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# If c is a positive integer less than 10 and n = 9446 + c, then what is

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Math Expert
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If c is a positive integer less than 10 and n = 9446 + c, then what is  [#permalink]

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16 Jul 2015, 01:18
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25% (medium)

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68% (01:05) correct 32% (01:03) wrong based on 133 sessions

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If c is a positive integer less than 10 and n = 9446 + c, then what is the value of c?

(1) n is divisible by 5.
(2) n is divisible by 9.

Kudos for a correct solution.

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Re: If c is a positive integer less than 10 and n = 9446 + c, then what is  [#permalink]

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16 Jul 2015, 03:22
1
Bunuel wrote:
If c is a positive integer less than 10 and n = 9446 + c, then what is the value of c?

(1) n is divisible by 5.
(2) n is divisible by 9.

Kudos for a correct solution.

GIven: 0<c<10 and n =9446+c

Per statement 1, n =5p ----> c = 4 or 9 ----> Statement is not sufficient

Per statement 2, n = 9p ----> c = 4 (sum of digits of n must be divisible by 9). Statement is sufficient. B is the correct answer.
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Re: If c is a positive integer less than 10 and n = 9446 + c, then what is  [#permalink]

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17 Jul 2015, 06:21
Bunuel wrote:
If c is a positive integer less than 10 and n = 9446 + c, then what is the value of c?

(1) n is divisible by 5.
(2) n is divisible by 9.

Kudos for a correct solution.

Statement 1: c=4 or 9.
insufficient

Statement 2: c can only = 9 in order for it to be divisible by 9
sufficient

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Re: If c is a positive integer less than 10 and n = 9446 + c, then what is  [#permalink]

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17 Jul 2015, 09:16
Bunuel wrote:
If c is a positive integer less than 10 and n = 9446 + c, then what is the value of c?

(1) n is divisible by 5.
(2) n is divisible by 9.

Kudos for a correct solution.

1. Adding 4 or 9 makes n divisible by 5. Insufficient.

2. Adding 3 makes n divisible by 9 (sum of the digits is divisible by 9). Sufficient.

B
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Re: If c is a positive integer less than 10 and n = 9446 + c, then what is  [#permalink]

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17 Jul 2015, 16:04
1
Bunuel wrote:
If c is a positive integer less than 10 and n = 9446 + c, then what is the value of c?

(1) n is divisible by 5.
(2) n is divisible by 9.

Kudos for a correct solution.

c could range from 1 to 9.

St 1: n is divisible by 5

=> n = 9446 + 4 => 9450
=> n = 9446 + 9 => 9455

Two values divisible by 5. Not sufficient.

St 2: n is divisible by 9.

=> n =9446 + 4 => 9450(sum of digits should be divisible by 9). Only one value possible in this range.
Hence Sufficient.
Option B
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Re: If c is a positive integer less than 10 and n = 9446 + c, then what is  [#permalink]

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17 Jul 2015, 23:50
(B)

1. c could be 4 or 9 while
2. c=4

As second statement returns a unique value, B is the answer
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Re: If c is a positive integer less than 10 and n = 9446 + c, then what is  [#permalink]

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18 Jul 2015, 07:01
Bunuel wrote:
If c is a positive integer less than 10 and n = 9446 + c, then what is the value of c?

(1) n is divisible by 5.
(2) n is divisible by 9.

Kudos for a correct solution.

Statement 1: n is divisible by 5. Two possible nos are 9450 and 9455. Then c will be 4 and 9 respectively. Insufficient
Statement 2: n is divisible by 9. Possible nos are 9450 and 9459. In case of 9450, c will be 4 and in case of 9459 c will be 13 which is not possible since c is less than 10.
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Re: If c is a positive integer less than 10 and n = 9446 + c, then what is  [#permalink]

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19 Jul 2015, 05:35
If c is a positive integer less than 10 and n = 9446 + c, then what is the value of c?

(1) n is divisible by 5.
(2) n is divisible by 9.

Given :
0 < C < 10

N = 9446 + C,

Statement 1 :
n is divisible by 5.
So for N to be divided by 5 completely, Unit digit of N has to be 0 or 5.
So two possible value for allowed values of C will satisfy this , C = 4 or C = 9
Hence No unique answer - Not sufficient.

Statement 2 :
n is divisible by 9
N = 9446 + C = 9*1049 + 5 + C
So for N to get completely divided by 9, (5+C) must get divided by 9, out of all allowed value of C , only C = 4 Satisfy this condition. Hence unique value of C -

Option B
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Posts: 49320
Re: If c is a positive integer less than 10 and n = 9446 + c, then what is  [#permalink]

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19 Jul 2015, 13:56
Bunuel wrote:
If c is a positive integer less than 10 and n = 9446 + c, then what is the value of c?

(1) n is divisible by 5.
(2) n is divisible by 9.

Kudos for a correct solution.

800score Official Solution:

As c is a positive integer less than 10, we are considering n to be an integer from 9447 to 9455 inclusive. Let’s consider the statement (1). For n to be divisible by 5, the last digit must be 0 or 5. So n can be 9450 or 9455. The corresponding values of c are 4 and 9. Two possible answer choices mean that we don’t have sufficient information using the statement (1) by itself.

Let’s consider the statement (2). For n to be divisible by 9, the sum of digits must be divisible by 9. If the first three digits are 944, then the sum will be an integer from 9 + 4 + 4 + 7 = 24 to 9 + 4 + 4 + 9 = 26 inclusive. Obviously, none of these, 24, 25, or 26, is divisible by 9.

If the first three digits of n are 945, then the sum will be an integer from 9 + 4 + 5 + 0 = 18 to 9 + 4 + 5 + 5 = 23 inclusive. Obviously, only 18 is divisible by 9, which yields 4 as the only possible value of c. Therefore the statement (2) by itself is sufficient and the correct answer is B.
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Re: If c is a positive integer less than 10 and n = 9446 + c, then what is  [#permalink]

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