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Math Expert V
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What is the remainder when positive integer n is divided by 4?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 72% (01:07) correct 28% (01:21) wrong based on 186 sessions

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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.

Kudos for a correct solution.

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What is the remainder when positive integer n is divided by 4?  [#permalink]

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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?
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Re: What is the remainder when positive integer n is divided by 4?  [#permalink]

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1
Bunuel 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.

Kudos for a correct solution.

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

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Re: What is the remainder when positive integer n is divided by 4?  [#permalink]

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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,
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: What is the remainder when positive integer n is divided by 4?  [#permalink]

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1
1
SavageBrother 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.

Picked a number

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

9 / 4 = 2 remainder 1
17 / 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?

Hi SavageBrother,

When dealing with the individual Facts in a DS question, you have to be careful about assuming that the logic/examples you use for one are the only options that you can use for the other.

Here, Fact 2 tells us: when N is divided by 2, the remainder is 1.

You should start here by TESTing the easiest values possible (not just the ones you used in Fact 1).

Here, N could be 1, 3, 5, 7, 9 etc.

IF...
N = 1
1/4 = 0 remainder 1

IF....
N = 3,
3/4 = 0 remainder 3
Fact 2 is INSUFFICIENT

GMAT assassins aren't born, they're made,
Rich
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GMAT 1: 630 Q49 V27 Re: What is the remainder when positive integer n is divided by 4?  [#permalink]

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1
Bunuel 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.

Kudos for a correct solution.

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

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GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 Re: What is the remainder when positive integer n is divided by 4?  [#permalink]

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2
1
Bunuel 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.

Kudos for a correct solution.

1) When some number n is divided x and give some remainder we will receive the same remainder if we divide this number n on factors of x (if factors not less than remainder)
so 8 = 2 * 2 * 2 and if divede n on 2 or 4 or 8 we will receive remainder 1
sufficient

2) We can't say about remainder if want to divide on the number that more than divider which we know.
insufficient

Additional example about quality that I mention in 1 statement:
If we have information that n is divided by 30 and the remainder is 1
we can say that all factors of 30 will be give remainder 1 with the number n

for example n = 31
31 / 30 = 1 and remainder 1

factors of 30 = 2 * 3 * 5
31 / 2 = 15 and remainder 1
31 / 3 = 10 and remainder 1
31 / 5 = 6 and remainder 1
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What is the remainder when positive integer n is divided by 4?  [#permalink]

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IMO OA is
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Re: What is the remainder when positive integer n is divided by 4?  [#permalink]

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EMPOWERgmatRichC wrote:
SavageBrother 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.

Picked a number

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

9 / 4 = 2 remainder 1
17 / 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?

Hi SavageBrother,

When dealing with the individual Facts in a DS question, you have to be careful about assuming that the logic/examples you use for one are the only options that you can use for the other.

Here, Fact 2 tells us: when N is divided by 2, the remainder is 1.

You should start here by TESTing the easiest values possible (not just the ones you used in Fact 1).

Here, N could be 1, 3, 5, 7, 9 etc.

IF...
N = 1
1/4 = 0 remainder 1

IF....
N = 3,
3/4 = 0 remainder 3
Fact 2 is INSUFFICIENT

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

Thanks for the explanation. Got it.
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Re: What is the remainder when positive integer n is divided by 4?  [#permalink]

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Bunuel 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.

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment: dividingby2and8_text.png [ 19.71 KiB | Viewed 4508 times ]

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Re: What is the remainder when positive integer n is divided by 4?  [#permalink]

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Top Contributor
Bunuel 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.

Kudos for a correct 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

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Re: What is the remainder when positive integer n is divided by 4?  [#permalink]

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_________________ Re: What is the remainder when positive integer n is divided by 4?   [#permalink] 28 Jul 2019, 07:11
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