CAT 2018 Quant Question: Mensuration
A parallelogram ABCD has area 48 sqcm. If the length of CD is 8 cm and that of AD is s cm, then which one of the following is necessarily true?
A. s ≥ 6
B. s ≠ 6
C. 5 ≤ s ≤ 7
D. s ≤ 6
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Answer:
Given that a parallelogram ABCD has an area 48 sq cm. The length of CD is 8 cm and that of AD is s cm
Since the area given here is 48 sq.cm the height can be found as 6 sq.cm
We have to find which of the following options is necessarily true
Since this (shaded portion) is a right angled triangle with 6 as its height and s as its hypotenuse so we can assure that s ≥ 6 and s cannot be less than 6 so we can eliminate the other options.
By this we can come to the conclusion that s ≥ 6
Hence, the answer is s ≥ 6
Choice A is the correct answer.
CAT 2018 Quant Question: Sequence & Series
The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + … + 95 x 99 is
A. 80707
B. 80751
C. 80730
D. 80773
Answer:
Here we have to find the value of the sum 7 × 11 + 11 × 15 + 15 × 19 + … + 95 × 99
Since increment of 4 takes place in every value , 4n is the term to be used
From the options we can take 80707 and check whether it is divisible by 23
⟹ option a) 80707 is a multiple of 23
⟹ option b) 80751 is 80707 + 44 so this doesn’t work
⟹ option c) 80730 is 80707 + 23 so this is also a multiple of 23
⟹ option d) 80773 is 80707 + 66 so this also doesn’t work
So let us check out with option a and c so we have to substitute and simplify and find
From the answer choices we have only two possibilities left out i.e. 23 ⨯ 3509 or 23 ⨯ 3510
Hence the value of the sum 7 × 11 + 11 × 15 + 15 × 19 + … + 95 × 99 is 80707
Hence, the answer is 80707
Choice A is the correct answer.
CAT 2018 Quant Question: Speed, Time and Distance
On a long stretch of east-west road, A and B are two points such that B is 350 km west of A. One car starts from A and another from B at the same time. If they move towards each other, then they meet after 1 hour. If they both move towards east, then they meet in 7 hrs. The difference between their speeds, in km per hour, is (TITA)
Answer:
Given that A and B are two points such that B is 350 km west of A. One car starts from A and another from B at the same time.
They meet after one hour or their relative velocity is (a + b)km/hr and their relative distance is 350kms
If they both move towards east, then they meet in 7 hrs.
We have to find the difference between their speeds, in km per hour. B is catching upon A, so once again their relative distance will be 350kms.
Relative speed = b – a , B travels faster so that it can meet a.
⟹ b - a = 50 km/hr
We know that b + a = 350 km/hr
By this we can find the values of a and b but they have asked for only the difference between their speeds which is b – a = 50km/hr
Hence, the answer is 50 km/hr
CAT 2018 Quant Question: Number Theory
If the sum of squares of two numbers is 97, then which one of the following cannot be their product?
A. 64
B. -32
C. 16
D. 48
Answer:
Given that the sum of squares of two numbers is 97 i.e. 
From the given options we have to find which one cannot be their product i.e. ab
A. 64 ⟹ 2ab = 128
B. −32 ⟹ 2ab = -64
C. 16 ⟹ 2ab = 32
D. 48 ⟹ 2ab = 96
2ab is found because we know that
By this we can know that 97 + 128 works but 97 - 128 doesn’t works so we can understand option A cannot be the product and the rest can be.
So here 2ab should lie between +97 and -97 or ab should be less than 
so except option A all the other options works so option A 64 cannot be the product
Hence, the answer is 64
Choice A is the correct answer.
CAT 2018 Quant Question: Mixtures and Alligations
A jar contains a mixture of 175 ml water and 700 ml alcohol. Gopal takes out 10% of the mixture and substitutes it by water of the same amount. The process is repeated once again. The percentage of water in the mixture is now
A. 25.4
B. 20.5
C. 30.3
D. 35.2
Answer:
Given that a jar contains a mixture of 175 ml water and 700 ml alcohol.
It is given that 10% of the mixture is removed and it is substituted by water of the same amount and the process is repeated once again
Now we have to find the percentage of water in the mixture.
Since the mixture is removed and substituted with water, we can deal with alcohol and the second step we can find how much amount of alcohol is retained and not about how much amount of alcohol is removed
As 10% of alcohol is removed, 90% of alcohol is retained
So alcohol remaining = 700 × 90% × 90%
⟹ 700 × 0.9 × 0.9 = 567
We totally have 875 ml overall mixture and of this 567 ml is alcohol.
Remaining 875 – 567 = 308 is the amount of water.
We have to find the percentage of water in the mixture i.e. 
Approximately 308 is 30% of 1000 so by this we know that 308 is more than 30%
Hence 35.2% is the percentage of water in the given mixture.
Hence, the answer is 35.2%
Choice D is the correct answer.
CAT 2018 Quant Question: Speed, Time and Distance
Points A and B are 150 km apart. Cars 1 and 2 travel from A to B, but car 2 starts from A when car 1 is already 20 km away from A. Each car travels at a speed of 100 kmph for the first 50 km, at 50 kmph for the next 50 km, and at 25 kmph for the last 50 km. The distance, in km, between car 2 and B when car 1 reaches B is (TITA)
Answer:
Given that points A and B are 150 km apart.
Cars 1 and 2 travel from A to B, but car 2 starts from A when car 1 is already 20 km away from A.
Each car travels at a speed of 100 kmph for the first 50 km, at 50 kmph for the next 50 km, and at 25 kmph for the last 50 km.
The Car 1 is 20km away from A and it travels at 100kmph and the time taken is 
So car 2 is 12 minutes behind car 1.
We have to find the distance in km, between car 2 and B when car 1 reaches B.
The distance, in km, between car 2 and B when car 1 reaches B is 5 kms.
Hence, the answer is 5 kms
CAT 2018 Quant Question: Pipes & Cisterns
A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank is full. On Monday, A alone completed filling the tank at 8 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along?
A. 4 : 12 PM
B. 4 : 24 PM
C. 4 : 48 PM
D. 4 : 36 PM
Answer:
Given that a tank is emptied everyday at a fixed time point and after that either pump A or B or both start working to fill the tank.
On Monday, A alone completed filling the tank at 8 pm.
On Tuesday, B alone completed filling the tank at 6 pm.
On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank.
We have to find at what time will the tank filled on Thursday if both were used simultaneously all along
A is doing 3 hours less work on Wednesday which B completes in 2 hours therefore B = 1.5 A
Starting from 2 pm, they fill the entire tank by 4:24 pm
Here the break through is figuring out the ratio or efficiency of the rate at which they fill is B : A = 3 : 2
The conventional way is
Solving this we get n = 6 and we can find solution using this n.
Hence, the answer is 4 : 24 PM
Choice B is the correct answer.
CAT 2018 Quant Question: Work & Time
Ramesh and Ganesh can together complete a work in 16 days. After seven days of working together, Ramesh got sick and his efficiency fell by 30%. As a result, they completed the work in 17 days instead of 16 days. If Ganesh had worked alone after Ramesh got sick, in how many days would he have completed the remaining work?
A. 12
B. 14.5
C. 13.5
D. 11
Answer:
Given that Ramesh and Ganesh can together complete a work in 16 days
After seven days of working together, Ramesh got sick and his efficiency fell by 30%.
To the original schedule of 16 days there are 9 more days and in this 9 days Ramesh fall short by 9 × 0.3x = 2.7x where x is the work done by Ramesh in a day
So the change = 2.7x (i.e. the gap because of drop in efficiency)
This 2.7x is compensated by one day of Ganesh + another 0.7 of Ramesh
2.7x = G + 0.7 x (Because the last day also he works with reduced efficiency)
2x = G
Hence Ganesh works twice as that of Ramesh.
If Ganesh had worked alone after Ramesh got sick means in the 7 days Ramesh would have completed 
of the task
Ganesh on each day can do 
of the task
Task to be completed by Ganesh is 
completely
One day he can complete 
If Ganesh had worked alone after Ramesh got sick, the no. of days needed for completing the remaining work is 20.5 – 7 = 13.5 days
Hence, the answer is 13.5
Choice C is the correct answer.
CAT 2018 Quant Question: Inequalities
If a and b are integers such that 
for all real numbers x, then the largest possible value of 2a − 6b is (TITA)
Answer:
Given that a and b are integers such that 
for all real numbers x
We have to find the largest possible value of 2a – 6b
Using the completion of squares method
Since we have to find the largest value as possible and it cannot be 4 so a = 3
Similarly b can be found in the following way
Since we have to find the largest possible value of 2a – 6b or b have to be very small so the smallest integer b can take -5
⟹ 2(3) - 6(-5)
⟹ 6 + 30 = 36
The largest possible value of 2a − 6b is 36
Hence, the answer is 36
CAT 2018 Quant Question: Ratio & Proportions
The scores of Amal and Bimal in an examination are in the ratio 11 : 14. After an appeal, their scores increase by the same amount and their new scores are in the ratio 47 : 56. The ratio of Bimal’s new score to that of his original score is
A. 3 : 2
B. 4 : 3
C. 5 : 4
D. 8 : 5
Answer:
Given that the scores of Amal and Bimal in an examination are in the ratio 11 : 14 i.e. 11x : 14x
After an appeal their scores increased by the same amount and their new scores are in the ratio 47 : 56
(11x + a) × 56 = (14x + a) × 47
616x + 56a = 658x + 47a
56a – 47a = 42x
9a = 42x
3a = 14x
Hence the ratio of Bimal’s new score to that of his original score is 4 : 3
Hence, the answer is 4 : 3
Choice B is the correct answer