CAT Prep 2022 | CAT Previous Year Question Papers With Solution | CAT 2022 Question Bank | PaGaLGuY

CAT 2020 Quant Question: Geometry

From the interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the perpendiculars is βsβ. Then the area of the triangle is

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

Here a2 to a9 is common to both the terms
So, a1 + (a2 to a9) = 42 Γ 9
a10 + (a2 to a9) = 47 Γ 9
Solving these two a10 - a1 = 45
a1, a2, a3,β¦β¦β¦β¦β¦β¦β¦β¦β¦, a9, (a1 + 45)
One instance is every number is 42
42, 42, β¦β¦β¦β¦β¦β¦β¦, 42, 42+45 (a1 to a9 are equal) -----------(1)
Another instance is every number is 47
47 β 45, 47, β¦β¦β¦β¦β¦β¦β¦, 47, 47 (a2 to a10 are equal) ---------(2)
Mean of (1) = 46.5
Mean of (2) = 42.5
(1) β (2) = 4

CAT 2020 Quant Question: Linear & quadratic equations

The number of pairs of integers(x,y) satisfying x β₯ y β₯ -20 and 2x + 5y = 99 is

x = 2 and y = 19 (Not possible), Given the condition x β₯ y β₯ - 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 (Canβ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 β€ b cannot be equal to

A. -0.5
B. 1
C. 0
D. -1

From the options,
x + 1/x β  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

k = n β 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 β m = 2
r = - 4 and n β m = 2 ----> r + n β m = - 2
-2 is the smallest possible value

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

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

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 = β{19.24}
PQ = 2 β{19.24}
PQ β 8.8