Odd Man Out and Series problems
- 1. The number of bacteria in a certain culture doubles every hour. If there were 50 bacteria present in the culture originally, how many bacteria will be born in 12th hour?
Options- A. 102460
- B. 120450
- C. 102400
- D. 120400 Discuss
Correct Answer: 102400
Explanation:
The number of bacteria at any given time forms a GP whose terms are given by 50, 100, 200, ... where
a = 50, r = 100/50 = 2
Tn = arn -1
? T12 = 50(2)12 - 1
= 50 x (2)11
= 102400
So, the number of bacteria born in 12th hour is 102400.
- 2. For doing a certain job, boy is offered ? 5 on the first day, ? 15 on the second day, ? 45 on the third day and so no. How much will the boy earn at the end of seven days?
Options- A. ? 5486
- B. ? 5484
- C. ? 5465
- D. ? 5450 Discuss
Correct Answer: ? 5465
Explanation:
This is a GP with a = 5 , r = 15/5 = 3, n = 7
Sn = a(rn - 1 )/(r - 1)
? S15 = 5(37 - 1)/(3 - 1)
= 5/2(37 - 1)
= 5/2 (2187 - 1)
= ? 5465
- 3. The age of the father of two children is twice that of the elder one added to four times that of the younger one. If the geometric mean of the ages of the two children is 4? 3 and their harmonic mean is 6, then what is the father's age?
Options- A. 48 yr
- B. 32 yr
- C. 40 yr
- D. 56 yr Discuss
Correct Answer: 40 yr
Explanation:
Given, F = 2E + 4Y ...(I)
?EY = 4?3
? EY = 48 ...(II)
and 2EY/ E + Y = 6 ? E + Y = 16 ...(III)
Now, (E -Y)2 = (E + Y)2 - 4EY
= (16)2 - 4 x 48
= 256 - 192 = 64
? E - Y = 8 ...(iv)
From Eqs. (iii) and (iv), we get
E = 12 and Y = 4
From Eq. (i) F = 2 x 12 + 4 x 4 = 40 yr
- 4. The fifth term of a GP is 81 and first term is 16. Find the 4th term.?
Options- A. 36
- B. 54
- C. 24
- D. 18 Discuss
Correct Answer: 54
Explanation:
The nth term of a GP is arn - 1 ,
5th term = ar5 - 1 = ar4 = 81
1st term = a = 16
? r4 = 81/16
? r = ?81/16 = 3/2
? 4th term = ar4 - 1 = ar3 = 16 x 3/2 x 3/2 x 3/2 = 54
- 5. How many terms are there in the GP 5, 20, 80, 320, ..., 20480?
Options- A. 7
- B. 6
- C. 5
- D. 10 Discuss
Correct Answer: 7
Explanation:
Let term = l = arn - 1 a = 5 and l = 20480
r = 20/5 = 4
? 20480 = 5 x (4)n-1
(4)n-1 = 20480/5 = 4096 = (4)6
n - 1 = 6
? n = 7
- 6. A and B are two number whose AM is 25 and GM is 7. Which of the following may be a value of A?
Options- A. 10
- B. 49
- C. 20
- D. 25 Discuss
Correct Answer: 49
Explanation:
(a + b)/2 = 25
a + b = 50
?ab = 7
ab = 49
Hence, A can either be 7 or 49.
So, 49 is the answer.
- 7. If the second term of an HP is 1/6 and the fourth terms is 1/14, then find the tenth term of the HP?
Options- A. 1/32
- B. 1/36
- C. 1/38
- D. 1/40 Discuss
Correct Answer: 1/38
Explanation:
The second and fourth term of the HP are 1/6 and 1/14 respectively,
Hence, for the corresponding AP, the second term is 6 and fourth term is 14.
Hence a + d = 6 and a + 3d = 14
? 2d = 8
? d = 4 and a = 2
Hence, the 10th term of this AP = a + (10 -1)d
= 2 + (10 - 1)x 4 = 2 + 9 x 4
= 2 + 36 = 38
Hence, for the corresponding HP, the 10th term is 1/38.
- 8. If five times the fifth term of an AP is equal to seven times the seventh term of the AP, then what is the twelfth term?
Options- A. - 1
- B. 0
- C. 1
- D. - 2 Discuss
Correct Answer: 0
Explanation:
T5 = a + 4d, T7 = a + 6d
? 5(a + 4d) = 7(a + 6d)
? 5a + 20d = 7a + 42d
? a = -11d
? T12 = a + 11d = - 11d + 11d = 0
So, the twelfth term is 0.
- 9. 2, 8, 18,?, 50, 72
Options- A. 33
- B. 38
- C. 36
- D. 32 Discuss
Correct Answer: 32
Explanation:
Series pattern
2 x 12, 2 x 22, 2 x 32, 2 x 42, 2 x 52, 2 x 62
? Missing term = 2 x 42 = 32
- 10. 2, 9, 28, 65, 126, .....?
Options- A. 195
- B. 199
- C. 208
- D. 217 Discuss
Correct Answer: 217
Explanation:
Series pattern
13 + 1, 33 + 1, 43 + 1, 53 + 1
? Missing term = 63 + 1 = 217
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