When the positive integer n is divided by 5, the remainder is 2. When

Question

When the positive integer n is divided by 5, the remainder is 2. When n is divided by 8, the remainder is 3. The least possible value of n lies between

A. 5 and 10
B. 10 and 15
C. 15 and 20
D. 20 and 25
E. 25 and 30

gchandana · Answer

Official Explanation
 
The set of positive integers having remainder 2 when divided by 5 is the same as the set of positive integers that are 2 more than a multiple of 5:
2, 7, 12, 17, 22,  27,  32,.....

The set of positive integers having remainder 3 when divided by 8 is the same as the set of positive integers that are 3 more than a multiple of 8:
3, 11, 19,  27 , 35,....

The smallest integer that appears in both lists is 27. Therefore, the least possible value of n lies between 25 and 30.
The correct answer is E.

Bunuel · Answer

When the positive integer n is divided by 5, the remainder is 2. When n is divided by 8, the remainder is 3. The least possible value of n lies between

A. 5 and 10
B. 10 and 15
C. 15 and 20
D. 20 and 25
E. 25 and 30

This question can be solved using formulas, but simple number checking is probably faster here.

Numbers that leave remainder 3 when divided by 8 are:

3, 11, 19, 27, 35, ...

Now check which of these leaves remainder 2 when divided by 5:

3 leaves remainder 3
11 leaves remainder 1
19 leaves remainder 4
27 leaves remainder 2

So the least possible value of n is 27.

27 lies between 25 and 30.

Answer: E.

MartyMurray · Answer

When the positive integer n is divided by 5, the remainder is 2. When n is divided by 8, the remainder is 3. The least possible value of n lies between

If x and y are integers

n = 5x + 2

n = 8y + 3

5x + 2 = 8y + 3

5x = 8y + 1

So, to find 5x, we can find a multiple of 5 that is 1 more than a multiple of 8, which will be an odd multiple of 5.

5 - 1 = 4

15 - 1 = 14

25 - 1 = 24 — There it is.

5x = 25

n = 5x + 2 = 27

A. 5 and 10
B. 10 and 15
C. 15 and 20
D. 20 and 25
E. 25 and 30

Correct answer:   E

vrinda6 · Answer

I did this question with simple susbtitution.

n= 5x+2
n=8y+3

substituting values of x-{0,1,2,3,4,5)
got the values of y-{1/2,9/8,7/4,19/8,3}

Got the first plausible value of x=-5 and y=3 and hence got the value of n between 25-30

AnishPassi · Answer

1. “When the positive integer n is divided by 5, the remainder is 2” —> Essentially, n is 2 more than a multiple of 5. So, 2 more than numbers like 5, 10, 15, 20, 25 ... 
So, no must be one of 7, 12, 17, 22, 27 ...

So, n must end in 2 or 7.

2. “When n is divided by 8, the remainder is 3“

How come the remainder is odd? When can we get an odd integer upon dividing by 8? n must be odd. An even number when divided by an even number will always give an even remainder. (Let me know if this idea is not clear - I’ll try to elaborate).

Combining 1 and 2, n must be a 7-ending number.

Since the question asks about the least possible value, we’re told n is a positive integer, and the ranges overall just go from 5 to 30, I’ll just start with 7 and go to other 7-ending integers till I find one that when divided by 8 leaves a remainder of 3.

7: 7 divided by 8, remainder is 7. Didn’t work. 
17: 17 divided by 8, remainder is 1. Didn’t work.
27: 27 divided by 8, remainder is 3! Fits.

Done.

Why can we stop here? Because the question asks for the least possible value of n. n can’t be lower than 27. So, that’s the least possible value.

(E) between 25 and 30 is the answer.

When the positive integer n is divided by 5, the remainder is 2. When

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When the positive integer n is divided by 5, the remainder is 2. When

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