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In a sequence, the sum of four consecutive odd numbers is equal to the
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09 Aug 2021, 06:22
09 Aug 2021, 06:22
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Question Stats:
17% (02:59) correct
82% (03:19) wrong based on 47 sessions
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In a sequence, the sum of four consecutive odd numbers is equal to the sum of three consecutive even numbers. Also, middle term of the even numbers is greater than 101 but less than 200.
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Number of such possible sequences |
12 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
In a sequence, the sum of four consecutive odd numbers is equal to the
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10 Aug 2021, 21:13
10 Aug 2021, 21:13
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Explanation:
Let,
Sum of Even numbers be: \((a - 2) + a + (a + 2)\)
Sum of Odd numbers be: \((b - 4) +(b - 2) + (b + 2) + (b + 4)\)
Given, \((b - 4) +(b - 2) + (b + 2) + (b + 4) = (a - 2) + a + (a + 2)\)
\(4b = 3a\)
\(a = \frac{4b}{3}\)
This means, \(b\) has to be a multiple of 3 which will make \(a\) as the multiple of 4
Also, \(101 < a < 200\)
i.e. \(102 ≤ \frac{4b}{3} ≤ 198\)
\(102(\frac{3}{4}) ≤ b ≤ 198(\frac{3}{4})\)
\(76.5 ≤ b ≤ 148.5\)
Since, \(b\) is odd, it can have \(\frac{(147 - 77)}{2} + 1 = 36\) values in total
But, it has to be a multiple of 3 as well, so we can have \(\frac{36}{3} = 12\) values for \(b\)
Therefore, \(a\) can take 12 values too.
Col. A: 12
Col. B: 12
Hence, Option C
Let,
Sum of Even numbers be: \((a - 2) + a + (a + 2)\)
Sum of Odd numbers be: \((b - 4) +(b - 2) + (b + 2) + (b + 4)\)
Given, \((b - 4) +(b - 2) + (b + 2) + (b + 4) = (a - 2) + a + (a + 2)\)
\(4b = 3a\)
\(a = \frac{4b}{3}\)
This means, \(b\) has to be a multiple of 3 which will make \(a\) as the multiple of 4
Also, \(101 < a < 200\)
i.e. \(102 ≤ \frac{4b}{3} ≤ 198\)
\(102(\frac{3}{4}) ≤ b ≤ 198(\frac{3}{4})\)
\(76.5 ≤ b ≤ 148.5\)
Since, \(b\) is odd, it can have \(\frac{(147 - 77)}{2} + 1 = 36\) values in total
But, it has to be a multiple of 3 as well, so we can have \(\frac{36}{3} = 12\) values for \(b\)
Therefore, \(a\) can take 12 values too.
Col. A: 12
Col. B: 12
Hence, Option C
General Discussion
Re: In a sequence, the sum of four consecutive odd numbers is equal to the
[#permalink]
10 Aug 2021, 02:18
10 Aug 2021, 02:18
solution plz .
