Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 3001:30 AM EDT
-02:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
May 0111:00 AM PDT
-12:00 PM PDT
Free- full-length test + 15 concept videos + 150+ short videos + study plan!
May 0306:30 AM PDT
-08:30 AM PDT
Verbal trouble on GMAT? Fix it NOW! Join Sunita Singhvi for a focused webinar on actionable strategies to boost your Verbal score and take your performance to the next level.
Updated on: 12 Apr 2026, 10:06
Originally posted by bhanuvemula on 29 Mar 2007, 18:53.
Last edited by Bunuel on 12 Apr 2026, 10:06, edited 2 times in total.
Last edited by Bunuel on 12 Apr 2026, 10:06, edited 2 times in total.
Kudos
Bookmarks
B
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:
60% (02:45) correct
40%
(02:48)
wrong
based on 592
sessions
History
Date
Time
Result
Not Attempted Yet
A sequence \(a_1=64\), \(a_2=66\), \(a_3=67\), and \(a_n=8+a_{(n-3)}\), which of the following is in the sequence?
A. 105
B. 786
C. 966
D. 1025
E. 1076
A. 105
B. 786
C. 966
D. 1025
E. 1076
19 Jan 2011, 20:30
Kudos
Bookmarks
A sequence, a1=64, a2=66, a3=67, an=8+an-3, which of the following is in the sequence?
105
786
966
1025
Given:
\(a_1 = 64\)
\(a_2 = 66\)
\(a_3 = 67\)
...
\(a_n = 8 + a_{n - 3}\)
So \(a_4 = 8 + a_1\) = 8 + 64
\(a_5 = 8 + a_2\) = 8 + 66
\(a_6 = 8 + a_3\) = 8 + 67
\(a_7 = 8 + a_4\) = 8 + 8 + 64
\(a_8 = 8 + a_5\) = 8 + 8 + 66
and so on...
So any number that belongs to this sequence will be sum of one of 64/66/67 and some number of 8s.
105 - 64 = 41 which is not a multiple of 8. 41 is 1 more than a multiple of 8 so when you subtract 2/3 out of 41 (in effect subtracting 66/67 out of 105), you will still not get a multiple of 8. Hence 105 is not in this sequence.
786 - 64 = 720 which is divisible by 8 hence it will be in the sequence. This is your answer and ideally you should stop here. But if you want to check the remaining two options:
966 - 64 = 902 which is not divisible by 8. Neither are 900 and 899. Or say that 902 is 6 more than a multiple of 8 so when you subtract 2/3 out of it, you will still not get a multiple of 8.
1025 - 64 = 961 which is not divisible by 8 and is 1 more than a multiple of 8 so when you subtract 2/3 out of it, it will still not give a multiple of 8.
105
786
966
1025
Given:
\(a_1 = 64\)
\(a_2 = 66\)
\(a_3 = 67\)
...
\(a_n = 8 + a_{n - 3}\)
So \(a_4 = 8 + a_1\) = 8 + 64
\(a_5 = 8 + a_2\) = 8 + 66
\(a_6 = 8 + a_3\) = 8 + 67
\(a_7 = 8 + a_4\) = 8 + 8 + 64
\(a_8 = 8 + a_5\) = 8 + 8 + 66
and so on...
So any number that belongs to this sequence will be sum of one of 64/66/67 and some number of 8s.
105 - 64 = 41 which is not a multiple of 8. 41 is 1 more than a multiple of 8 so when you subtract 2/3 out of 41 (in effect subtracting 66/67 out of 105), you will still not get a multiple of 8. Hence 105 is not in this sequence.
786 - 64 = 720 which is divisible by 8 hence it will be in the sequence. This is your answer and ideally you should stop here. But if you want to check the remaining two options:
966 - 64 = 902 which is not divisible by 8. Neither are 900 and 899. Or say that 902 is 6 more than a multiple of 8 so when you subtract 2/3 out of it, you will still not get a multiple of 8.
1025 - 64 = 961 which is not divisible by 8 and is 1 more than a multiple of 8 so when you subtract 2/3 out of it, it will still not give a multiple of 8.
A sequence \(a_1=64\), \(a_2=66\), \(a_3=67\), and \(a_n=8+a_{(n-3)}\), which of the following is in the sequence?
A. 105
B. 786
C. 966
D. 1025
E. 1076
Easier way would be to write down several terms from the sequence:
\(a_1 = 64\)
\(a_2 = 66\)
\(a_3 = 67\)
\(a_4 = 8 + a_1 = 72\)
\(a_5 = 8 + a_2 = 74\)
\(a_6 = 8 + a_3 = 75\)
...
\(a_n = 8 + a_{n - 3}\)
Note that the terms in the sequence have remainder of 0 (\(a_1\), \(a_4\), \(a_7\), ...), 2 (\(a_2\), \(a_5\), \(a_8\), ...) or 3 (\(a_3\), \(a_6\), \(a_9\), ...) upon division by 8. Only 786 has appropriate remainder of 2 (105 and 1025 has a remainder of 1 upon division by 8, 966 has a remainder of 6, 1076 has a remainder of 4).
Answer: B.
Hope it's clear.
A. 105
B. 786
C. 966
D. 1025
E. 1076
Easier way would be to write down several terms from the sequence:
\(a_1 = 64\)
\(a_2 = 66\)
\(a_3 = 67\)
\(a_4 = 8 + a_1 = 72\)
\(a_5 = 8 + a_2 = 74\)
\(a_6 = 8 + a_3 = 75\)
...
\(a_n = 8 + a_{n - 3}\)
Note that the terms in the sequence have remainder of 0 (\(a_1\), \(a_4\), \(a_7\), ...), 2 (\(a_2\), \(a_5\), \(a_8\), ...) or 3 (\(a_3\), \(a_6\), \(a_9\), ...) upon division by 8. Only 786 has appropriate remainder of 2 (105 and 1025 has a remainder of 1 upon division by 8, 966 has a remainder of 6, 1076 has a remainder of 4).
Answer: B.
Hope it's clear.
Bhanu
