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# If $represents a digit in the 7-digit number 3,62$,215, what is the

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If $represents a digit in the 7-digit number 3,62$,215, what is the [#permalink]
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If $$\square$$ represents a digit in the 7-digit number 3,62 $$\square$$ ,215,
what is the value of $$\square$$?

(1) The sum of the 7 digits is equal to 4 times an integer.

(2) The missing digit is different from any of the other
digits in the number.
1) Not Sufficient : current sum is 19 . So the number can assume 1,5, or 9 to satisfy the statement :The sum of the 7 digits is equal to 4 times an integer.
2) Not Sufficient : Missing digits are :0,4,7,8, and 9
1+2) Sufficient : There is a common element in the 2 aforementioned sets. i.e., 9
Hence Ans C
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Re: If [m]\square[/m] represents a digit in the 7-digit number [#permalink]
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If $$\square$$ represents a digit in the 7-digit number 3,62 $$\square$$ ,215,
what is the value of $$\square$$?

(1) The sum of the 7 digits is equal to 4 times an integer.
(2) The missing digit is different from any of the other digits in the number.

7-digit: 362x215 where x={0,1,2,3,4,5,6,7,8,9}

(1) The sum of the 7 digits is equal to 4 times an integer: insufic.
sum(3,6,2,2,1,5,x)=19+x=4m… m=19+x/4… 19+x must be a factor of 4: {20,24,28…}, so x={1,5,9}

(2) The missing digit is different from any of the other digits in the number: insufic.
used={3,6,2,1,5} x={4,6,7,8,9}

(1&2): x={1,5,9} but used={3,6,2,1,5}, so x={9}; sufficient.

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Re: If $represents a digit in the 7-digit number 3,62$,215, what is the [#permalink]
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Bunuel

Tough and Tricky questions: Word Problems.

If $represents a digit in the 7-digit number 3,62$,215, what is the value of $? (1) The sum of the 7 digits is equal to 4 times an integer. (2) The missing digit is different from any of the other digits in the number Given:$ represents a digit in the 7-digit number 3,62$,215 Target question: What is the value of$?

Statement 1: The sum of the 7 digits is equal to 4 times an integer.
In other words, the sum is a multiple of 4.
We have: 3 + 6 + 2 + $+ 2 + 1 + 5 = 19 +$
19 + $will be a multiple of 4 when$ = 1, 5 or 9
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The missing digit is different from any of the other digits in the number
In other words, $cannot equal 3, 6, 2, 1 or 5, which means$ COULD equal 0, 4, 7, 8, or 9
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that $could equal 1, 5 or 9 Statement 2 tells us that$ could equal 0, 4, 7, 8, or 9
The only value that satisfies both statements is $= 9 Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer: C Cheers, Brent Non-Human User Joined: 09 Sep 2013 Posts: 34861 Own Kudos [?]: 879 [0] Given Kudos: 0 Re: If$ represents a digit in the 7-digit number 3,62$,215, what is the [#permalink] Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. Re: If$ represents a digit in the 7-digit number 3,62\$,215, what is the [#permalink]
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