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

Question

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

Archit3110 · Answer

given
K= 100a+10b+c
#1
A = 3B = 9C
only possible K = 931
2k = 1862
sufficient
#2
AC=B^2
in this case ABC = 931 ; 421; insufficient
IMO A

Kinshook · Answer

Given: 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.

Asked: If none of the three digits is 0, what is the value of 2k?

(1) A = 3B = 9C
Since A cannot be greater than 9; A must be 9;
k = ABC = 931 is the only possibility
2k = 2* 931 = 1862
SUFFICIENT

(2) A/B = B/C
ABC = 931 or 421
NOT SUFFICIENT

IMO A

fauji · Answer

S1  - it's a 3 digit number and C(A=3C) can't be greater than 1 and 0 is not applicable, we get only one result as number ABC = 931. --  Sufficient.

S2  - from this statement, we get multiple results. for e.g. 391, 142 --- Not Sufficient

Hence Answer  Option A

minustark · Answer

Statement 1, for A = 3B = 9C , only 931 fulfills the criteria.  SUFFICIENT.

Statement 2, 1/2 = 2/4, or 2/4 = 4/8, or 1/3 = 3/9.  NOT SUFFICIENT.

IMO  A  is the OA.

GMATWhizTeam · Answer

Step 1: Analyse Question Stem

The number k is a three-digit positive integer, that has A as hundreds’ digit, B as tens’ digit and C as units’ digit. Therefore, k can be expressed as ABC.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1:  A = 3B = 9C

Since A, B and C represent the individual digits of a number, the only set of values that satisfy the above equation is A = 9, B = 3 and C = 1.
Therefore, k = 931 and hence 2k = 1962.

The data in statement 1 is sufficient to find a unique value for 2k.
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.

Statement 2:   \frac{A}{B}  =  \frac{B}{C}

This means that A, B and C are in continued proportion, which does not tell us the exact values of A, B and C.
Without knowing the exact values of the digits, a unique value of k and hence that of 2k cannot be calculated.

The data in statement 2 is insufficient to find a unique value for 2k.
Statement 2 alone is insufficient. Answer option D can be eliminated.

The correct answer option is A.

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

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GMAT Data Sufficiency (DS) Questions

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

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