Answer:
Hence, the answer is 1
Choice B is the correct answer.
CAT Prep 2023 | CAT Previous Year Question Papers With Solution | CAT 2022 Student Review | PaGaLGuY
Answer:
Now, for any number to be a perfect square, it must have an even number of factors.
So, if we consider 
only powers of 0, 2, 4, 6, 8 can lead to perfect squares - 5 ways
If we consider 
only powers of 0, 2, 4 can lead to perfect squares - 3 ways
If we consider 
only powers of 0. 2, 4 can lead to perfect squares - 3 ways
So, total number of possibilities = 5 x 3 x 3 ways = 45 ways
Since we need to find the number of factors greater than 1,
Required number of ways = 45 -1 = 44 ways
Hence, the answer is 44
I am from Mumbai, completed BMS. I have 7 point grading scale. I have scored 5.71/7 . Can someone help me to convert it to percentage
CAT 2019 Quant Question: Geometry
Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, is
Answer:
For three circles to have a common tangent, the third circle must lie in between the two circles. Let the radius of the third circle be r cms
Now, Connect the centres of the circles with one another and with the intersection points. Let them be A,B,C,D,E respectively.
Now, from observing the constructed diagram, we find
AB = 8cms
AC = (4 + r) cms
BC = (4 + r) cms
OC = (4 - r) cms
Now, consider the right triangle OBC,
Applying Pythagoras theorem,
16r = 16
r = 1 cms
Hence, the answer is 1
Choice B is the correct answer.
CAT 2019 Quant Question: Linear & quadratic equations
What is the largest positive integer such that 
is also positive integer?
A. 6
B. 8
C. 16
D. 12
Answer:
n cannot be -3
And this value has to be equal to 1, for n to be high
8 = n - 4
n = 12
Hence, the answer is 12
Choice D is the correct answer.
CAT 2019 Quant Question: Percentages
In 2010, a library contained a total of 11500 books in two categories - fiction and non-fiction. In 2015, the library contained a total of 12760 books in these two categories. During this period, there was 10% increase in the fiction category while there was 12% increase in the non-fiction category. How many fiction books were in the library in 2015?
A. 6600
B. 6160
C. 6000
D. 5500
Answer:
Increase in books = 12760 - 11500 = 1260
+ 
x (11500 - x) = 1260
10x + 12 x 11500 - 12x = 126000
x = 6000 books
So, Fiction books in 2015, 6000 + 600 = 6600 books
Hence, the answer is 6600
Choice A is the correct answer.
CAT 2019 Quant Question: Functions
Let f be a function such that f (mn) = f (m) f (n) for every positive integers m and n. If f (1), f (2) and f (3) are positive integers, f (1) < f (2), and f (24) = 54, then f (18) equals [TITA]
Answer:
It is given that f (2) > 1 and f(mn) = f(m) f(n)
So, f (2) = f (2) f (1), as m and n are positive integers.
Only possible value for f (1) = 1
f (2) > 1
Now we know, f (24) = 54
So, f (2) f (3) f (4) = 54
Therefore, f (2) = 3, f (3) =2 and f (1) = 1
Now, we need to find the value of f (18)
f (18) = f (3) x f (2) x (3)
f (18) = 2 x 3 x 2 = 12
f (18) = 12
Hence, the answer is 12
CAT 2019 Quant Question: Geometry
Let A and B be two regular polygons having a and b sides, respectively. If b = 2a and each interior angle of B is 3/2 times each interior angle of A, then each interior angle, in degrees, of a regular polygon with a + b sides is [TITA]
Answer:
Sum of the interior angles of a n-sided Polygon = (n-2) x 180
Measure of each interior angle = 
So, Interior angle of the polygon with side a = 
Interior angle of the polygon with side b = 
It is given that interior angle of side b is 3/2 times to that of the polygon with side A
= 
x
(2a-2) x 180 = (3a - 6) x 180
2a - 2 = 3a - 6
a = 4
So, b = 8
(a + b) sides = 8 + 4 = 12 sides
Interior angle = 
= 150
Hence, the answer is 150
CAT 2019 Quant Question: Speed, Time & distance
A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motorcycle leaves A and moves towards B. Forty-five such motorcycles reach B by 11 am. All motorcycles have the same speed. If the cyclist had doubled his speed, how many motorcycles would have reached B by the time the cyclist reached B?
A. 22
B. 20
C. 15
D. 23
Answer:
It is given that the cyclist starts at 10:00 am from A and reaches B at 11:00 am
Now, Motorcyclists start every minute from 10:01 am, and 45 such motorcyclists reach B before 11:00 am
If they leave one by one every minute, the 45th motorcyclist would have left by 10:45 am to reach B at 11:00 am.
Thus, time taken by one motorcyclist to reach B from A = 15 minutes.
Now, the cyclist doubles his speed. This means, he reaches B at 10:30 am
So, the last motorcyclist should have left A by 10:15 am
Thus, 15 motorcyclists would have reached B by the time the cyclist reaches B
Hence, the answer is 15
Choice C is the correct answer.
CAT 2019 Quant Question: Linear & quadratic equations
Let A be a real number. Then the roots of the equation 
= 0 are real and distinct if and only if
Answer:
For roots of any Quadratic equation to be real and distinct, D > 0
Hence, the answer is 
Choice C is the correct answer.
CAT 2019 Quant Question: Races
John jogs on track A at 6 kmph and Mary jogs on track B at 7.5 kmph. The total length of tracks A and B is 325 metres. While John makes 9 rounds of track A, Mary makes 5 rounds of track B. In how many seconds will Mary make one round of track A? [TITA]
