There is a sequence An for a positive integer n such that when An is d

Question

There is a sequence An for a positive integer n such that when An is divided by An-1 the remainder is An-2. If A2=7, A1=0, which of the following can be the value of A4?

A. 48 
B. 50 
C. 52 
D. 56 
E. 58

KarishmaB · Accepted Answer

The sequence would be like this:

Rem, Divisor, Dividend.............
.............Rem, Divisor, Dividend............
..........................Rem, Divisor, Dividend.............

A1, A2, A3, A4, A5 ...
0, 7, ....

A3 must a number such that when divided by 7, it leaves remainder 0 i.e. A3 is divisible by 7.
A4 must be such a number that when divided by a multiple of 7 gives a remainder 7. So A4 itself must be a multiple of 7 too.

Only (D) is a multiple of 7.

gurmukh · Answer

0, 7, 49, 56..... is one such series...

Posted from my mobile device

chetan2u · Answer

The series is  A_1,A_2, A_3, A_4, .... =>0, 7, ...

Now  A_3   divided by  A_2   should give remainder as  A_1 .
So,  A_3   divided by  7   should give remainder as  0 , that is  A_3  can be any multiple of 7 
=> A_3=7x , where x is an integer.

Now  A_4   divided by  A_3   should give remainder as  A_2 .
So,  A_4   divided by  7x   should give remainder as  7 , that is  A_4  will be 7 more than a multiple of 7 
=> A_4=7x+7 , so  A_4  is a multiple of 7.

Only 56 is a multiple of 7 in the choices.

D

Kinshook · Answer

Given: There is a sequence An for a positive integer n such that when An is divided by An-1 the remainder is An-2. 
Asked: If A2=7, A1=0, which of the following can be the value of A4?

When A3 is divided by A2 = 7 the remainder is A1 = 0;
A3 = 7k

When A4 is divided by A3 = 7k, the remainder is A2 = 7

A4 = 14k 
Since 56 = 14*4 ; 56 is a valid answer.

IMO D

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

There is a sequence An for a positive integer n such that when An is d

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

There is a sequence An for a positive integer n such that when An is d

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards