CRE 4 - Means | Algebra - Progressions
Join our Telegram Group for CAT/MBA Preparation.
1. CRE 4 - Means | Algebra - Progressions
Find the Arithmetic mean of series of all such two-digit numbers which are divisible by 7.
Answer: 56
Join our Telegram Group for CAT/MBA Preparation.
Explanation :
2-digit numbers which are divisible by 7 are: 14, 21, 28. …, 98.
We know the Arithmetic mean of an A.P. is same as the average of first and last term.
⇒ AM = (14 + 98)/2 = 56.
Hence, 56.
2. CRE 4 - Means | Algebra - Progressions
Find the Geometric Mean of the following terms: 4, 8, 16, …, 1024.
Answer: 64
Join our Telegram Group for CAT/MBA Preparation.
Explanation :
The given terms are in geometric progression.
We know the geometric mean of a G.P. is same as the geometric mean of first and last term.
∴ Geometric mean = √(4×1024) = 2 × 32 = 64.
Hence, 64.
3. CRE 4 - Means | Algebra - Progressions
Find the geometric mean of 40, 54, and 100.
(a) 40
(b) 60
(c) 75
(d) None of these
Answer: Option
B
Join our Telegram Group for CAT/MBA Preparation.
Explanation :
Geometric mean = (40 × 54 × 100)1/3
= (23 × 5 × 33 × 2 × 22 × 52 )1/3
= (26 × 33 × 53 )1/3
= 22 × 3 × 5 = 60.
Hence, option (b).
4. CRE 4 - Means | Algebra - Progressions
Geometric mean of two distinct positive numbers is 50. What can be said about their Arithmetic mean?
(a) < 50
(b) = 50
(c) > 50
(d) Cannot be determined
Answer: Option
C
Join our Telegram Group for CAT/MBA Preparation.
Explanation :
We know for any two positive numbers
When numbers are equal: AM = GM
When numbers are distinct: AM > GM.
Hence, option (c).
5. CRE 4 - Means | Algebra - Progressions
If A1 , A2 and A3 are three arithmetic means between 3 and 24. Their sum is?
(a) 41
(b) 33
(c) 28
(d) 39
Answer: Option
D
Join our Telegram Group for CAT/MBA Preparation.
Explanation :
Here we need to insert three arithmetic means between 3 and 23.
Let the AM’s be a, b and c
∴ 3, a, b, c and 23 are in AP.
Let the common different of this AP be ‘d’.
⇒ 23 = 3 + (5 - 1) × d
⇒ d = 5.
First AM = 3 + d = 8
⇒ AMs are 8, 13, 18.
∴ Sum of the three AMs = 8 + 13 + 18 = 39.
Hence, option (d).
6. CRE 4 - Means | Algebra - Progressions
If G1 , G2 and G3 are the geometric means between 2 and 162, find the value of G3 .
(a) 81
(b) 45
(c) 54
(d) None of these
Answer: Option
C
Join our Telegram Group for CAT/MBA Preparation.
Explanation :
Here we need to insert three geometric means between 2 and 162.
Let the geometric means be a, b and c.
∴ 2, a, b, c and 162 are in G.P.
Let r be the common ratio of this G.P.
⇒ 162 = 2 × r4
⇒ r4 = 81
⇒ r = 3.
∴ G3 = 2 × r3 = 2 × 27 = 54.
Hence, option (c).
7. CRE 4 - Means | Algebra - Progressions
If the A.M. of two numbers is greater than G.M. of the number by 6 and the ratio of the numbers is 9 : 1, then the numbers are
(a) 9, 1
(b) 18, 2
(c) 27, 3
(d) Cannot be determined
Answer: Option
C
Join our Telegram Group for CAT/MBA Preparation.
Explanation :
Since the numbers are in the ratio of 9 : 1, let the numbers be 9x and x.
Now,
A.M. = (a + b)/2 = 5x and
G.M. = √ab = 3x
Given, A.M. = G.M. + 6
⇒ 5x = 3x + 6
⇒ x = 3
∴ The numbers are 27 and 3.
Hence, option (c).
8. CRE 4 - Means | Algebra - Progressions
The arithmetic, harmonic and geometric means between two positive numbers are 144/15, 15 and 12 but not necessarily in this order, then the H.M. G.M. and A.M. respectively are.
(a) 15, 12, 144/15
(b) 12, 15, 144/15
(c) 144/15, 12, 15
(d) 12, 144/15, 15
Answer: Option
C
Join our Telegram Group for CAT/MBA Preparation.
Explanation :
We know for two positive numbers: AM ≥ GM ≥ HM.
∴ AM = 15 (highest of the three numbers)
GM = 12
HM = 144/15 (lowest of the three numbers)
Hence, option (c).
9. CRE 4 - Means | Algebra - Progressions
If G.M. = 18 and A.M. = 27 then H.M. is
(a) 1/8
(b) 1/12
(c) 12
(d) 9√6
Answer: Option
C
Join our Telegram Group for CAT/MBA Preparation.
Explanation :
We know for two positive numbers, GM2 = AM × HM.
∴ 182 = 27 × HM
⇒ HM = 324/27 = 12
Hence, option (c).
10. CRE 4 - Means | Algebra - Progressions
If the harmonic mean of two numbers to their geometric mean is 12 : 13, find the ratio of the numbers
(a) 4/9 or 9/4
(b) 2/3 of 3/2
(c) 2/5 or 5/2
(d) 3/4 or 4/3
Answer: Option
A
Join our Telegram Group for CAT/MBA Preparation.
Explanation :
Let the two no’s be a & b.
We know, G.M. = √ab and H.M. = 2ab/(a+b)
∴ 2 a b a + b a b = 12 13
⇒ 2 a b a b = 12 13 ( a + b )
⇒ 13√ab = 6a + 6b
Dividing the whole equation by √ab, we get
⇒ 13 = 6 a b + 6 b a
Substituting a b
⇒ 13 = 6x + 6/x
⇒ 6x2 – 13x + 6 = 0
⇒ (3x - 2)(2x - 3) = 0
⇒ x = 2/3 or 3/2
∴ a/b = x2 = 4/9 or 9/4.
Hence, option (a).
Solution
Discuss
Report