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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. Answer B

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,

Asked 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 -

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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07 Oct 2017, 16:04

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