Discussion Room : Quant

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?

@aadirs 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...

is it 14 ?

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


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√3What is the OA ?

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 :)

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

x/x is 1 when x > 0
x/x is 1 when x < 0x/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 < 0.3So every x which satisfies x/x < x should have x > 1
Is OA B ?


@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  2yx^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(14436)=6sqrt 3.
Now cant proceed further...................

Shyama and Ramesh walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Ramesh’s steps. Shyama gets to the top of the escalator after having taken 25 steps, while Ramesh (because his slower pace lets the escalator do a little more of the work) takes only 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?

Speed of escalator = x steps/sec
Speed of Shyama = (3 + x) steps/sec
Speed of Ramesh = (2 + x) steps/sec
Time taken by Shyama = 25/3
Time taken by Ramesh = 20/2 = 10
Distance covered is same
So, (3 + x) * 25/3 = (2 + x) * 10
x = 3 steps/sec
total number of steps (distance covered) = 50
So it would take 50 steps if the escalator was off. (OA matching with this?)@PulkitSancheti instead of tackling this one question, we will finish the topic itself :)
Please go through below concept notes covering the fundas in escalator problems
https://www.mbatious.com/topic/934/problemsonescalatorsfromtimespeedanddistanceravihanda
https://www.mbatious.com/topic/506/tacklingescalatorproblemssaquibhasnain
Collection of 30 questions from escalator topic  https://www.mbatious.com/topic/933/catquestionbankescalatorstimespeeddistance
If you find any concept tough to understand, please let us know.. will discuss!
happy learning!