# TCS Arrangements and Series Questions

1. If all the numbers between 11 and 100 are written on a piece of paper. How many times will the number 4 be used?
a.19
b.21
c.34
d.22
Explaination: We have to consider the number of 4’s in two digit numbers. _ _
If we fix 4 in the 10th place, unit place be filled with 10 ways.  If we fix 4 in units place, 10th place be filled with 9 ways (0 is not allowed)
So total 19 ways.
Alternatively:
There are total 9 4’s in 14, 24, 34…,94
& total 10 4’s in 40,41,42….49
thus, 9+10=19.

2. 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4……
In the above sequence what is the number of the position 2888 of the sequence.
a) 1
b) 4
c) 3
d) 2
Explaination: First if we count 1223334444. they are 10
In the next term they are 20
Next they are 30 and so on
So Using n(n+1)2×10 ≤ 2888
For n = 23 we get LHS as 2760.  Remaining terms 128.
Now in the 24th term, we have 24 1’s, and next 48 terms are 2’s.  So next 72 terms are 3’s.The 2888 term will be “3”.

3.Series 1, 4, 2, 8, 6, 24, 22, 88 ?
a.43
b.86
c.65
d.73
Explaination:  The given series is in the format: x 4, -2, x4, -2, x4, -2, x4….
1×4 = 4
4-2=2
8-2=6
6×4=24
24-2=22
22×4=88
88-2=86

4.How many 4-digit numbers contain no.2?
a.3168
b.5832
c.3245
d.3424
Explaination: Total number of four digit numbers =9000 (i.e 1000 to 9999 )
We try to find  the number of numbers not having digit 2 in them.
Now consider the units place it can be selected in 9 ways (i.e 0,1,3,4,5,6,7,8,9)
Tens place it can be selected in 9 ways (i.e 0,1,3,4,5,6,7,8,9)
Hundreds place it can be selected in 9 ways (i.e 0,1,3,4,5,6,7,8,9)
Thousands place can be selected in 8 ways (i.e 1,3,4,5,6,7,8,9) here ‘0’ cannot be taken
Total number of numbers not having digit 2 in it =9 x 9  x 9 x 8 =5832
Total number of numbers having digit 2 in it = 9000-5832 =3168

5.Cara, a blue whale participated in a weight loss program at the biggest office. At the end of every month, the decrease in weight from original weight was measured and noted as 1, 2, 6, 21, 86, 445, 2676. While Cara made a steadfast effort, the weighing machine showed an erroneous weight once. What was that.
a) 2676
b) 2
c) 445
d) 86
Explaination: This is a number series problem nothing to do with the data given.
1x 1+1=2
2 x 2+2=6
6 x 3+3=21
21 x 4+4=88 and not 86
88 x 5+5 = 445
445*6+6 = 2676

6. Find the missing in the series:  70, 54, 45, 41,____.
a.38
b.40
c.39
d.37
Explaination: 70-54 = 16 = 4242
54-45 = 9 = 3232
45-41 = 4 = 2222
41-40 = 1 = 1212

7.A farmer has a rose garden. Every day he picks either 7,6,24 or 23 roses. When he plucks these number of flowers the next day 37,36,9 or 18 new flowers bloom. On Monday he counts 189 roses. If he continues on his plan each day, after some days what can be the number of roses left behind? (Hint : Consider number of roses remaining every day)
a)7
b)4
c)30
d)37
Explaination:let us consider the case of 23. when he picks up 23 roses the next day there will be 18 new, so in this case., 5 flowers will be less every day. So when he counts 189, the next day 184, 179,174,169,…………….
finally the no. of roses left behind will be 4.

8.In how many different ways can the letters of the word “LEADING” be arranged in such a way that the vowels always come together.
a. 360
b. 720
c. 480
d. 5040
Explaination:Given letters are A, E, I, D, L, N, G
Of which AEI are vowels. Let us combine them into a single letter x.  Now total letters are x, D, L, N, G
These letter are arranged in 5! ways.  But 3 vowels can arrange themselves in 3! ways.  So total ways 5! x 3! = 720

9.What will be in the next series 1, 7, 8, 49, 56, 57, 343, …
a.324
b.344
c.315
d.564
Explaination: 1 = 1
7 = 1 x 7
8 = 1 x 7 + 1
49 = 7 x 7 + 1
50 = 7 x 7 + 1
56 = 8 x 7
57 = 8 x 7 + 1
343 = 49 x 7
Next term should be 49 x 7 + 1 = 344

10.Find the option to replace the question mark in the series below
5 ? 15 75 525 4725
a.10
b.5
c.9
d.12