What is the remainder when positive integer n is divided by 4?

What is the remainder when positive integer n is divided by 4?

(1) When n is divided by 8, the remainder is 1.

(2) When n is divided by 2, the remainder is 1.

Picked a number

1)
9 / 8 = 1 remainder 1
17 / 8 = 2 remainder 1

9 / 4 = 2 remainder 1
16 / 4 = 4 remainder 1

Sufficient.

2)
9 / 2 = 4 remainder 1
17 / 2 = 8 remainder 1

9 / 4 = 2 remainder 1
17 / 4 = 4 remainder 1

Both sufficient, D?

Option a
n=8k+1
Will always give remainder 1 when divided by 4

Option b
n=2k+1
if k is even remainder will be 1
if k is odd remainder will be 3

Option A answer

IMO OA is

1. Method 1: 8 is a multiple of 4. So when n is divided by 4 the remainder will also be 1.
Sufficient

Method 2: Picking numbers: 1,9,17,25,33,41,49,57...all have a remainder of 1 if they are divided by 8 or 4

2. Method 1:n is an odd number. 2 is a factor of 4. So when n is divided by 4, the remainder will either be 1 or 3.
Not Sufficient.

Method 2: Picking numbers: 1,3,5,7,9,11,13,15
1,5,9,13 have a remainder of 1 when divided by 4
3,7,11,15 have a remainder of 3 when divided by 4


Answer: A

n is +ive integer; n/4=R=reminder=?

1.n/8=R=1, assume n =1,9,17...; so n/8 = 1/8 =R=1=9/8=17/8; 1/4=9/4=17/4=R=1 For all numbers remainder =1; so sufficient.

2. n/2=R=1, assume n=1,3,5,7,9...; so n/2=1/2=R=1=3/2=5/2=7/2; but for 1/4=5/4=R=1, 3/4=7/4=R=3; so not sufficient.

Hence answer is A

Thanks,

Thanks for the explanation. Got it.

MAGOOSH OFFICIAL SOLUTION:

Target question: What is the remainder when positive integer n is divided by 4?

Statement 1: When n is divided by 8, the remainder is 1.

APPROACH #1
There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2

Statement 1 essentially says, When n is divided by 8, we get some integer (say k) and the remainder is 1.
So, we can use our nice rule to write: n = 8k + 1 (where k is an integer)
At this point, we can take n = 8k + 1 and rewrite it as n = (4)(2)k + 1
We can rewrite THIS as n = (4)(some integer) + 1
This means that n is 1 greater than some multiple of 4.
In other words, if we divide n by 4, we'll get remainder 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

APPROACH #2
Let's test a few possible values of n.
When it comes to remainders, we have another nice rule that says:
If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

So, if n divided by 8 leaves remainder 1, then some possible values of n are: 1, 9, 17, 25, 33 etc.

Let's test a few of these possible values to see what happens when we divide them by 4
n = 1: n divided by 4 leaves remainder 1
n = 9: n divided by 4 leaves remainder 1
n = 17: n divided by 4 leaves remainder 1
n = 25: n divided by 4 leaves remainder 1
n = 33: n divided by 4 leaves remainder 1
It certainly seems that statement 1 guarantees that the remainder will be 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: When n is divided by 2, the remainder is 1.
In other words, statement 2 tells us that n is ODD
Let's test some possible values of n
Case a: n = 3, in which case n divided by 4 leaves remainder 3
Case b: n = 5, in which case n divided by 4 leaves remainder 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer =

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