If k is a positive integer

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Mon Feb 05, 2018 7:13 pm

If k is a positive integer and has exactly two digits, what is k?

(1) The sum of the digits is 3.
(2) k is odd.

Which is the sufficient statement?

OA C

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Source: Beat The GMAT — Data Sufficiency | Mon Feb 05, 2018 7:13 pm

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ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 amFollowed by: 15 members; Thanked: 86 times; GMAT Score:770

by ErikaPrepScholar » Tue Feb 06, 2018 6:01 am

We go into this question knowing that k is a positive integer with exactly two digits.

Statement 1
If the sum of the digits is 3, we only have a couple options for what the digits could be: 0 and 3 or 1 and 2. What numbers can we make with these digits?

03 --> NOT two digits
30
12
21

Based on Statement 1 alone, there are three options for k. Not sufficient.

Statement 2
If k is odd, k can be any odd number from 11 and 99. Not sufficient.

Both

Looking at our three options from Statement 1 (30, 12, 21), we can eliminate 30 and 12 for being even. 21 is the only odd option, so k must be 21. Sufficient.

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by [email protected] » Tue Feb 06, 2018 3:32 pm

Hi lehannie07,

We're told that K is a positive integer and has EXACTLY two digits. We're asked for the value of K. This question can be solved by TESTing VALUES.

1) The sum of the digits of K is 3.

Since K has exactly 2 digits, K could be 12, 21 or 30.
Fact 1 is INSUFFICIENT

2) K is ODD.

Since K has exactly 2 digits, K could be 11, 13, 15, or any other odd 2-digit number.
Fact 2 is INSUFFICIENT

Combined, we know:
-The sum of the digits of K is 3.
-K is ODD.

The only value that 'fits' both of the Facts is 21.

Final Answer: C

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Rich

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Feb 12, 2018 4:26 pm

lheiannie07 wrote:If k is a positive integer and has exactly two digits, what is k?

(1) The sum of the digits is 3.
(2) k is odd.

We are given that k is a positive integer and has exactly two digits, and we need to determine the value of k.

Statement One Alone:

The sum of the digits is 3.

k could be equal to either 21, 12, or 30. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

k is odd.

k could be 11 or 13 or some other two-digit odd number. The information in statement two is not sufficient to answer the question.

Statements One and Two Together:

Using both statements, since the sum of k's two digits is 3 and k is odd, k must be 21.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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