Daily Practice Questions Questions for CAT with Answers PDF

Statement I and either statement II or statement III are sufficient.

Statements I and III are sufficient to answer the question.

Using statement I and either II or III, we can find who is sitting to the immediate right of A.
It means statements III or II are redundant.

Let the numbers of blue and red balls be 3x and 4x, respectively.
As per statement I:
If the red balls had been twice their actual number, the ratio would have been 3 : 8, which is clear from the question itself.
As per statement II:

On solving, we can find x and hence, the number of red balls.
As per statement III:

On solving, we can find x and hence, the number of red balls.

Question can be answered using statement I and either II or III.

As per statement I, it is clear that the bag contains a total of 15x balls containing 3x red balls, 5x white balls and 7x blue balls, where x is not given.
As per statement II, the bag contains 75 balls.
As per statement III, the number of red balls is 0.6 times the number of white balls.
Using statement I and II,
15x = 75
x = 5
Number of red balls = 15
Number of white balls = 25
Number of red balls = 35
Probability of picking 1 red and 1 white ball =  = 
Using statement I and III, we didn't find the number of balls of different colors.
Using statement II and III, we didn't find the number of balls of different colors.
So, option 4 is correct.

Using statements I and III, question can be answered.

As per statement I, 50% of x + y is equal to 30.
i.e. x + y = 60
So, we cannot find the value of x + 2y.
Hence, statement I alone is not sufficient.
As per statement II, y = 1.5x
But without finding any one value out of x and y, we cannot find the other value; so statement II alone is also not sufficient.
As per statement III, x + 3y = 132
But we cannot find the value of x + 2y without knowing the value of y.
So, statement III alone is also not sufficient.
To find the value of x + 2y, we need to find the values of x and y; which we can find by using any two of the given three statements.
So, option 4 is correct.

Using statement I with either II or III

It is clear from statement I that 5000 students appeared for the exam, but no information is given as to how many students got more than 80% marks; so statement I alone is not sufficient.
It is clear from statement II that out of the students who appeared, 34% secured less than 80% marks in the exam, but still no information is given as to how many students got more than 80% marks; so statement II alone is not sufficient.
As per statement III, the number of students who got more than 80% marks in the exam is double the number of students who got 80% marks in the exam. So, using statements II and III, we can conclude that 44% students got more than 80% marks in the exam; but by using all three statements, we can conclude that 2200 students got more than 80% marks in the exam. So, option 3 is correct.

Using statement I and either II or III, we get the relations mentioned in the diagram. Using statements II and III, we do not get exact relations with anyone. Relation of R and D is clear in the diagram.

From I, P(C) = ; P(B) = 

P(A) = 
Let, E = Event that the driver meets an accident.

From II, P
P
P
From I and II,
P 
Thus, Only I and II are required.

Using statements I and II we get that I and F will be in the middle.

We need to check if k⁵ + l⁴ + m³ + n² > 0 or not.
Numbers having even powers are always positive.
So, l⁴ and n² will always be positive, irrespective of values of l and n.
Now, the whole term being negative or positive depends on whether k⁵ + m³ is positive or negative and the values of m and k.
Since k is the term with the highest power, it will dominate the expression k⁵ + l⁴ + m³ + n² and for highly negative value, the expression will be always negative even if l, m and n are positive.
Now, even if we use statements A, B and C, m is greater than (-k).
For m = 5, k = -3, l = 2 and n = -2 
The value k⁵ + l⁴ + m³ + n² < 0
So, even all the three statements together are not sufficient.

Statements I and either II or III are sufficient.

If the triangle is equilateral, we can find the inradius from its area also. Thus, we can find the length of the inradius using statements A and B together.Lets say s is the side of an equilateral triangle.
Inradius of equilateral triangle = 
We can find the inradius of the triangle using its area and perimeter. Thus, we can find the length of the inradius using statements B and C together.
Lets say a, b and c are three sides of a triangle.
Inradius of triangle = 
Semi perimeter = 
Similarly, we can find the length of the inradius of the triangle using statements A and C.
Thus, option (4) is correct.

Statement III and either statement I or statement II are sufficient to answer the question.

Statement A alone is sufficient as product of m and n is already given in question.
Using statement A, we find m = 1.25n, through which we can find individual values of m and n.
Similarly, we can find the values of m and n, respectively from statement B also.
By using statement C alone, we can form a quadratic equation as both sum and product of m and n is given, but cannot find their respective values as we do not know whether m is greater than n or vice versa.

Using statement A, we can find the average number of balls in boxes A, B and C, respectively as we are given the value of average when 5 balls were drawn from each of the boxes. So, by simply adding five to that value, we can find the average number of balls in boxes A, B and C. Similarly, we can also find the average number of balls in boxes A, B and C using statement B. Using statement C, we can find the number of balls in box A and by using relationship between number of balls in box A and total number of balls in boxes B and C, we can find the total number of balls in three boxes and hence, their average.

We need speed of Aksh to find the answer.
Any two of the given statements are sufficient.
Using statements I and II:
Speed of Aksh is 2x kmph and speed of Ankush is 3x kmph.


30 = 12x
x = 2.5
Speed of Aksh is 5 kmph.
Time taken by Aksh to cover 30 km is 6 hours.
Using statements II and III:
Let speed of Aksh be 2x kmph and speed of Ankush be 3x kmph.
If we double the speed of Aksh, it becomes 4x.


30 = 12x
x = 2.5
Speed of Aksh is 5 kmph.
Time taken by Aksh to cover 30 km is 6 hours.
Using statements I and III:
Let speed of Aksh be x kmph. When his speed is doubled, Aksh takes 3 hours less time.


30 = 6x
x = 5
Speed of Aksh is 5 kmph.
Time taken by Aksh to cover 30 km is 6 hours.