The number 3 divides a with a result of b and a remainder of 2. The nu

Question

The number 3 divides a with a result of b and a remainder of 2. The number 3 divides b with a result of 2 and a remainder of 1. What is the value of a ?

(A) 13

(B) 17

(C) 21

(D) 23

(E) 27

Tulkin987 · Answer

a=3*b+2

b=3*2+1

So,  b=7  and  a=23 .

Answer: D

EgmatQuantExpert · Answer

Solution

Given:  
 • The number 3 divides ‘a’ with result b and remainder 2
• The number 3 divides ‘b’ with result 2 and remainder 1

To find:  
 • The value of a

Approach and Working:   
As 3 divides ‘a’, giving a result b and remainder 2, we can write
 • a = 3b + 2

Similarly, 3 divides ‘b’, giving a result 2 and remainder 1, we can write
 • b = 3 * 2 + 1 = 7

Replacing the value of b in the first equation, we can write
 • a = 3 * 7 + 2 = 21 + 2 = 23

Hence, the correct answer is option D.

Answer: D

SaikatRoy · Answer

We know that
Dividend= (Divisor x Quotient) + Remainder.

It's given that 3 divides ‘a’, giving a result b and remainder 2, 
ie a = 3b + 2

Also 3 divides ‘b’, giving a result 2 and remainder 1, 
ie b = 3 * 2 + 1 = 7

Replacing the value of b in the previous equation, we get
a = 3 * 7 + 2 = 21 + 2 = 23

Hence, answer is option D.

CrackverbalGMAT · Answer

This is a fairly easy question on the concepts of divisibility. The specific concept to be used here is the Euclidean Division Algorithm. For more on the Euclidean Division Algorithm and remainders, you may go through my post on Remainders, the URL is pasted below:

https://gmatclub.com/forum/remainders-tips-and-hints-175000.html#p2424422

When ‘a’ is divided by 3, the result is b and the remainder is 2. This means that that the dividend is a, the divisor is 3, the quotient (result is nothing but the quotient) is ‘b’ and the remainder is 2.

Similarly, when ‘b’ is divided by 3, the result is 2 and the remainder is 1. This means that that the dividend is b, the divisor is 3, the quotient is 2 and the remainder is 1.

When we use the above values in the Euclidean algorithm, we get two equations:

a = 3b + 2 and b = 3*2 + 1 = 7.

Substituting the value of b=7 in the first equation, we have a = 3*7 + 2 = 21 + 2 = 23.

The correct answer option is D.

Questions like these are the best for you to get a hang of basic divisibility concepts; solve a few of these and you will internalize the concepts well which will help you in applying these in the advanced questions.

Hope that helps!

BrushMyQuant · Answer

Dividend = Divisor * Quotient + Remainder

The number 3 divides a with a result of b and a remainder of 2 
Dividend = a
Divisor = 3
Quotient = b
Remainder = 2
=> Dividend = Divisor * Quotient + Remainder
=> a = 3b + 2 ...(1)

The number 3 divides b with a result of 2 and a remainder of 1 
Dividend = b
Divisor = 3
Quotient = 2
Remainder = 1
=> Dividend = Divisor * Quotient + Remainder
=> b = 3*2 + 1 => b = 7 ...(2)

What is the value of a 
a = 3b + 2  
=> a = 3*7 + 2  
=> a = 21 + 2 = 23

So,  Answer will be D 
Hope it helps!

Watch the following video to learn the Basics of Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

bumpbot · Answer

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The number 3 divides a with a result of b and a remainder of 2. The nu

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