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Manager  Joined: 16 Feb 2011
Posts: 182
What is the remainder when positive integer x is divided by 4?  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 69% (01:26) correct 31% (01:40) wrong based on 229 sessions

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

(1) When x is divided by 6, the remainder is 3.
(2) When x is divided by 8, the remainder is 5.

Originally posted by DeeptiM on 28 Aug 2011, 12:18.
Last edited by Bunuel on 13 Nov 2014, 06:37, edited 1 time in total.
Renamed the topic and edited the question.
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Re: What is the remainder when positive integer x is divided by 4?  [#permalink]

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X=6A+3
6A/4 + 3/4 if A is EVEN then 6a/4 has no reminder and 3/4 has reminder of 3. but if A is odd the reminder is 1. so not sufficient

x=8b+5

8b/4= no reminder 5/4 allways 1 so B is sufficient
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Re: What is the remainder when positive integer x is divided by 4?  [#permalink]

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you can also pick numbers to see a pattern:
A- 3 9 15 21 27 33 THE REMAINDER WILL BE 3,1
B- 5 13 21 29 37- THE REMAINDER WILL BE 1 ONLY.
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Re: What is the remainder when positive integer x is divided by 4?  [#permalink]

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Why not option C ? Bunuel could you please put some light on this .
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Re: What is the remainder when positive integer x is divided by 4?  [#permalink]

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monty6000 wrote:
Why not option C ? Bunuel could you please put some light on this .

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

(1) When x is divided by 6, the remainder is 3 --> x = 6q + 3. Thus, x could be 3, 9, 15, 21, ... So, the remainder when x is divided by 4 could be 3 or 1. Not sufficient.

(2) When x is divided by 8, the remainder is 5 --> x = 8p + 5 = 8p + 4 + 1 = 4(2p + 1) + 1. The remainder when x is divided by 4 is 1. Sufficient.
Or: from x = 8p + 5, x could be 5, 13, 21, 29, 37, ... Each of this numbers when divided by 4 gives the remainder of 1. Sufficient.

Hope it's clear.
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Re: What is the remainder when positive integer x is divided by 4?  [#permalink]

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DeeptiM wrote:
What is the remainder when positive integer x is divided by 4?

(1) When x is divided by 6, the remainder is 3.
(2) When x is divided by 8, the remainder is 5.

We need to determine the remainder when x is divided by 4.

Statement One Alone:

When x is divided by 6, the remainder is 3.

We see that x could be 3 because the remainder is 3 when 3 is divided by 6. If x is 3, the remainder when 3 is divided by 4 is 3.

We see that x also could be 9 because the remainder is 3 when 9 is divided by 6. If x is 9, the remainder when 9 is divided by 4 is 1. We have two different remainders when x is divided by 4. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

When x is divided by 8, the remainder is 5.

We see that x could equal 5 because the remainder when 5 is divided by 8 is 5. If x is 5, the remainder when 5 is divided by 4 is 1.

We see that x also could be 13 because the remainder is 5 when 13 is divided by 8. If x is 13, the remainder when 13 is divided by 4 is 1. It seems that the remainder is always 1 when x is divided by 4. Let’s show that that is exactly the case.

Since x leaves a remainder of 5 when it’s divided by 8, we can express x as:

x = 8m + 5 for some integer m.

Now let’s divide x by 4:

x/4 = (8m + 5)/4

x/4 = 8m/4 + 5/4

x/4 = 2m + (1 + 1/4)

x/4 = (2m + 1) + 1/4

Since 2m + 1 is an integer, we see that the remainder is 1 (the numerator of the fraction 1/4).

Statement two alone is sufficient to answer the question.

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

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_________________ Re: What is the remainder when positive integer x is divided by 4?   [#permalink] 18 Feb 2019, 14:32
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