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

 It is currently 28 Feb 2020, 14:42

### 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

# Letters of the word 'ARRANGEMENT' are first written in ascending order

Author Message
TAGS:

### Hide Tags

Manager
Joined: 20 Aug 2017
Posts: 105
Letters of the word 'ARRANGEMENT' are first written in ascending order  [#permalink]

### Show Tags

26 Dec 2019, 06:49
2
8
00:00

Difficulty:

75% (hard)

Question Stats:

29% (01:43) correct 71% (02:20) wrong based on 31 sessions

### HideShow timer Statistics

Q. Letters of the word 'ARRANGEMENT' are first written in ascending order and then in descending order, and this process is continued. The 8^(12)th letter of the above series is:

A. A
B. R
C. E
D. N
E. T
VP
Joined: 19 Oct 2018
Posts: 1314
Location: India
Re: Letters of the word 'ARRANGEMENT' are first written in ascending order  [#permalink]

### Show Tags

26 Dec 2019, 14:21
2
2
There are 11 letters in ARRANGEMENT; there will be 22 letters in 1 cycle.

We need to find the remainder when 8^{12} or 2^{36} is divided by 22.

22=2*11

$$2^{36}$$= 0 mod 2

$$2^{5}$$= -1 mod 11

$$[2^5]^7$$= (-1)^7 mod 11

$$[2^5]^7$$= (-1) mod 11

$$[2^{35}]$$= (-1) mod 11

$$[2^{35}]*2$$= (-1*2) mod 11

$$2^{36}$$= -2 mod 11= 9 mod 11

$$2^{36}$$= LCM(2,11)k+20

$$2^{36}$$= 22k+20

Hence 8^{12}th word is 20th word of the first cycle, that is E.

uchihaitachi wrote:
Q. Letters of the word 'ARRANGEMENT' are first written in ascending order and then in descending order, and this process is continued. The 8^(12)th letter of the above series is:

A. A
B. R
C. E
D. N
E. T
Intern
Joined: 07 Jan 2019
Posts: 28
Re: Letters of the word 'ARRANGEMENT' are first written in ascending order  [#permalink]

### Show Tags

10 Jan 2020, 01:15
nick1816

Ascending order and then discending order would lead to this cycle:

ARRANGEMENT-TNEMEGNARRA --> 20th letter is R

Where am I wrong?
VP
Joined: 19 Oct 2018
Posts: 1314
Location: India
Re: Letters of the word 'ARRANGEMENT' are first written in ascending order  [#permalink]

### Show Tags

10 Jan 2020, 02:07
It's a very good question; Poorly written tho.

You gotta write the 'Arrangement' in alphabetical order in the case of ascending order and in reverse of alphabetical order in the case of descending order.

Camach700 wrote:
nick1816

Ascending order and then discending order would lead to this cycle:

ARRANGEMENT-TNEMEGNARRA --> 20th letter is R

Where am I wrong?
Intern
Joined: 16 Dec 2019
Posts: 18
Re: Letters of the word 'ARRANGEMENT' are first written in ascending order  [#permalink]

### Show Tags

22 Jan 2020, 07:51
nick1816 wrote:
There are 11 letters in ARRANGEMENT; there will be 22 letters in 1 cycle.

We need to find the remainder when 8^{12} or 2^{36} is divided by 22.

22=2*11

$$2^{36}$$= 0 mod 2

$$2^{5}$$= -1 mod 11

$$[2^5]^7$$= (-1)^7 mod 11

$$[2^5]^7$$= (-1) mod 11

$$[2^{35}]$$= (-1) mod 11

$$[2^{35}]*2$$= (-1*2) mod 11

$$2^{36}$$= -2 mod 11= 9 mod 11

$$2^{36}$$= LCM(2,11)k+20

$$2^{36}$$= 22k+20

Hence 8^{12}th word is 20th word of the first cycle, that is E.

uchihaitachi wrote:
Q. Letters of the word 'ARRANGEMENT' are first written in ascending order and then in descending order, and this process is continued. The 8^(12)th letter of the above series is:

A. A
B. R
C. E
D. N
E. T

Can you explain this without using mod ?
Thanks
VP
Joined: 19 Oct 2018
Posts: 1314
Location: India
Re: Letters of the word 'ARRANGEMENT' are first written in ascending order  [#permalink]

### Show Tags

22 Jan 2020, 10:03
1
22 = 2*11

$$2^{36}$$ when divided by 2 leaves 0 remainder.

$$2^5 = (33-1)$$

$$(2^5)^7 = (33-1)^7$$

$$(2^5)^7= (33-1)^7$$ = Rem (-1)^7 / 11 = Rem (-1) / 11

$$(2^5)^7*2$$= Rem(-1*2) / 11

$$2^{36}$$ when divided by 11 leaves -2 or (11-2=9) remainder.

So basically our question stem is The remainder$$2^{36}$$ when divided by 2 is 0, and when divided by 11 is 9. What is the remainder when $$2^{36}$$ is divided by 22.

LCM (2, 11)= 22

Find the numbers less than 22 when divided by 11 leaves 9 remainder.

9 and 20

only 20 when divided by 2 leaves 0 remainder.

hence $$2^{36}$$ when divided by 22 leaves 20 remainder.

allkagupta wrote:
nick1816 wrote:
There are 11 letters in ARRANGEMENT; there will be 22 letters in 1 cycle.

We need to find the remainder when 8^{12} or 2^{36} is divided by 22.

22=2*11

$$2^{36}$$= 0 mod 2

$$2^{5}$$= -1 mod 11

$$[2^5]^7$$= (-1)^7 mod 11

$$[2^5]^7$$= (-1) mod 11

$$[2^{35}]$$= (-1) mod 11

$$[2^{35}]*2$$= (-1*2) mod 11

$$2^{36}$$= -2 mod 11= 9 mod 11

$$2^{36}$$= LCM(2,11)k+20

$$2^{36}$$= 22k+20

Hence 8^{12}th word is 20th word of the first cycle, that is E.

uchihaitachi wrote:
Q. Letters of the word 'ARRANGEMENT' are first written in ascending order and then in descending order, and this process is continued. The 8^(12)th letter of the above series is:

A. A
B. R
C. E
D. N
E. T

Can you explain this without using mod ?
Thanks
Re: Letters of the word 'ARRANGEMENT' are first written in ascending order   [#permalink] 22 Jan 2020, 10:03
Display posts from previous: Sort by