Good one from Time and Work!

CAT 2019 slot 2 question

Anil alone can do a job in 20 days while Sunil alone can do it in 40 days. Anil starts the job, and after 3 days, Sunil joins him. Again, after a few more days, Bimal joins them and they together finish the job. If Bimal has done 10% of the job, then in how many days was the job done?

What will be the next term?

12 33 66 132 ?

Direction (38-42): Study the following information carefully and answer the questions. Four family members P, Q, R and S are going to the different Mall viz; Wave, DLF, Ambience and Sahara (not neccesarily in the same order), for the shopping of different items on the same day viz; Saree, Jewellery, Jeans, Gown but not necessarily in the same order, at different time which are 9am, 12pm, 10am and 11am (not necessarily in the same order). S is going to just after when another member is going to WAVE, which is going just after the member who is going for the shopping of Saree. The member, who is going to SAHARA, is going at least two hours later than Q. The member, who is going to AMBIENCE, is going just after the member who is going for the shopping of Gown, who is going just after P. The definite information which was given about three among four was: R, the one who is going for the shopping of Jewellery and the one who is going at 11am.

Eight members of a committee, A, B, C, D, E, F, G and H are sitting around a circular table facing away from the centre. Each member has a different zodiac sign, viz Leo, Virgo, Libra, Cancer, Aries, Gemini, Pisces and Scorpio, but not necessarily in the same order. G is third to the right of C. The one whose sun-sign Leo is second to the left of the one whose sun-sign is Libra.

H's sun-sign is Libra and is sitting exactly between C and A. The one whose sun-sign is Pisces sits second to the right of B. The one whose sun-sign is Aries is second to the right of the person whose sun-sign is Gemini. C sits third to the left of the person whose sun-sign is Virgo. Neither F nor A is the immediate neighbour of B. F is fourth to the left of A. B's sun-sign is neither Cancer nor Ariel. The person whose sun-sign is Leo is sitting second to the right of the person whose sign is Cancer. D’s sun-sign is Leo and is not an immediate neighbor of B.

For detailed explaination and solution Plz see :-

https://unacademy.com/lesson/complex-circular-arrangement-problems/G4JF8H13

For Basic and High level seating arrangement questions and Floor arrangement questions along with their detailed explainations you can watch my lessons on the UnAcademy.

4 10 40 300 3430 ?

In a bag there are four types of colored balls of red, Blue, Yellow and white color. The probability of selecting one Blue ball out of total ball is 1/3 and the probability of selecting one red ball out of total ball is 1/9 .Number of yellow and white colored balls together are 10. What is the probability of selecting two yellow balls at random out of total balls, if the no. of white colored balls are 50% more than the no. of yellow colored balls (a) 1/51 (b) 2/51 (c) 1/17 (d) 2/17 (e) None of these

**Divisibilty Methods** For checking divisibility by any 'prime/odd' number except for factors of 5', you have the concept of base number.

Number Add Base Number Subtract Base Number

---------------------------------

3: 1 2

7: 5 2

9: 1 8

11: 10 1

13: 4 9

17: 12 5

19: 2 17

21: 19 2

23: 7 ?

27: ? 8

29: 3 ?

...

...

And so on....(i'll describe a method to get these below)

Now for checking divisibility either add the last digit*add base number to the number "formed by removing last digit" or you can subract last digit*subtract base number from the "formed by removing last digit"

for e.g. check for 51/17 either 5- 1*5 =0 or 5 + 1*12 =17 hence divisible.

to check 312/13 we can 31+2*4 =39 hence dvisible or we can 31-2*9 = 13 ence divisible.

to check 61731/19 = 6173 + 1*2 = 6175 = 617 + 5*2 = 627 = 62 + 7*2 = 76 hence divisible.

to check 357976/29 = 35797 + 6*3 = 35815 = 3581 +5*3 = 3596 = 359 + 6*3 = 377 = 37 + 7*3 = 58 hence divisible..

to check 382294/11 = 38229-4*1 =38225 = 3822-5 = 3817 = 381 - 7 = 374 = 37 -4 =33 Hence divisible..

The Subract base Number for a number can be obtained as the {(samllest multiple of number which ends in one)-1}/10

i.e. for 3 or 7 it is (21-1)/10 =2

for 13 it is 91-1/10 = 9.

The AddbaseNumber for a number can be obtained as the {(samllest multiple of number which ends in nine)+1}/10

i.e. for 13 it is (39+1)/10 =4.

for 7 it is 49+1/10 = 5

Proof:

For SubtactBaseNumber say the number abcde...

I want to check divisibility by 17 where subtractbasenumber is 5

I can always write abcde... as 10X+Y (where Y is last digit and X is number formed by removing last digit)

Now X-Y*5 = (10X -50Y)/10 = (10X + Y -51Y)/10 = (OriginalNumber - 51 Y ) / 10

The number '51 Y' is a multiple of 17 so if "OriginalNumber" is divisible by 17 then "OriginalNumber - 51*Y" got to be.. i.e. "10X - 50Y"

as 10 and 17 are co-prime if "10X- 50Y" is divisible the "X-5Y" got to be.....

same theory hold's for addbasenumbers too....

This also defines why it is so easy to check divisibility by 3 or 9 just keep on adding the digits...

And you can check divisibility by 11 just by keeping on subrating digits form previous number.. (which is same as taking sum of even/odd location separately..) **Divisibility by 7**

**Only for those interested in Number theory (Not a Cat short-cut)**

say the number is :

38,391,787

Separate into pairs of digits

38 39 17 87

Consider the difference between each pair of digits and the nearest multiple of seven, beginning for the first pair at right, lower (upper) for the first, upper (lower) for the second and so on, alternating for each new pair.

**4** -----**4** (21-17)

38 39 17 87

**---4** ------**3** (87-84)

The resulting digits, read from right are **3444** (which is also a number multiple of 7).

Proceed in the same way with 3,444

**1**

34 44

**----2**

The final pair **21** is a multiple of seven, so is the original number 38,391,787.

**ANOTHER EXAMPLE**

Look how fast this method is.

Consider the 15-digit number 531,898,839,909,822

**2 ----2--- 3 ----0**

5 31 89 88 39 90 98 22

**---3 ---4 ----6 ----1**

Now we have **10,634,232**

**4 -----0**

10 63 42 32

**----0 ----4**

And now **4,004**

**2**

40 04

**---4**

Which gives **42**, a multiple of 7.

We only need three steps for a 15-digit number. This is called TOJA's method of divisibility. Incidentally this also works for 11 and 13. Just a little manupulation is required, (in case you get a remainder of more than 9)

Let A = 5,962

**7**

59 62 77 which is a multiple of 1

**--7**

EXAMPLE 2

Let A = 5, 971,845

**6---- 4**

5 97 18 45

**--9 ----1**

**8**

**14 96 -> 88 ->divisible**

**----8**

EXAMPLE 3

Let A = 80,714,546

**8 ----10**

80 71 45 46

----**5**-------**2**

The resulting numbers ( 2 10 5 8 ) don’t form a decimal number, so proceed in this way: Put the exceeding number 1 from 10, below the 2 and sum.

**2 0 5 8 -> 3 0 5 8**

**1**

**3**

30 58 33

**---3**

https://www.facebook.com/groups/632112500304610/?ref=bookmarks

Please solve it with elaborate method (DISCUSSION on this problem will be highly appreciated).

**And if u have any systematic approach known to solve such puzzles, please share it here.**

**I find it very difficult to solve such puzzle within 10 mins.**

**Qestion:**

In an annual function of a school five students C, K, J, L and B participated in discuss throw competition.

All of them throw discus but discus was thrown by them to different distances. The distances were 27, 29, 31, 33, and 35 feet, but not necessarily in the same order as the names are. Similarly the colour of shirt of each person was different. Shirt colours were black, blue, brown, green and red.

Each person was called to throw discus one by one.

1) K and the person who was given the chance at fifth position threw the discus more than 30 feet. And neither of the two was in blue shirt.

2) J's shirt was green. He threw the discus immediately before the person who got the first rank.

3) The person in red shirt threw the discus two feet less than the person who threw the discus only after one person.

4) B was called first to throw the discus. But he did not get the last rank.

5) One who threw the discus immediately after C was in brown shirt.

6) L was not the person who threw the discus at 31 or at 35 feet.

7) The person in black shirt did not throw the discus at 33 feet.

8) The person in blue shirt did not throw the discus at 2nd or 4th position.

If each side of a cube is decreased by 19%, then decrease in surface area is

a) 40% b) 38.4% c) 35% d) 34.39%

Can anyone explain the solution to me without using any formula?

@rohitjindal69 i got it,in the top data, we have to consider data of R, the one at 11 and jewellery to be true...

@jack45