Given that, the area of a regular hexagon is equal to the area of an equilateral triangle of side 12cm.
Let’s consider ‘a’ be the side of the regular hexagon.
a2 = 24
a = 2√6
Hence, the answer is 2 √6
Choice C is the correct answer.
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CAT 2021 Quant Question
Onion is sold for 5 consecutive months at the rate of Rs 10, 20, 25, 25, and 50 per kg, respectively. A family spends a fixed amount of money on onion for each of the first three months, and then spends half that amount on onion for each of the next two months. The average expense for onion, in rupees per kg, for the family over these 5 months is closest to
A. 18
B. 26
C. 16
D. 20
Answer
Given that onion is sold for 5 consecutive months at the rate of Rs 10, 20, 25, 25, and 50 per kg respectively.
Let’s consider the amount spend on onions in these five months to be 100, 100, 100, 50, 50.
Hence, the number of kgs in these five months should be 10, 5, 4, 2, 1 respectively.
The average expense on onions per kg over these five months is given by
Therefore, the closest average would be 18.
The answer is ‘18’
Choice A is the correct answer.
CAT 2021 Quant Question
Amal purchases some pens at ₹ 8 each. To sell these, he hires an employee at a fixed wage. He sells 100 of these pens at ₹ 12 each. If the remaining pens are sold at ₹ 11 each, then he makes a net profit of ₹ 300, while he makes a net loss of ₹ 300 if the remaining pens are sold at ₹ 9 each. The wage of the employee, in INR, is
Answer:
Let’s consider the total number of pens to be
(100 +x)
Let’s consider the fixed-wage of the labour to be ‘w’
case (i): the net profit is 300
CP = 8(100 +x) + w
SP = 12 x 100 + 11 x = 1200 + 11x
Profit = SP - CP
300 = 1200 + 11x - 8(100 +x) - w
w - 3x = 100 → eq(1)
Case (ii): the net loss is 300
CP = 8(100 +x) + w
SP = 12 x 100 + 9 x = 1200 + 9x
Loss = CP - SP
300 = 8(100 +x) + w - 1200 - 9x
w - x = 700 → eq(2)
By solving equation (1) & (2) we get w = 1000.
Therefore, the wage of the employee is 1000.
Alternate solution:
We can also do this with a little intuition. The Rs 2 decrease per pen results in 300 loss from the case of 300 profit.
The net value of 600 resulted by selling the remaining pens at Rs 2 lesser.
If the number of remaining pens is x, then 2x = 600
So, x = 300.
Total pens = 100 + 300 = 400.
We can get the wage of an employee(w) by considering profit/loss
Profit = 300
100(12) + 300(11) - 400(8) -w = 300
w = 1000
The answer is '1000’
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CAT 2021 Quant Question
If r is a constant such that 
has exactly three distinct real roots, then the value of r is
A. 15
B. 18
C. 17
D. 21
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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.
From these 63, we need to remove the subsets which have {3, 5, 7, 8}
{3, 5, 7, 8, 1, 2, 4, 6} except 3, 5, 7, 8 remaining all numbers {1, 2, 4, 6} have two possible outcomes that either it is in the set or out of the set.
Therefore, the answer would be 63 - 16 = 47.
Hence, the answer is 47
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.