Answer:
Given Max. mark = N and Pass mark = 45% of N
A scores 36 marks and falls short of the pass mark by 68%
This means the pass mark must be reduced by (100 - 68)% = 32%
So, A scored 32% (45% N) = 36
N = 250 marks
The only option whose range falls within the obtained value is (B) 243 ≤ N ≤ 252
Hence, the answer is 243 ≤ N ≤ 252
Choice B is the correct answer.
CAT 2018 Quant Question: Sequence & Series
Let x, y, z be three positive real numbers in a geometric progression such that x < y < z. If 5x, 16y, and 12z are in an arithmetic progression then the common ratio of the geometric progression is
Answer:
CAT 2018 Quant Question: Number Theory
The number of integers x such that 0.25 < 
is perfectly divisible by either 3 or 4, is [TITA]
Answer:
Substituting the values and checking for divisibility
Number of Integers x = 5
Hence, the answer is 5 integers
CAT 2018 Quant Question: Set Theory
Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H is [TITA]
Answer:
Let us draw a Three set Venn diagram from values given
Since its given that n(H) = n(E) and n(only P) = 0
a + b + 20 + 10 = c + d + 20 + 10
a + b = c + d
As N = 74, a + b + 20 + 10 + c + d = 74
2(a + b) = 44 => a + b = 22
n(H) = a + b + 20 + 10 = 22 + 20 +10 = 52 students
Hence, the answer is 52 students
CAT 2018 Quant Question: Speed Time Distance
Train T leaves station X for station Y at 3 pm. Train S, traveling at three quarters of the speed of T, leaves Y for X at 4 pm. The two trains pass each other at a station Z, where the distance between X and Z is three-fifths of that between X and Y. How many hours does train T take for its journey from X to Y? [TITA]
Answer:
From question, XZ = 3d, YZ = 2d
As their speeds are in ratio 4:3
Let their speeds be 4V and 3V
We need to find the time taken for T To travel from X to Y
Hence, the answer is 15 hours
CAT 2018 Quant Question: Geometry
Points E, F, G, H lie on the sides AB, BC, CD, and DA, respectively, of a square ABCD. If EFGH is also a square whose area is 62.5% of that of ABCD and CG is longer than EB, then the ratio of length of EB to that of CG is:
A. 1 : 3
B. 4 : 9
C. 2 : 5
D. 3 : 8
Answer:
Given, Area(EFGH) = 62.5% Area(ABCD)
Area(EFGH) = 
Area(ABCD)
Let EB = 1 and CG = r
Similarly, the rest other dimensions are also of lengths 1 or r units
As CG > EB
r = 3 and ratio (EB : CG)= (1:r) = (1:3)
Hence, the answer is 1 : 3
Choice A is the correct answer
CAT 2018 Quant Question: Exponents
Answer:
Hence, the answer is 
Choice D is the correct answer.
CAT 2018 Quant Question: Ratio and Proportion
Raju and Lalitha originally had marbles in the ratio 4 : 9. Then Lalitha gave some of her marbles to Raju. As a result, the ratio of the number of marbles with Raju to that with Lalitha became 5 : 6. What fraction of her original number of marbles was given by Lalitha to Raju?
Answer:
Given that original ratio is 4 : 9
Let us assume Lalitha gives ‘a’ chocolates to Raju ending up in a ratio of 5 : 6
We need to find the fraction of number of marbles given by Lalitha to the initial number of Chocolates
Choice D is the correct answer.
CAT 2018 Quant Question: Logarithms
then a + b is equal to
A. 32
B. 59
C. 67
D. 40
Answer:
a + b = 27 + 32 = 59
Hence, the answer is 59
Choice B is the correct answer.
CAT 2018 Quant Question: Work and Time
Humans and robots can both perform a job but at different efficiencies. Fifteen humans and five robots working together take thirty days to finish the job, whereas five humans and fifteen robots working together take sixty days to finish it. How many days will fifteen humans working together (without any robot) take to finish it?
A. 40
B. 32
C. 36
D. 45
Answer:
Let a Human complete ‘H’ units of work per day and a Robot complete ‘R’ units of work per day
Given,
No of days required for 15 humans to complete the work = 32 days
Hence, the answer is 32 days
Choice B is the correct answer.
CAT 2018 Quant Question: Mensuration
In a parallelogram ABCD of area 72 sq cm, the sides CD and AD have lengths 9 cm and 16 cm, respectively. Let P be a point on CD such that AP is perpendicular to CD. Then the area, in sq cm, of triangle APD is
A. 18√3
B. 24√3
C. 32√3
D. 12√3
