GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 29 Jan 2020, 05:24 ### 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

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # There is a sequence such that an = a(n-2) + 12, where n is an integer

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 60778
There is a sequence such that an = a(n-2) + 12, where n is an integer  [#permalink]

### Show Tags 00:00

Difficulty:   75% (hard)

Question Stats: 42% (03:13) correct 58% (02:15) wrong based on 30 sessions

### HideShow timer Statistics

There is a sequence such that $$a_n=a_{n-2}+12$$, where n is an integer greater 2. Is 417 contained in the sequence $$a_n$$?

(1) $$a_1=21$$
(2) $$a_2=23$$

Are You Up For the Challenge: 700 Level Questions

_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 8322
Re: There is a sequence such that an = a(n-2) + 12, where n is an integer  [#permalink]

### Show Tags

Bunuel wrote:
There is a sequence such that $$a_n=a_{n-2}+12$$, where n is an integer greater 2. Is 417 contained in the sequence $$a_n$$?

(1) $$a_1=21$$
(2) $$a_2=23$$

Are You Up For the Challenge: 700 Level Questions

$$a_n=a_{n-2}+12$$

A bit of look into this equation to help understand the question better..
1) The equation will give 2 series... one for odd numbers..$$a_1, a_3, a_5$$... and one for even numbers..$$a_2, a_4, a_6$$...
2) We require to know one in odd series and one in even series to answer for sure.
3) If 417 does not belong to the series, you will have to check both series, hence C
4) But if 417 is in one of the series, then the answer will be series in which it is there, hence A or B

$$a_n=a_{n-2}+12$$, where n is an integer greater 2.

(1) $$a_1=21$$
$$a_n=a_{n-2}+12........a_3=a_1+12=21+12....$$..
Hence the series will be 21, 21+12, 21+2*12... so 417-21 or 396 should be a multiple of 12
396 = 12*33..........417=21+33*12
Yes, 417 is in the sequence.

(2) $$a_2=23$$
We know the answer can be only A, B or C. So we can skip this and answer A.
But let us solve it..
$$a_n=a_{n-2}+12........a_4=a_2+12=23+12....$$..
Hence the series will be 23, 23+12, 23+2*12... so 417-23 or 394 should be a multiple of 12
394 = 12*32+10..........
No, 417 is not in the EVEN sequence, but it may be in ODD sequence. Hence, insufficient.

A
_________________ Re: There is a sequence such that an = a(n-2) + 12, where n is an integer   [#permalink] 15 Nov 2019, 05:58
Display posts from previous: Sort by

# There is a sequence such that an = a(n-2) + 12, where n is an integer  