HarDeep Gautam
1 year, 5 months ago

Johan has x children by his first wife. Mary has (x+1) children by her first husband. They marry and have chil dren of their own. The whole family has 24 children. Assuming that two children of the same parents do not fight, which of the following cannot be the number of fights that can take place between the children. 1. 191 2. 173 3. 185 4. 201

CrackMBA 2015
1 year, 5 months ago

A regular octagon is inscribed in a circle of radius 1 units. The product of the distances from a fixed vertex to the other seven vertices is?

Pv Aaditya
0 Likes Posted 1 year, 5 months ago

When an n-sided polygon is inscribed in a unit circle, the product of the distance of the vertices from a fixed vertex is n.

This is easier to prove using complex numbers. If one of the vertices is at 1, then the other vertices are the nth roots of 1. The product of the diagonals will be |1-w||1-w^2|...|1-w^n|.

where w = exp(2*pi*i/n)

To prove: (1-w)(1-w^2)...(1-w^{n-1}) = n

Since (z^n - 1) = (z-1)(z^n-1 + z^n-2 +.... 1)

so, (z^n-1 + z^n-2 + ... 1) = (z-w)(z-w^2)....(z-w^n-1)

Put z = 1, so (1-w)(1-w^2)...(1-w^{n-1}) = n

So, for an octagon, the value is 8

Vikas Bansal
0 Likes Posted 1 year, 5 months ago

The answer will be 16.

Distance from the fixed vertex to its adjacent vertex will be = 1^2 + 1^2 - 2*1*1 cos45 = 2-2^(1/2) (Where 45 degree is the angle between the lines which are drawn from the centre to fixed vertex and its adjacent vertex)

Let's number the vertices clockwise starting from the fixed vertex as 1 then others will be 2,3,4,5,6,7,8.

Now distance 12 will be equal to 18 i.e. = 2-2^(1/2)

Similarly distance 13 will be equal to 17 i.e = 2^(1/2)

14 will be equal to 16 i.e. = 2+2^(1/2)

And 15 will be equal to = 2 (Diameter of the circle)

After multiplying all the distances, you will the value of product as 16

CrackMBA 2015
1 year, 5 months ago

number of non negative integral solutions for a+b+c = 71 where a>b>c

Manu Jindal
3 Likes Posted 1 year, 5 months ago

The answer is 420.

See the solution for a+b+c = 71 is 73C2 = 2628.

These 2628 solutions are non negative integral solutions from which we have to deduct the solutions having 2 equal values.

(0,0,71),(1,1,67).......(35,35,1). These are 36 solutions with each solution arranged in 3 ways. Total = 36*3 = 108

Total unequal sol = 2628-108 = 2520

Now a>b>c can occur in 1 way out of 3! ways.

Required sol = 2520/3! = 420

Swaroop Garg
1 year, 5 months ago

when we apply this formula n+r-1Cr-1

Manu Jindal
1 Likes Posted 1 year, 5 months ago

This formula is applied when we have to find the number of non negative integral solutions of the equation, This equation is represented as

x1+x2+x3....+xr = n

Where r is the number of variables and n is the sum of all these variables.

This equation can also be applied in permutations and combinations when we have tp find the number of ways of distributing n identical things into r different boxes.

Swaroop Garg
1 year, 5 months ago

what is the concept behind to find the minimum value

Manu Jindal
0 Likes Posted 1 year, 5 months ago

Hi Swaroop,

The basic concept involved in solving these questions is AM>= GM. This condition is applicable only for positive numbers. In CAT level questions, this formula is only used to solve these questions. We might have to make slight adjustments in the given question to apply this concept. One question can come from this specific topic in CAT.

Swaroop Garg
1 year, 5 months ago

what is the concept behind to find the minimum value

Manu Jindal
0 Likes Posted 1 year, 5 months ago

The basic concept involved in solving these questions is AM>= GM. This condition is applicable only for positive numbers. In CAT level questions, this formula is only used to solve these questions. We might have to make slight adjustments in the given question to apply this concept. One question can come from this specific topic in CAT.

Swaroop Garg
1 year, 5 months ago

what is the concept behind to find the minimum value

Vikas Bansal
0 Likes Posted 1 year, 5 months ago

Hi Swaroop, please make your question a little more clear about the context. What I can tell you from this question is, there are various methods and techniques which are used to find the minimum value of x in an equation, minimum requirement of an area for geometry problems and multiple endless possibilities. Please be more specific Swaroop. :)

Swaroop Garg
1 year, 5 months ago

i have been regularly score 150-160 in nmat, score 45 in english weak in vocab barely score 2-3 answers correct out of 10 and grammar i leave rcs in nmat because it take too much time and unable to solve implicit questions in logical reasoning part, i have no idea about these questions..in quant sometimes i score 90+ , 70-75 and sometimes 50 based on difficulty level.

Vikas Bansal
0 Likes Posted 1 year, 5 months ago

Hi Swaroop, From your post it seems you are facing problem in the verbal section which you have figured out after giving many mocks. I appreciate your strategy as you already have figured out where your weaknesses are, now start giving extra efforts to make them better and be assure of it that next time when you hit a mock, you won't repeat the same mistakes. Here are some links where you can improve your verbal section

Reading Comprehension: https://cracku.in/cat/verbal-and-lr/reading-comprehension/cheatsheet

Grammar and Sentence correction: https://cracku.in/cat/verbal-and-lr/grammar-sentence-correction/cheatsheet

If anything else we can do, please let us know.

Swaroop Garg
1 year, 5 months ago

In an isosceles triangle ABC with AB=AC, AD and AE trisects BC such that BD = DE = EC. IF angle DAE is equal to angle ABC and the area of triangle ABC is equal to , then find AC.

Manu Jindal
0 Likes Posted 1 year, 5 months ago

Since AB = AC

Angle B = Angle C

Let BD = DE = EC = x

BD = EC = x, AB = AC and Angle B = Angle C

Triangle ABD is congruent to triangle ACE

AD = AE

Angle ADE = Angle AED

Now Angle ADE = Angle B + Angle BAD

Angle AED = Angle DAE + Angle BAD

Angle AED = Angle BAE

AB = AC = 2x

BC = 3x

Now you know all the sides of isosceles triangle, Calculate and equate the area and find x.

CrackMBA 2015
1 year, 5 months ago

If x, y , z are three distinct positive real numbers such that x+ y+ z= 1 then the values of (1/x - 1)(1/y -1 ) (1/z - 1) is? (Answer is 8)

135 points

46 points

28 points

26 points

25 points

Answer is d. Johan and Mary have 23 - 2x kids. Maximum value of x can be 11. Maximum Number of fights = 24C2 - xC2-( x+1)C2 -( 23-2x) C2 (every 2 kids fight)

Maximum value for number of fights is 191