I: The height of the triangle is 8 cm.
Statement II: The triangle is an isosceles.

A. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C. Either Statement I or Statement II alone is sufficient to answer the question. D. The data in both the statements I and II is not sufficient to answer the question. E. The data in both the statements I and II together is necessary to answer the question.

Answer: Option A
Explanation: Area of a triangle = ½ × base × height In statement I, height is given then we can conclude the area by the formula. In statement II, we only have information that the triangle is isosceles Therefore, statement II alone is not sufficient to conclude our answer. Therefore, the data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
4. What is the marked price of an article?
Statement I: The selling price after giving 25% discount on the marked price is Rs. 600.
Statement II: If the article was sold on the marked price then the profit earned on the cost price would be either 60% or Rs. 300.

A. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C. Either Statement I or Statement II alone is sufficient to answer the question. D. The data in both the statements I and II is not sufficient to answer the question. E. The data in both the statements I and II together is necessary to answer the question.

Answer: Option C
Explanation: From statement I, discount percentage is given and selling price is given then we can conclude the marked price as Rs. 800 In statement II, Let CP = Rs. 100x then Selling price = MP = Rs. 160x Profit = 160x – 100x = 60x = 300 x = 5 It means, MP = 160x = Rs. 800 Therefore, either Statement I or Statement II alone is sufficient to answer the question.
5. What is the speed(in metres per hour) of motorboat in still water?
Statement I: The motorboat covers 100 km downstream in 10 hours.
Statement II: The motorboat covers 60 km in still water in 10 hours.

A. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C. Either Statement I or Statement II alone is sufficient to answer the question. D. The data in both the statements I and II is not sufficient to answer the question. E. The data in both the statements I and II together is necessary to answer the question.

Answer: Option B
Explanation: From statement I alone, we can conclude downstream speed but we could not conclude the speed of motorboat in still water. From statement II alone, we can conclude that the speed of motorboat in still water = 6 km per hour Now, we can change it in the term of meters per hour Therefore, the data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.