When the positive integer n is divided by 8, the remainder is 3, and

Question

When the positive integer n is divided by 8, the remainder is 3, and when n is divided by 5, the remainder is 2. What is the remainder when the smallest possible value of n is divided by 6?

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

Source: Math Revolution

This is a  PS Butler Question

Check the links to other Butler Projects:

Data Sufficiency Butler  
  Critical Reasoning Butler

suntprovident · Answer

When n is divided by 8 the remainder is 3 (possible values 3,11,19,27,35..)

when n is divided by 5 the remainder is 2 ( possible values 2,7,12,17,22,27)

Lowest common value is 27 so n is 27

27 divided by 6 gives a remainder of 3

odionam · Answer

n = 8a+3, n= 5b+2 both should be equal 8a+3 = 5b+2 then b=5 a=3 is minimum possible value for this to happen n mimimum 27 so divide by 6 gives 3

onlyPlanA · Answer

n = 8p + 3 (possible values = 11, 19, 27, 35)
n = 5q + 2 (possible values = 7, 12, 17, 22, 27)

Thus, smallest possible value of n = 27
27/6 gives 3 as remainder.

answer is D.

gautamK0206 · Answer

Let us assume n = 8k + 3, and 5m+2.
Both the expressions are equal to n, hence 8k+3 = 5m+2
5m = 8k+1,
We need to find the smallest value of m and k for this equation to be valid, which gives us m=5, k=3, giving n = 27.
Now, when 27/6, the remainder is 3.
Therefore, the correct answer is  D. 3

counterclash1 · Answer

Correct Answer: D (3)

GIVEN:
n = 8k + 3
n = 5m + 2
 Target: Remainder when smallest n is divided by 6

CALCULATION:
List values of n = 8k + 3:
n = 3 => 3 mod 5 = 3
n = 11 => 11 mod 5 = 1
n = 19 => 19 mod 5 = 4
n = 27 => 27 mod 5 = 2 (MATCH)

Smallest n = 27

27 / 6 = 4 remainder 3.

Conclusion: Answer Choice D (3).

When the positive integer n is divided by 8, the remainder is 3, and

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

When the positive integer n is divided by 8, the remainder is 3, and

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