Discussion Room : Quant

• 3 individuals john wright, greg chappell and gary kristen are in the race for the appointment of new
coach of team india. The probabilities of their appointment are 0.5, 0.3 and 0.2 respectively. If john
wright is appointed then probability of ganguly appointed as a captain will be 0.7 and corresponding
probability if greg chappell or gary kristen is appointed are 0.6 and 0.5 respectively. find the overall
probability that ganguly will appointed as a captain

• @rahul-jodavula
In general,
If you have OR, ADD the probabilities.
If you have AND, multiply the probabilities.

Here, Ganguly can be the captain in the following manner
(John AND Ganguly) OR (Greg AND Ganguly) OR (Gary AND Ganguly)
(0.5 * 0.7) + (0.3 * 0.6) + (0.2 * 0.5) = 0.63 should be our answer.
What's the OA ?

• @zabeer zabeer sir ek profit loss ka doubt hai i cant calculate the initial and final amount plz help..

A reduction of 20% in the price of sugar enables a housewife to purchase 6 kg more for Rs. 240. What is the original price per kg of sugar?

• @vinaycat2017
Let original price be x per kg
So initially, we could buy 240/x kg for 240 rupees
Now the new price is 0.8 x (20% reduction in x)
So now we can buy 240/0.8x kg for 240 rupees
The difference, 240/0.8x - 240/x = 6 kg (given)
240/x (1.25 - 1) = 6
x = 240 * 0.25/6 = 40 * 0.25 = 10 rs / kg would be the original price.

• Find number of whole number solutions of a + b + c + d = 20 where a, b, c and d ≤ 8

= 23c3 - 4 * 14c3 + 4c2 * 5c3
= 1771 - 1456 + 60
= 375

why 60 is as added here, if we go by the common way for odthis instead of coefficient method:

(9+a')+(b+c+d) =20
a'+b+c+d=11

so total ways= 23C3- 4*14c3.=315
which 60 cases need to be added here?
Could anyone expalin the part?

• Question : A does half as much work as B in 3/4th of the time. Together they take 18 days to complete the work. How much time shall B take to do it?

Did it as follows.
Assumed B takes 12 days to to do 12 work. (Rate 1w/day)
So, A does 6 work(half as much as B) in 9 days (3/4th of the time taken by B to do the same) so the rate is 6/9 = 2/3 work per day)
Given they take 18 days to complete the work. One day they do (1+2/3) = 5/3 work, in 18 days they do 30 work.
Hence B shall take 30 days to do 30 work since the rate of B is 1w/ day.

But the answer given is 45 days.
Is there any logic fail in the method I used?

• In how many ways 8 friends be arranged in a row if three of the friends do not want to sit at the
extremes?

pls explain?

• @aadi-rs 30 days is correct I guess.

1/a + 1/b = 1/18
we know, a = 3b/2 (half the work in 3/4th time means full work in 1.5 times the time taken by b)
2/3b + 1/b = 1/18
5/3b = 1/18
b = 18 * 5/3 = 30

• @zabeer
SIr • Sir one more...  • @vinaycat2017

is it 14 ?

• 4 dice are rolled, what is the probability that sum of numbers on 4 dice is 18?

• @zabeer • @vinaycat2017

For a regular hexagon, Diagonal = 2L and W = √3 L

So in our diagram, BC = xz = 12
Bx = Cz = 6√3
Shaded area = Area of Rectangle (BxzC) - Area of Right Triangle Czy
= 12 * 6√3 - 1/2 * 6 * 6√3
= 72√3 - 18√3
= 54√3

What is the OA ?

• @tanu21

a + b + c + d = 18
Number of ways = (n - 1) C (k - 1) = 18C3 = 816 (If a, b, c and d can be any natural number)
But in our case a, b, c and d can only be natural numbers less than 6.
So cases like 12 + 2 + 2 + 2 = 18 should be removed.
Say a = A + 6 (To find cases where a is > 6)
A + 6 + b + c + d = 18
A + b + c + d = 12
Number of ways = 11C3 = 165
similarly for b, c and d.
So we have 816 - 4 * 165 = 156 favourable cases.

What's the OA ? Not sure about the calculations.. logic should be as explained.

This concept and various question types are explained in detailed in the below link - Please have a look, you won't have any issues with similar questions :)

Finding Number of Positive & Non-Negative Integral Solutions For a + b + c + ... = N & Its Applications

• x/|x| < x . Which of the following must be true about x ?
a. x > 1
b. x > -1
c. |x| < 1
d. |x| = 1
e. |x|^2 > 1

• @supriya-shinde

x/|x| is 1 when x > 0
x/|x| is -1 when x < 0

x/|x| < x is not possible when x > 0
now if 0 > x > -1 then x/|x| < x
example, take x = -0.3, -0.3/|-0.3| = -1 < -0.3

So every x which satisfies x/|x| < x should have x > -1

Is OA B ?

• @zabeer • @vinaycat2017 please share the steps so that we can continue from the point you got stuck. will benefit you better this way :) Let side of regular octagon be a.

AB = a + 2x and BC = a + 2y
a + 2x = 22
a + 2y = 26
22 - 2x = 26 - 2y
2x = 2y - 4
x = y - 2
a = 26 - 2y

x^2 + y^2 = a^2
(y - 2)^2 + y^2 = (26 - 2y)^2
solve for y and substitute to get a.

• @zabeer Sir , Let centre of Triangle PQR be 'O'. Considering triangle ORF OR=Sqrt(144-36)=6sqrt 3.
Now cant proceed further...................

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