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05 Jan 2022, 03:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
64% (02:06) correct
36%
(02:09)
wrong
based on 141
sessions
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Not Attempted Yet
In a sequence S, each term after the second term is 3 less than preceding term, If the sum of first five terms is 57, what is the first term?
(1) Sum of first 4 terms is 51
(2) First term is 3 more than the third term
(1) Sum of first 4 terms is 51
(2) First term is 3 more than the third term
18 Jan 2022, 21:48
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Bunuel
Let the first term be 'F'
&
Let the second term be 'S'
Now according to the question: series from second term is S , S-3 , S-3(2) ...
So sum of first five terms will be F + S + S-3 + S-6 + S-9 = 57
F+4S-18 = 57
F+4S = 75. |eq1
We are having two variables and one equation, we need one more equation to solve this and get the value of F and S.
(1) Sum of first 4 terms is 51
This will give us one more equation in terms of F and S and will be sufficient to find the value of F.
But for the namesake will solve this:
F+S+S-3+S-6 = 51
F+3S-9 = 51
F+3S =60. |eq2
Subtracting eq2 from eq1 will give the value of S and we can put the value of S in any equation to get the value of F.
Sufficient.
(2) First term is 3 more than the third term
Again this will give us one more equation with the relationship between F and S.
So will be sufficient to get the value of both F and S.
Again for the namesake:
Third term will be S-3
It's saying first term is 3 more than the first term, so first term = S
F = S.
putting this value in eq1:
5S = 75
S = 15
So, F = 15
Again we don't need to go through this equation to get the answer, a simple awareness about, what the question is demanding and what information we are having was sufficient.
Sufficient.
Answer: D as in Delta.
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