Data Sufficiency

Hi outty,

These types of DS questions are perfect for TESTing Values.

We're told that N is a positive integer. We're asked what the remainder is when N is divided by 4?

Fact 1: N/8 has a remainder of 1

This Fact means that N = (multiple of 8) + 1

So, N could = 1, 9, 17, 25, etc.

1/4 = 0 remainder1
9/4 = 2 remainder1
17/4 = 4 remainder1
25/4 = 6 remainder1

The remainder will ALWAYS = 1.
Fact 1 is SUFFICIENT.

Fact 2: N/2 has a remainder of 1

This Fact means that N = (multiple of 2) + 1

So, N could = 1, 3, 5, 7 etc.

1/4 = 0 remainder1
3/4 = 0 remainder3
5/4 = 1 remainder1
7/4 = 1 remainder3

The remainder changes (sometimes it's 1, sometimes it's 3)
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

outty wrote: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.

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 = A

Cheers,
Brent