BANK & INSURANCE (NEW PATTERN SERIES)

Total Questions: 50

31. A series is given below. Read the given information carefully and answer the related question.

Series: 132, 68, 36, ___, 6(r - q), (p - q), (q + 2)
Equation I: a² - (p - 1)a + 3r = 0
Equation II: b² - 3qb + (2r - 1) = 0

What is the difference between the larger root of equation I and smaller root of equation II?

Correct Answer: (b) 8
Solution:

Logic for the given series:

132 − 64 = 68
68 − 32 = 36
36 − 16 = 20
20 − 8 = 12 = 6(r − q) => r = q + 2
12 − 4 = 8 = (p − q) => p = q + 8
8 − 2 = 6 = (q + 2) => q = 4

Then, r = 4 + 2 = 6
p = 4 + 8 = 12

Now, Equation I:
a² − (p − 1)a + 3r = 0
a² − (12 − 1)a + 3 × 6 = 0
a² − 11a + 18 = 0
a² − 9a − 2a + 18 = 0
(a − 9)(a − 2) = 0
a = 9, 2

Equation II:
b² − 3qb + (2r − 1) = 0
b² − 3 × 4 × b + (2 × 6 − 1) = 0
b² − 12b + 11 = 0
(b − 11)(b − 1) = 0
b = 11, 1

Larger root of equation I = 9
Smaller root of equation II = 1

Therefore, difference = 9 − 1 = 8

32. Directions (32-33): Study the data carefully and answer the following questions:

Series I: 190, 191, 255, 498, P, 879, 915
Series II: 44, 48, 75, 91, Q, 252
Series III: 919, 922, 932, R, 1027, 1154

32. What is the unit digit of [5^P + 2^Q + 6^R]?

Correct Answer: (b) 7
Solution:

Series I: 190, 191, 255, 498, P, 879, 915

190 + 1⁷ = 191
191 + 2⁶ = 255
255 + 3⁵ = 498
498 + 4⁴ = 754 = P
754 + 5³ = 879
879 + 6² = 915

Series II: 44, 48, 75, 91, Q, 252

44 + 2² = 48
48 + 3³ = 75
75 + 4² = 91
91 + 5³ = 216 = Q
216 + 6² = 252

Series III: 919, 922, 932, R, 1027, 1154

919 + 1³ + 2 = 922
922 + 2³ + 2 = 932
932 + 3³ + 2 = 961 = R
961 + 4³ + 2 = 1027
1027 + 5³ + 2 = 1154

Unit digit of [5ᴾ + 2ᑫ + 6ᴿ] = [5⁷⁵⁴ + 2²¹⁶ + 6⁹⁶¹]
= 5 + 6 + 6 = 17 = 7

33. What is the value of [P/29 + ³√Q - √R]?

Correct Answer: (a) 1
Solution:

Series I: 190, 191, 255, 498, P, 879, 915

190 + 1⁷ = 191
191 + 2⁶ = 255
255 + 3⁵ = 498
498 + 4⁴ = 754 = P
754 + 5³ = 879
879 + 6² = 915

Series II: 44, 48, 75, 91, Q, 252

44 + 2² = 48
48 + 3³ = 75
75 + 4² = 91
91 + 5³ = 216 = Q
216 + 6² = 252

Series III: 919, 922, 932, R, 1027, 1154

919 + 1³ + 2 = 922
922 + 2³ + 2 = 932
932 + 3³ + 2 = 961 = R
961 + 4³ + 2 = 1027
1027 + 5³ + 2 = 1154

Value of [P/29 + ³√Q − √R]
= [754/29 + ³√216 − √961]
= 26 + 6 − 31 = 1

34. Directions (34-36): Read the following information carefully and answer the related questions.

Three series I, II and III are given below and in each of them one term is wrong.

Series I: 317, 294, 248, 179, 109, -28
Series II: 89, 92.5, 99.5, 110, 120, 141.5
Series III: 19, 28, 46, 114, 316, 1396

34. If P, Q and R are wrong terms in series I, II and III respectively while S, T and U are correct terms that will replace P, Q and R respectively,
then which of the following combinations is correct?

Correct Answer: (a) P > S, Q U
Solution:

Logic for series I:
317 − 23 × 1 = 294
294 − 23 × 2 = 248
248 − 23 × 3 = 179
179 − 23 × 4 = 87
87 − 23 × 5 = −28

So, wrong term = 109

Logic for series II:
89 + 3.5 × 1 = 92.5
92.5 + 3.5 × 2 = 99.5
99.5 + 3.5 × 3 = 110
100 + 3.5 × 4 = 124
124 + 3.5 × 5 = 141.5

So, wrong term = 120

Logic for series III:

19  →  28  →  46 →  100   →  316   →   1396
     +9       +18     +54       +216      +1080
           ×2       ×3         ×4          ×5

So, wrong term = 114

Here, P = 109, Q = 120, R = 114
And S = 87, T = 124, U = 100

Therefore, P > S, Q < T, R > U

35. If Y is the difference between wrong terms of series I and II while Z is the difference between the wrong terms of series II and III, then which of the following equation(s) is/are correct?

(i) 3Y - 4Z = 9
(ii) 2Y - Z = 12
(iii) Y - 2Z = -1

Correct Answer: (d) Only (i) and (iii)
Solution:

Logic for series I:
317 − 23 × 1 = 294
294 − 23 × 2 = 248
248 − 23 × 3 = 179
179 − 23 × 4 = 87
87 − 23 × 5 = −28

So, wrong term = 109

Logic for series II:
89 + 3.5 × 1 = 92.5
92.5 + 3.5 × 2 = 99.5
99.5 + 3.5 × 3 = 110
100 + 3.5 × 4 = 124
124 + 3.5 × 5 = 141.5

So, wrong term = 120

Logic for series III:

19   →   28   →   46   →   100   →   316   →   1396
      +9        +18        +54         +216       +1080
            ×2          ×3            ×4            ×5

So, wrong term = 114

Here, Y = difference between wrong terms of series I and II
= 120 − 109 = 11

And Z = difference between wrong terms of series II and III
= 120 − 114 = 6

Now, 3Y − 4Z = 3 × 11 − 4 × 6 = 9
2Y − Z = 2 × 11 − 6 = 16 ≠ 12
Y − 2Z = 11 − 2 × 6 = −1

Hence, only (i) and (iii) are correct

36. If the series IV given below follows the same pattern as followed by series I, then calculate its 5th term.

Series IV: 5p - 6, 251, 8q + 5, ...

Correct Answer: (c) p - q + 13
Solution:

Logic for series I:
317 − 23 × 1 = 294
294 − 23 × 2 = 248
248 − 23 × 3 = 179
179 − 23 × 4 = 87
87 − 23 × 5 = −28

So, wrong term = 109

Logic for series II:
89 + 3.5 × 1 = 92.5
92.5 + 3.5 × 2 = 99.5
99.5 + 3.5 × 3 = 110
100 + 3.5 × 4 = 124
124 + 3.5 × 5 = 141.5

So, wrong term = 120

Logic for series III:

19   →   28   →   46   →   100   →   316   →   1396
      +9       +18         +54        +216        +1080
            ×2         ×3           ×4           ×5

So, wrong term = 114

Series IV follows the same pattern as followed by series I.
So, in series IV:

1st term: 5p − 6

2nd term: (5p − 6) − 23 × 1 = 251
5p − 29 = 251
5p = 280
p = 56

3rd term: 251 − 23 × 2 = 8q + 5
251 − 46 = 8q + 5
8q = 200
q = 25

4th term: (8q + 5) − 23 × 3 = 8q − 64 = 8 × 25 − 64 = 136

5th term: 136 − 23 × 4 = 44

Now, p − 10 = 56 − 10 = 46
q + 20 = 25 + 20 = 45
p − q + 13 = 56 − 25 + 13 = 44
3q − p = 3 × 25 − 56 = 19

Hence, 5th term of series IV = 44 = p − q + 13

37. Given below is the sequence of series. Analyse the pattern of the series and answer the given following questions.

25, 60, 115, 190, ..., 1060.

If 400 is the nth term, then what is the value of n?

Correct Answer: (a) 6
Solution:

The logic in the given series is:

10 × 0.5 + 20 = 25
20 × 1.5 + 30 = 60
30 × 2.5 + 40 = 115
40 × 3.5 + 50 = 190
50 × 4.5 + 60 = 285
60 × 5.5 + 70 = 400
70 × 6.5 + 80 = 535
80 × 7.5 + 90 = 690
90 × 8.5 + 100 = 865
100 × 9.5 + 110 = 1060

38. Directions (38-39): A set of 2 number series is given below. Both series follow a similar pattern. Answer the questions based on it using information given below.

6120, 3060, 1224, 612, p, q, ... (1)
r, s, 960, 480, t, 96, ... (2)

What is the difference between q and t?

Correct Answer: (b) 69.6
Solution:

Logic for the series 1):
1st term = 6120
2nd term = 6120 × 0.5 = 3060
3rd term = 3060 × 0.4 = 1224
4th term = 1224 × 0.5 = 612
5th term = p = 612 × 0.4 = 244.8
6th term = q = 244.8 × 0.5 = 122.4

Similarly, in series 2) 3rd term = 960
2nd term = s = 960/0.4 = 2400
1st term = r = 2400/0.5 = 4800
4th term = 960 × 0.5 = 480
5th term = t = 480 × 0.4 = 192
6th term = 192 × 0.5 = 96

q = 122.4, t = 192
Therefore, difference = 192 − 122.4 = 69.6

39. Find the value of ps - qr.

Correct Answer: (c) 0
Solution:

Logic for the series 1) 1st term = 6120
2nd term = 6120 × 0.5 = 3060
3rd term = 3060 × 0.4 = 1224
4th term = 1224 × 0.5 = 612
5th term = p = 612 × 0.4 = 244.8
6th term = q = 244.8 × 0.5 = 122.4

Similarly, in series 2) 3rd term = 960
2nd term = s = 960/0.4 = 2400
1st term = r = 2400/0.5 = 4800
4th term = 960 × 0.5 = 480
5th term = t = 480 × 0.4 = 192
6th term = 192 × 0.5 = 96

p = 244.8, q = 122.4, r = 4800, s = 2400

Therefore, ps − qr = 244.8 × 2400 − 122.4 × 4800
= 2 × 122.4 × 2400 − 122.4 × 2 × 2400 = 0

40. Directions (40-41): Read the data carefully and answer the following questions.

Three series I, II and III are given below with one missing term in each series represented as P, Q and R.

Series I: 8, P, 36, 216, 2592
Series II: 369, 306, 261, 234, Q
Series III: 162, 54, 27, R, 4.5, 1.5

40. Find the average of P, Q and R.

Correct Answer: (a) 82
Solution:

Logic in series I:
8 × 1.5 = 12
12 × 3 = 36
36 × 6 = 216
216 × 12 = 2592

So, missing term in series I = P = 12

Logic in series II:
369 − 63 = 306
306 − 45 = 261
261 − 27 = 234
234 − 9 = 225

So, missing term in series II = Q = 225

Logic in series III:
162/3 = 54
54/2 = 27
27/3 = 9
9/2 = 4.5
4.5/3 = 1.5

So, missing term in series III = R = 9

Required average = (12 + 225 + 9)/3 = 82