Answer:
From any point on a equilateral triangle, if we draw three perpendiculars on other sides
Those three perpendicular will add up to = Altitude of an equilateral triangle
We take the point to be A, and try to draw 3 perpendiculars (Can draw only one)
And is same as altitude of the equilateral triangle
By substituting the value in Area of an equilateral triangle 
CAT 2020 Quant Question: Averages
In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by
A. 5
B. 3
C. 4
D. 6
Answer:
Here a2 to a9 is common to both the terms
So, a1 + (a2 to a9) = 42 × 9
a10 + (a2 to a9) = 47 × 9
Solving these two a10 - a1 = 45
a1, a2, a3,………………………, a9, (a1 + 45)
One instance is every number is 42
42, 42, …………………, 42, 42+45 (a1 to a9 are equal) -----------(1)
Another instance is every number is 47
47 – 45, 47, …………………, 47, 47 (a2 to a10 are equal) ---------(2)
Mean of (1) = 46.5
Mean of (2) = 42.5
(1) – (2) = 4
The answer is, "4"
CAT 2020 Quant Question: Linear & quadratic equations
The number of pairs of integers(x,y) satisfying x ≥ y ≥ -20 and 2x + 5y = 99 is
Answer:
x = 2 and y = 19 (Not possible), Given the condition x ≥ y ≥ - 20
x should increase/decrease in the coefficient of y and same for y
x = 7 and y = 17 (Not possible)
x = 12 and y = 15 (Not possible)
x = 17 and y = 13 (Possible)
. y = 11
. y = 9
. .
. .
. .
. y = -19 (Can’t go any further)
By counting totally 17 values are there
Hence, the answer is, " 17"
CAT 2020 Quant Question: Logarithms
The value of 
for 1 < a ≤ b cannot be equal to
A. -0.5
B. 1
C. 0
D. -1
Answer:
From the options,
x + 1/x ≠ 1
Hence, the answer is, "1"
CAT 2020 Quant Question: Sequence & series
Let teh m-th and n-thterms of a Geometric progression be 
and 12, respectively, when m < n. If the common ratio of the progression is an integer r, then the smallest possible value of r + n - m is
A. -4
B. -2
C. 6
D. 2
Answer:
k = n – m (From m how many terms we have to jump to reach n)
We have two cases r = - 2 and n - m = 4 ----> r + n – m = 2
r = - 4 and n – m = 2 ----> r + n – m = - 2
-2 is the smallest possible value
The answer is, "-2"
CAT 2020 Quant Question: Simple interest & Compound interest
For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125. Then the principal amount in rupees is
Answer:
Hence, the answer is, " 90000"
CAT 2020 Quant Question: Geometry
Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the length of PQ, in meters, is nearest to
A. 6.6
B. 7.2
C. 8.8
D. 7.8
Answer:
O is the center of the circle and radius of circle = 5
In triangle AOB, using pythagorean triplet AB = 5
Since OR if from the center it bisects the chord,
PR = RQ
Now in triangle POR,
PR = √{19.24}
PQ = 2 √{19.24}
PQ ≅ 8.8
The answer is, "8.8"
CAT 2020 Quant Question: Polynomials
For real x, the maximum possible value of 
Answer:
Dividing by x on both numerator and denominator
CAT 2020 Quant Question: Profit & Loss
Anil buys 12 toys and labels each with the same selling price. He sells 8 toys initially at 20% discount on the labeled price. Then he sells the remaining 4 toys at an additional 25% discount on the discounted price. Thus, he gets a total of Rs 2112, and makes a 10% profit. With no discounts, his percentage of profit would have been
A. 60
B. 50
C. 55
D. 54
Answer:
Let’s take Selling Price = P
= {(8 × 0.8 P) + 4 × (0.6P)}
Total Selling Price = 8.8 P
SP = 12P
The answer is, "50"
CAT 2020 Quant Question: Inequalities
If x and y are non-negative integers such that x + 9 = z, y + 1 = z and x + y < z + 5, then the maximum possible value of 2x + y equals
Answer:
x + x + 8 < x + 9 + 5
2x + 8 < x + 14
x < 6
Maximum possible of x = 5, then y = 13
2x + y = 2(5) + 13 = 23
Hence, the answer is, "23"
CAT 2020 Quant Question: Set Theory
Students in a college have to choose at least two subjects from chemistry, mathematics and physics. The number of students choosing all three subjects is 18, choosing mathematics as one of their subjects is 23 and choosing physics as one of their subjects is 25. The smallest possible number of students who could choose chemistry as one of their subjects is
A. 22
B. 19
C. 20
D. 21