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When p is divided by 9, the remainder is 4. All of the following are

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Bunuel
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When p is divided by 9, the remainder is 4. All of the following are [#permalink] New post   11 Apr 2016, 04:02
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E

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When p is divided by 9, the remainder is 4. All of the following are possible values of p, except for which of the following?

A. 13
B. 31
C. 49
D. 57
E. 67
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D
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Re: When p is divided by 9, the remainder is 4. All of the following are [#permalink] New post   11 Apr 2016, 07:40
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Bunuel wrote:
When p is divided by 9, the remainder is 4. All of the following are possible values of p, except for which of the following?

A. 13
B. 31
C. 49
D. 57
E. 67


(Answer_choice - 4) should NOT be divisible by 9.

Only 57 follows.

hence D
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When p is divided by 9, the remainder is 4. All of the following are [#permalink] New post   11 Apr 2016, 08:10
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If a number is divisible by 9, the sum of its digits must be divisible by 9. --> If a number leaves a remainder 4 when divided by 9 the sum of its digits must be 4.

57 = 5 + 7 = 12--> 1 + 2 = 3

Answer: D
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BrentGMATPrepNow
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Re: When p is divided by 9, the remainder is 4. All of the following are [#permalink] New post   11 Apr 2016, 08:25
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Bunuel wrote:
When p is divided by 9, the remainder is 4. All of the following are possible values of p, except for which of the following?

A. 13
B. 31
C. 49
D. 57
E. 67


When it comes to remainders, we have a 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 p is divided by 9, leaves a remainder 4, then the possible values of p are: 4, 4+9, 4+(2)(9), 4+(3)(9), ...etc
In other words, the possible values of p are 4, 13, 22, 31, 40, 49, 58, 67...
As you can see, 57 is not in the list.
Answer: D

Related Resource
The following free video covers the concepts/strategies that are useful for answering this question:
- Remainders: https://www.gmatprepnow.com/module/gmat ... /video/842

Cheers,
Brent
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OptimusPrepJanielle
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Re: When p is divided by 9, the remainder is 4. All of the following are [#permalink] New post   11 Apr 2016, 09:17
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Bunuel wrote:
When p is divided by 9, the remainder is 4. All of the following are possible values of p, except for which of the following?

A. 13
B. 31
C. 49
D. 57
E. 67


P is of the form 9n + 4

On checking the options:

A. 13 = 9 + 4
B. 31 = 9*3 + 4
C. 49 = 9*5 + 4
D. 57. This cannot be expressed as 9n + 4
E. 67 = 9*7 + 4

Correct Option: D
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Re: When p is divided by 9, the remainder is 4. All of the following are [#permalink] New post   11 Apr 2016, 10:42
d is answer 9*6=54
54+4=58
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Re: When p is divided by 9, the remainder is 4. All of the following are [#permalink] New post   13 Apr 2016, 02:06
p / 9 = k (4) with k the quotient and 4 the remainder
--> p = 9k + 4
--> possible value of p : 4, 13, 22, 31, 40, 49, 58, 67...
All answer choices fit, except 57...

answer D
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Re: When p is divided by 9, the remainder is 4. All of the following are [#permalink] New post   14 Jun 2016, 04:38
The number can be expressed in the form of 9x+4 where x can 0,1,2,3,4....
by evaluating the answer choices carefully we can clearly observe that 57 is the only number which can't be expressed in the form of 9x+4
In other words we can also say that the (answer - 4) will not be divisible by 9.57 is the number which doesn't follow this condition
Correct Answer - D
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Re: When p is divided by 9, the remainder is 4. All of the following are [#permalink] New post   14 Jun 2016, 07:01
p=9k+4
13=9*1+4
31=9*3+4
49=9*5+4
57=9*6+3
so D !!
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Re: When p is divided by 9, the remainder is 4. All of the following are [#permalink] New post   26 Jan 2017, 13:40
Check multiples of 9 in options
Only option is D reminds 3
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Re: When p is divided by 9, the remainder is 4. All of the following are [#permalink] New post   06 Nov 2017, 21:10
Bunuel wrote:
When p is divided by 9, the remainder is 4. All of the following are possible values of p, except for which of the following?

A. 13
B. 31
C. 49
D. 57
E. 67


p-4 has to be a multiple of 9
57-4=53, which isn't
D
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Re: When p is divided by 9, the remainder is 4. All of the following are [#permalink] New post   18 Jun 2018, 08:49
we need to check nultiples of 9, only D is not
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Re: When p is divided by 9, the remainder is 4. All of the following are [#permalink] New post   10 Dec 2020, 08:26
Bunuel wrote:
When p is divided by 9, the remainder is 4. All of the following are possible values of p, except for which of the following?

A. 13
B. 31
C. 49
D. 57
E. 67


Min possible value of p is 4...

So, Possible values of p are : 4 , 13 , 22 , 31 , 40 , 49 , 58 , Answer must hence be (D)
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Re: When p is divided by 9, the remainder is 4. All of the following are [#permalink]
10 Dec 2020, 08:26
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