When positive integer n is divided by 5, the remainder is 3, and when

Question

When positive integer n is divided by 5, the remainder is 3, and when n is divided by 6, the remainder is 3. What is the remainder when the smallest possible integer value of n is divided by 7?
 
A. 0 
B. 1 
C. 2
D. 3 
E. 4

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Bunuel · Accepted Answer

When positive integer n is divided by 5, the remainder is 3: n = 5q + 3. n can be 3, 8, 13, 18, 23, 28, 33, ...
When positive integer n is divided by 6, the remainder is 3: n = 6p + 3. n can be 3, 9, 15, 21, 27, 33, ...

As you can see the smallest possible value of n is 3, not 33. 3 divided by 7 gives the reminder of 3.

Notice that q and p are quotients and each of them can be 0.

gmatophobia · Answer

n is divided by 5, the remainder is 3

Therefore, n can be represented as  n = 5*p_1 + 3

n is divided by 6, the remainder is 3

Therefore, n can be represented as  n = 6*p_2 + 3

Hence, the general form of n

n = LCM(5,6)p + 3

3 is the first common term

n = 30p + 3

Remainder( \frac{n}{7} ) = Remainder( \frac{30p+3}{7} )

= Remainder( \frac{30p}{7} ) + Remainder( \frac{3}{7} )

= Remainder( \frac{30p}{7} ) + 3

Question  : What is the remainder when the smallest possible integer value of n is divided by 7

Hence we need to minimize the remainder of  \frac{30p}{7} ; the minimum value of any remainder = 0

Minimum remainder = 3

Option D

Maria240895chile · Answer

could you please, explain this last part?

" = Remainder(\frac{30p}{7}+3)

Question: What is the remainder when the smallest possible integer value of n is divided by 7

Hence we need to minimize the remainder of  \frac{30p}{7} 
the minimum value of any remainder = 0

Minimum remainder = 3"

How you say that 3/7 is equal to 3, and that minimum reminder is 3?

gmatophobia · Answer

3 when divided by 7 leaves a remainder = 3

I am assuming you're referring to this part of the solution

Remainder( \frac{n}{7} ) = Remainder( \frac{30p+3}{7} )

= Remainder( \frac{30p}{7} ) + Remainder( \frac{3}{7} )

We can add remainders to get the net remainder.

In this case, Remainder( \frac{n}{7} ) (  read as Remainder when n is divided by 7  ) = Remainder( \frac{30p}{7} ) + Remainder( \frac{3}{7} )

Remainder( \frac{3}{7} ) = 3

So we have have the expression as

Remainder( \frac{n}{7} ) = some value + 3

The remainder will be least, when the term we are adding is least, i.e. when the term is 0.

Hence the minimum value = 3

NehaKalani · Answer

When positive integer n is divided by 5, the remainder is 3, and when n is divided by 6, the remainder is 3. What is the remainder when the smallest possible integer value of n is divided by 7?

A. 0
B. 1
C. 2
D. 3
E. 4

Why is it wrong to think this way?

n = 5x+3 but also n = 6x+3
So n can be 8, 18, 23, 28, 33, 38, 43, 48 and so on...
But n also can be 9, 15, 21, 27, 33, 39 and so on...

The smallest value of n that satisfies both the conditions is 33.

And 33 when divided by 7 leaves a remainder of 5.

Bunuel , can you please explain why my approach is incorrect?

Pasl · Answer

I thought 0 is not defined as "positive" integer... So in this turn, the least value would be 33...?

Bunuel · Answer

Yes, 0 is neither positive nor negative integer but what does this has to do with the least value of n being 3?

Ritze · Answer

Please show me a precise calculation where 3 divided by 7 gives a remainder of 3. Because i'm always arriving at the remainder of 2 and why 33 is not considered as the smallest value of n? do we have to factorize it or just pick the smallest single digit number in 33 which happens to be 3?

hr1212 · Answer

Build equations:

n = 5x + 3
n = 6y + 3

n = 7z + a?

When n is divided by both 5 and 6, remainder is 3. This occurs only when n is divided by 30 (5x6) and remainder is also 3 => n = 30p + 3

So numbers in this list can be derived by substituting values for p = 0,1,2,3,4,... which would result in 3, 33, 63, 93, 123,...

Smallest integer in this list is 3, which when divided by 7, would also give a remainder of 3

Bunuel · Answer

If you had 3 apples and wanted to distribute them evenly among 7 baskets, each basket would get 0 apples and 3 apples would be left over (remainder).

A remainder is the leftover quantity when a number is divided into equal parts. So when you divide 3 by 7, you are trying to split 3 into groups of 7. Since 7 is larger than 3, you cannot make even one full group, so you have 0 full groups and the leftover is 3. That leftover is the remainder.

When the divisor is larger than the dividend, the remainder is the same as the dividend. For example:

3 divided by 4 yields a remainder of 3: 3 = 4*0 + 3.
9 divided by 14 yields a remainder of 9: 9 = 14*0 + 9.
1 divided by 9 yields a remainder of 1: 1 = 9*0 + 1.

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Hope it helps.

When positive integer n is divided by 5, the remainder is 3, and when

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When positive integer n is divided by 5, the remainder is 3, and when

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