**Statement I**: The circum radius of the triangle is 6 cm.

**Statement II**: Angle ABC = 60 degrees

**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 = \(\frac{height}{hypotenuse}\) 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.

**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.

**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.

**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.

**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.

**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.

**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%.

**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.

**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.

**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 \(\frac{1}{3}\)\(^{rd}\) 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.

**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

**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.

**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**: \(\frac{1}{x}\) is greater than 1.

**Statement II**: \(\frac{1}{x}\) is less than \(\frac{1}{y}\).

**Answer**: Option E

**Explanation**:

**From statement I**, \(\frac{1}{x}\)

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**, \(\frac{1}{x}\)

is less than \(\frac{1}{y}\)

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.

**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.

**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.

**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.