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The number k is a three-digit positive integer that has A as its

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Math Expert
Joined: 02 Sep 2009
Posts: 46991
The number k is a three-digit positive integer that has A as its [#permalink]

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21 Aug 2017, 05:30
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Difficulty:

25% (medium)

Question Stats:

78% (01:26) correct 22% (01:58) wrong based on 68 sessions

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The number k is a three-digit positive integer that has A as its hundreds’ digit, B as its tens’ digit, and C as its units’ digit. If none of the three digits is 0, what is the value of 2k?

(1) A = 3B = 9C

(2) A/B = B/C

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Re: The number k is a three-digit positive integer that has A as its [#permalink]

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21 Aug 2017, 05:37
Bunuel wrote:
The number k is a three-digit positive integer that has A as its hundreds’ digit, B as its tens’ digit, and C as its units’ digit. If none of the three digits is 0, what is the value of 2k?

(1) A = 3B = 9C

(2) A/B = B/C

(1) tells us that C can only take 1, hence b will be 3 and A will be 9
ABC = 931 = k
2k = 2*931 = 1862
Sufficient

(2) A,B,C can take (1,2,4), (1,3,9) and (2,4,8) and hence no unique value of k
Not sufficient

hence A
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Joined: 19 Sep 2016
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Re: The number k is a three-digit positive integer that has A as its [#permalink]

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23 Aug 2017, 04:46
The number k is a three-digit positive integer that has A as its hundreds’ digit, B as its tens’ digit, and C as its units’ digit. If none of the three digits is 0, what is the value of 2k?

(1) A = 3B = 9C : as these are single digit numbers, and a=9c & 3b=9c, so c has to be 1 as any number above that would mean a=9c is not a single digit (i.e. max value can be of 9 only between 0-9) so c=1, a=9 and b=3 so that number k =931 and hence 2k can be calculated and is sufficient.

(2) A/B = B/C : the equation can also be written as ac=b^2 so values can be 222, 333,444 and so on and also can take values of 124, 139. so no concrete value comes out.

hence answer is A as statement 1 is sufficient to answer the question.
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Joined: 15 Jan 2017
Posts: 362
The number k is a three-digit positive integer that has A as its [#permalink]

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23 Sep 2017, 07:02
The number k is a three-digit positive integer that has A as its hundreds’ digit, B as its tens’ digit, and C as its units’ digit. If none of the three digits is 0, what is the value of 2k?

(1) A = 3B = 9C --> Clear A: we get the values of each digit, so we can get 2K in terms of C

(2) A/B = B/C -->corrected: B sq=AC
The number k is a three-digit positive integer that has A as its   [#permalink] 23 Sep 2017, 07:02
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