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07 Aug 2022, 08:14
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
24% (01:01) correct
76%
(01:17)
wrong
based on 171
sessions
History
Date
Time
Result
Not Attempted Yet
What is the value of \(t_5\) of sequence X?
(1) In sequence X, \(t_1 = 3\), \(t_2 =7\), \(t_3 = 15\), and \(t_4 = 31\)
(2) In sequence X, \(t_6 = 127\), \(t_7 =255\), \(t_8 = 511\), and \(t_9 = 1023\)
(1) In sequence X, \(t_1 = 3\), \(t_2 =7\), \(t_3 = 15\), and \(t_4 = 31\)
(2) In sequence X, \(t_6 = 127\), \(t_7 =255\), \(t_8 = 511\), and \(t_9 = 1023\)
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07 Aug 2022, 08:53
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BrentGMATPrepNow
Clearly E as we do not know the nth term. The sequence could be anything.
Let us see
(1) In sequence X, \(t_1 = 3\), \(t_2 =7\), \(t_3 = 15\), and \(t_4 = 31\)
The pattern in first four terms is every succeeding term is one more than twice the previous term.
The \(t_5\) could follow the same pattern and be 63 or it could be just any other number.
(2) In sequence X, \(t_6 = 127\), \(t_7 =255\), \(t_8 = 511\), and \(t_9 = 1023\)
Same as above.
Combined
We know that first 4 terms and 6th to 9th terms follow same pattern.
Possibility 1: All follow same pattern - 3,7,15,31,63,127,255,511….
Possibility 2: pattern could be 2(previous term)+1 for first 4 terms, followed by 4(previous term), then previous term+3.
The same pattern follows then - 3,7,15,31,124,127,255,511,1023,4092,4095….
Insufficient
E
10 Aug 2022, 07:18
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BrentGMATPrepNow
I created this question to highlight the fact that the GMAT does not test our ability to find missing terms in a sequence unless the sequence is defined for us.
The reason is that there's no way that we can definitively determine ONE (and ONLY ONE) pattern in a given sequence.
Consider this example: 1, 2, 4, __
What's the missing term here?
Well, if we read the sequence as doubling from one term to the next, the next term is 8
HOWEVER, if we notice that we keep adding successively larger integers to each term (i.e., add 1, then add 2, then add 3, etc.) the next term is 7
Likewise, (if we want to get a bit silly), we might look at the given sequence (5, 10, 15, 20, 25, __) and say that the next term is 88. Why?
Because 5 is my favorite number, 10 is my 2nd favorite number, 15 is my 3rd favorite number, ... and 88 is 6th favorite number.
Likewise, in this this official GMAT question https://gmatclub.com/forum/what-is-the- ... 24942.html, we’re told the first five terms of sequence S are 1², 2², 3², 4², and 5², but that still isn’t enough information to determine the 1000th term.
So, although you might have found a certain pattern in the sequence (double and add 1), we can't be certain that this is THE pattern.
This means t_5 can have ANY numeric value.
Answer: E
