Answer:
Method of solving this CAT Question from Geometry
As the triangle progresses infinitely and the side length decreases, it follows an infinite GP series
Hence, the answer is 192 √3 sq cms.
Choice A is the correct answer.
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CAT 2018 Quant Question Number Theory:
While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is: [TITA]
Answer:
Let the three real numbers be a, b, c. c is taken as 73 instead of 37
So, 73ab = 37ab + 720
36 ab = 720
Hence, the answer is 40.
CAT 2018 Quant Question: Logarithm
Answer:
Taking log on both sides, we get
Let us consider the base as 3,
Going through the options, Simplifying (B)
Choice B is the correct answer.
CAT 2018 Quant Question: Logarithm
CAT 2018 Quant Question: Mensuration
A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With π = 22/7, the volume, in cubic ft, of the remaining part of the cone is:[TITA]
Answer:
From the diagram, △OAD is similar to △OBC
Volume of the remaining part = 198 cubic ft
Hence, the answer is 198 cubic ft.
CAT 2018 Quant Question: Number theory
How many numbers with two or more digits can be formed with the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 so that in every such number, each digit is used at most once and the digits appear in the ascending order?[TITA]
Answer:
Let us consider the case of 2-digit numbers
2 numbers can be chosen from the given set by 
ways. There is only one way of arranging them in ascending order.
Similarly, the remaining numbers can be chosen and arranged in ascending order by
512-10 = 502
Hence, the answer is 502 units.
CAT 2018 Quant Question: SI & CI
John borrowed Rs. 2,10,000 from a bank at an interest rate of 10% per annum, compounded annually. The loan was repaid in two equal instalments, the first after one year and the second after another year. The first instalment was interest of one year plus part of the principal amount, while the second was the rest of the principal amount plus due interest thereon. Then each instalment, in Rs., is:[TITA]
Answer:
Method of solving this CAT Question from SI and CI
Given, money borrowed = Rs. 2,10,000
At 10% Interest, after 1 year
Outstanding amount = Rs. 1.1 × 2,10,000 = Rs. 2,31,000
Let the First Installment be x
So, Due amount = Rs. 2,31,000 - x
This due amount is carried over to the second year, with an interest of 10%
So, Outstanding amount for Second year = Rs. 1.1 × (2,31,000 - x)
This amount will be payed as Second Installment
We know, Installment for year 1 = Installment for year 2 = Rs. x
1.1 × (2,31,000 - x) = x
2.1 x = 2,54,100
x = Rs. 1,21,000
Hence, the answer is Rs. 1,21,000.
CAT 2018 Quant Question: Linear and Quadratic Equations
Answer:
CAT 2018 Quant Question: Speed, Time and Distance
Point P lies between points A and B such that the length of BP is thrice that of AP. Car 1 starts from A and moves towards B. Simultaneously, car 2 starts from B and moves towards A. Car 2 reaches P one hour after car 1 reaches P. If the speed of car 2 is half that of car 1, then the time, in minutes, taken by car 1 in reaching P from A is:[TITA]
Answer:
Let us take the distance AP = x and BP = 3x
6t = t + 60
5t = 60
t = 12 minutes
Hence, the answer is 12 minutes.
CAT 2018 Quant Question: Geometry
Let ABCD be a rectangle inscribed in a circle of radius 13 cm. Which one of the following pairs can represent, in cm, the possible length and breadth of ABCD?
A. 25 , 10
B. 24 , 12
C. 25 , 9
D. 24 , 10
Answer:
Since, ABCD is a rectangle inscribed inside a circle
ABC must be a Right triangle
Given that radius of Circle = 13 cms
5, 12, 13 forms a Pythagorean Triplet
10, 24, 26 is also a Pythagorean triplet
So, 10 and 24 are possible length and breadth of ABCD
Hence, the answer is 10 , 24.
Choice D is the correct answer.
CAT 2018 Quant Question: Percentages
In an examination, the maximum possible score is N while the pass mark is 45% of N. A candidate obtains 36 marks, but falls short of the pass mark by 68%. Which one of the following is then correct?
A. N ≤ 200
B. 243 ≤ N ≤ 252
C. N ≥ 253
D. 201 ≤ N ≤ 242