A number when divided by 3 leaves a remainder 1. When the quotient is

Question

A positive integer when divided by 3 leaves a remainder 1. When the quotient is divided by 2, it leaves a remainder1. What will be the remainder when the number is divided by 6 ?

A. 1
B. 2
C. 3
D. 4
E. 5

RohitKakkar · Accepted Answer

When a positive integer is divided by 3 the remainder is 1

X= 3Q+1

When Q is divided by 2 the remainder is 1

Q=2P+1

X=3( 2P+1)+1
X=6P+4
When Integer X is divided by 6 the remainder will be 4, hence Answer is D

Archit3110 · Answer

Let the +be integer be x
x=3a+1
x=2b+1
3a+1=2b+1
3a=2b
a=b=0
or else b:3 and a:2
X will be least 1 or can be 7
Remainder when divided by 6 is 1

Option A.

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Momsspaghetti · Answer

Tried with numbers.

When 7 is divided by 3 and 2, it gives a remainder of 1, which satisfies the requirement.

7/6 remainder is 1.

Option A.

Maria240895chile · Answer

x:3=y with a reminder of 1 so X=3y+1

y:2=z with a reminder of 1 so y=2z+1

now X=3(2z+1)+1
 X=6z+3+1
 X=6z+4

bc 6z is a multiple of 6, the reminder should be 4

IMO D

gmatophobia · Answer

Let the number be n

n = 3q + 1

q is the quotient

q = 2x + 1

n = 3(2x+1)+1

n = 6x + 4

Remainder( \frac{n}{6} ) = Remainder( \frac{6x + 4 }{ 6} )

= 4

Option D

SaquibHGMATWhiz · Answer

Solution:

Algebraic Method:

Let the positive integer be  x=3q+1  where q is the quotient 
 Accordign to the question,  q=2k+1 . So, let us plug this in the value of x above 
 We have  x=3q+1=3(2k+1)+1=6k+4  
 So, when the positive integer  x  is divided by 6, the remainder we will get is  (\frac{x}{6})_R=(\frac{6k+4}{6})_R=4

Picking Numbers  
  Let us assume the positive integer be  x  
 Since this positive integer when divided by 3 leaves a remainder 1,  the possible values of  x  is 1 (3*0 + 1), 4 (3*1 + 1), 7(3*2 + 1), 10(3*3 + 1),... and so on  
 However, when the quotient is divided by 2, it leaves a remainder 1 which means the quotient needs to be odd 
 So,  ultimately possible values of  x  is 4 (3*1 + 1), 10(3*3 + 1),..... and so on  
 We can pick anyone and check the value of  (\frac{x}{6})_R=(\frac{10}{6})_R=4

Hence the right answer is    Option D

BrushMyQuant · Answer

A positive integer when divided by 3 leaves a remainder 1. When the quotient is divided by 2, it leaves a remainder 1. What will be the remainder when the number is divided by 6 ?

When the quotient is divided by 2, it leaves a remainder 1

Dividend = Divisor * Quotient + Remainder
=> Dividend = 2k + 1 (where k is an integer)

=> Quotient which was divided by 2 = 2k + 1

A positive integer when divided by 3 leaves a remainder 1

Integer = 3 * Quotient + 1 = 3 * (2k + 1) + 1 = 6k + 3 + 1 = 6k + 4

What will be the remainder when the number is divided by 6

Remainder of number by 6 = Remainder of 6k + 4 by 6 = Remainder of 6k by 6 + Remainder of 4 by 6 = 0 + 4 = 4

So,  Answer will be D 
Hope it helps!

Watch the following video to MASTER Remainders

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

chetan2u · Answer

Let us do it logically.

A positive integer when divided by 3 leaves a remainder 1.  The number could be 1, 4, 7, 10.. and so on
 When you divide by 6, the remainders are 1, 4, 1, 4.... . Thus, only possibilities are 1 and 4.

Next,  When the quotient is divided by 2, it leaves a remainder 1. 
 This means the quotient is ODD.

The number now becomes 3*ODD+1 or it is an even number.
 EVEN number divided by 6 should give us EVEN remainder.

Out goes 1, and we are left with only 4.

D

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A number when divided by 3 leaves a remainder 1. When the quotient is

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A number when divided by 3 leaves a remainder 1. When the quotient is

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