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
Answer:
Given Area (ABCD) = 72 sq cm, CD = 9cms, AD = 16cms
Area of Parallelogram = Base × Height
CD × 16 = 72
CD = 
cms
We extend CD till P such that ∠APD = 90°
So, again by applying the area formula considering CD as base
CD × AP = Area of Parallelogram ABCD
9 × AP = 72
AP = 8 cms
We have AP = 8 cms, AD = 16 cms We observe that the ratio of the sides form a 1 : √3 : 2 triangle Therefore DP = 8√3 cms Area (△APD) = 1/2 × AD × DP = 1/2 × 8 × 8√3 sq cms Area (△APD) = 32 √3 sq cms
Hence, the answer is 32√3 sq cms
Choice C is the correct answer.
CAT 2018 Quant Question: Geometry
In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is
A. √13
B. √14
C. √11
D. √12
Let set A be a set having first 50 perfect squares and set B be a set having Square of first 20 positive prime numbers which have three factors. Then sum of all elements in set (B - A) is
Answer:
Given that Chords lie on the same side of diameter with lengths 4 cms and 6 cms
Draw a perpendicular from the origin to both the chords and mark the points of intersection as P and Q respectively
Consider radius of circle as ‘r’ and distance OP as ‘x’
Draw lines from origin to the end of the chord and mark the points as D and B respectively
Thus, △OQB and △OPD form a right Triangle
Applying Pythagoras Theorem on both triangles,
We find that there is an increase and decrease by 1 in both equations
r = √13 cms
Hence, the answer is √13 cms
Choice A is the correct answer.
CAT 2018 Quant Question: Pipes & Cisterns
A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hours when 5 filling and 6 draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on? [TITA]
Answer:
Given, Tank gets filled in 6 hours when 6 filling and 5 draining pipes are on
Let, F be the rate at which a single filling pipe fills the tanks and D be the rate at which a single draining pipe drains the pipe
Also, Tank gets filled in 60 hours when 5 filling and 6 draining pipes are on
Solving both (1) and (2) we get,
44F = 55D
F:D = 5:4
15D – 10D = 1/3
D = 1/15 and F = 1/12
When two filling pipes and one draining pipes are on,
Therefore, they can fill the tank in 10 hours
Hence, the answer is 10 hours
CAT 2018 Quant Question: Set Theory
If among 200 students, 105 like pizza and 134 like burger, then the number of students who like only burger can possibly be
A. 26
B. 23
C. 96
D. 93
