Answer:
Hence, the answer is, 
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CAT 2020 Quant Question: Number Theory
Q. 10. The mean of all 4 digit even natural numbers of the form ‘aabb’, where a>0, is
A. 5544
B. 4466
C. 4864
D. 5050
Answer:
Even numbers so b = 0
1100 1122 1144 1166 1188
2200 2222 2244 … …
.
.
.
9900 … … … …
By adding
= 5544
Hence, the answer is, "5544"
CAT 2020 Quant Question: Linear & quadratic equations
Q. 11. The number of distinct real roots of the equation 
Answer:
Hence, the answer is, " 1"
CAT 2020 Quant Question: Profit & Loss
Q. 12. A person spent Rs 50000 to purchase a desktop computer and a laptop computer. He sold the desktop at 20% profit and the laptop at 10% loss. If overall he made a 2% profit then the purchase price, in rupees, of the desktop is
Answer:
D = Price of Desktop and L = Price of Laptop
0.2 D – 0.1 L = 2 % of 50000
0.2 D – 0.1 L = 1000
D – L = 10000
D + L = 50000
Solving D = 20000
The answer is, " 20000"
CAT 2020 Quant Question: Digits
Q. 13. Among 100 students, 
have birthdays in January, 
have birthdays in February, and so on. If 
then the smallest possible value of 
A. 8
B. 10
C. 12
D. 9
Answer:
= 100 (If all 100 had their birthdays on January)
If = 3 (Not possible, because all 
together will be only 36)
So will be lesser when the numbers are as close as possible
So if we add 8 (12 times) = 96
So, need to have 8,8,8,8,8,8,8,8,9,9,9,9 (Adding these 12 we will get 100)
= 9
The answer is, "9"
CAT 2020 Quant Question: Speed, time & distance
Q. 14. Two persons are walking beside a railway track at respective speeds of 2 and 4 km per hour in the same direction. A train came from behind them and crossed them in 90 and 100 seconds, respectively. The time, in seconds, taken by the train to cross an electric post is nearest to
A. 87
B. 82
C. 78
D. 75
Answer:
Two person to be A and B
A = 2km/hr and B = 4 km/hr
Speed of the train = t km/hr
Given, Train crosses A in 90 seconds (Length of the train is the distance)
t – 2 in 90 seconds and t – 4 in 100 seconds
Ratio of speed is opposite to time
(t – 2) 90 = (t - 4) 100
Solving t = 22km/hr
For A, Speed = t – 2 = 20 km/hr in 90 seconds
The answer is, "82"
CAT 2020 Quant Question: Linear & quadratic equations
Q. 15. How many distinct positive integer-valued solutions exist to the equation 
A. 6
B. 2
C. 4
D. 8
Answer:
(x – 6) (x – 7) = 0
x = 6 or x = 7
(x – 2) (x – 5) = 0
x = 2 or x = 5
At this moment we have 4 values possible, But there is one more way we can arrive this
(x – 3) (x – 4) = 0
x = 3 or x = 4
So, 4 + 2 = 6 values
Hence, the answer is, "6"
CAT 2020 Quant Question: Co-ordinate Geometry
Q. 16. The area of the region satisfying the inequalities |x| - y ≤ 1, y ≥ 0, and y ≤ 1 is
Answer:
|x| – y = 1
y = |x| – 1
We got a trapezium with h = 1
And parallel sides = 2 and 4
= 
(2+4)×1
= 3 square units
Hence, the answer is, " 3"
CAT 2020 Quant Question: Mensuration
Q. 17. A solid right circular cone of height 27 cm is cut into 2 pieces along a plane parallel to it’s base at a height of 18 cm from the base. If the difference in the volume of the two pieces is 225 cc, the volume, in cc, of the original cone is
A. 264
B. 232
C. 243
D. 256
Answer:
When we consider top part of the triangle
Height is = 
of original height
If height becomes then radius also becomes
If both height and radius become , Volume will be 
So, Top part’s volume = V
Remaining part = 26V
Totally = 27V
Given 26 V – V = 225
V = 9
27 V = 243
The answer is, "243"
CAT 2020 Quant Question: Geometry
Q. 18. A circle is inscribed in a rhombus with diagonals 12 cm and 16 cm. The ratio of the area of the circle to the area of the rhombus is
Answer:
Diagonals of a rhombus are perpendicular bisectors of each other
If diagonals are 12 and 16
Half of diagonals are 6 and 8 third side will become 10 = side of rhombus
Radius of the circle will be perpendicular to the side of the rhombus
Because side of the rhombus is tangent to the circle
The triangle is taken by half a diagonal (6) and (8) from the original figure
Just equating the areas
Now, area of circle : area of rhombus
CAT 2020 Quant Question: Speed, time & distance
Q. 19. Leaving home at the same time, Amal reaches office at 10:15 am if he travels at 8kmph, and at 9:40 am if he travels at 15kmph. Leaving home at 9:10 am, at what speed, in kmph, must he travel so as to reach office exactly at 10:00 am?
A. 12
B. 11
C. 13
D. 14