CAT 2021 Quant Question
Anil invests some money at a fixed rate of interest, compounded annually. If the interests accrued during the second and third year are ₹ 806.25 and ₹ 866.72, respectively, the interest accrued, in INR, during the fourth year is nearest to
A. 931.72
B. 926.84
C. 929.48
D. 934.65
Answer
The answer is 931.72
Choice A is the correct answer.
The strength of an indigo solution in percentage is equal to the amount of indigo in grams per 100 cc of water. Two 800 cc bottles are filled with indigo solutions of strengths 33% and 17%, respectively. A part of the solution from the first bottle is thrown away and replaced by an equal volume of the solution from the second bottle. If the strength of the indigo solution in the first bottle has now changed to 21% then the volume, in cc, of the solution left in the second bottle is.
Answer:
Given that, there are two 800cc bottles of indigo solution with strengths of 33% and 17% respectively.
Some amount of the solution from bottle 1 is replaced by the same amount of solution from bottle 2.
In 800cc of a new solution of strength 21% has two solutions in the ratio 1:3.
200cc of 33% solution and 600cc of 17% solution combined to give 21% solution of indigo
Hence, the remaining solution in the bottle 2 is 200cc.
The answer is ‘200’
CAT 2021 Quant Question
Amar, Akbar and Anthony are working on a project. Working together Amar and Akbar can complete the project in 1 year, Akbar and Anthony can complete in 16 months, Anthony and Amar can complete in 2 years. If the person who is neither the fastest nor the slowest works alone, the time in months he will take to complete the project is.
Answer
Let’s consider the efficiencies of Amar, Akbar, and Anthony to be x, y, z respectively.
Hence, x is neither the fastest nor the slowest.
Amar can complete the project in 32 months.
The answer is ‘32’
CAT 2021 Quant Question
The number of groups of three or more distinct numbers that can be chosen from 1, 2, 3, 4, 5, 6, 7 and 8 so that the groups always include 3 and 5, while 7 and 8 are never included together is
Answer
Given that the numbers 3 and 5 should be present in every subset and contain at least 3 numbers in it.
First, we need to find the subsets possible
{3, 5, 1, 2, 4, 6, 7, 8} except 3 and 5, remaining all numbers have two possible outcomes that either it is in the set or out of the set.
CAT 2021 Quant Question:
A circle of diameter 8 inches is inscribed in a triangle ABC where ∠ABC = 90°. If BC = 10 inches then the area of the triangle in square inches is
Answer
From, Pythagoras theorem
We will get x = 20.
= 120 sq inches
Hence, the answer is 120
CAT 2021 Quant Question:
Suppose the length of each side of a regular hexagon ABCDEF is 2 cm. It T is the mid point of CD, then the length of AT, in cm, is
A. √15
B. √13
C. √12
D. √14
Answer:
In a regular hexagon, each internal angle is equal to 120°.
From isosceles triangle ABC, we know the length of two sides and including angle.
We will be able to find the third side (AC) using the Pythagoras theorem or the sine rule.
Hence, AC = 2√3cm
Given that, T is the midpoint.
So, CT = 1cm.
From the right-angled △ ACT,
Hence, the answer is '√13’
Choice B is the correct answer.
CAT 2021 Quant Question:
Suppose hospital A admitted 21 less Covid infected patients than hospital B, and all eventually recovered. The sum of recovery days for patients in hospitals A and B were 200 and 152, respectively. If the average recovery days for patients admitted in hospital A was 3 more than the average in hospital B then the number admitted in hospital A was
Answer:
Let’s consider the number of patients admitted in hospital A and hospital B to be ‘x’ and ‘x + 21’
Given that, the sum of recovery days for patients in hospitals A and B were 200 and 152, respectively.
The average recovery days for patients admitted in hospital A was 3 more than the average in-hospital B.
By solving the above equation we get x = 35.
Hence, the number of patients admitted to hospital A is 35.
The answer is '35’
CAT 2021 Quant Question
The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days. The amount Sita and Neeta together earn in a day equals what Geeta alone earns in 2 days. The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is
A. 7 : 3
B. 11 : 3
C. 11 : 7
D. 3 : 2
Answer
Let’s consider the one-day earnings of Neeta, Geeta, Sita to be n, g, s respectively.
The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days
n + g = 6(s) → eq(1)
The amount Sita and Neeta together earn in a day equals what Geeta alone earns in 2 days
s + n = 2(g) → eq(2)
By solving eq (1) & (2) you will get the ratio n : g : s = 11 : 7 : 3
The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is 11:3
The answer is 11 : 3
Choice B is the correct answer.
CAT 2021 Quant Question
The natural numbers are divided into groups as (1), (2, 3, 4), (5, 6, 7, 8, 9), …… and so on. Then, the sum of the numbers in the 15th group is equal to
A. 6119
B. 7471
C. 4941
D. 6090
Answer
The natural numbers are divided into groups as (1), (2, 3, 4), (5, 6, 7, 8, 9), …… and so on.
Choice A is the correct answer.
2a+4o+6m=1a+4o+8m=8o+7m
1a=2m
1a+4o+8m=10m+4o
10m+4o=8o+7m
4o=3m
1a+4o+8m=2m+3m+8m=13m
CAT 2021 Quant Question
Anu, Vinu and Manu can complete a work alone in 15 days, 12 days and 20 days, respectively. Vinu works everyday. Anu works only on alternate days starting from the first day while Manu works only on alternate days starting from the second day. Then, the number of days needed to complete the work is
A. 8
B. 6
C. 5
D. 7
