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

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Bunuel
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If $ represents a digit in the 7-digit number 3,62$,215, what is the [#permalink] New post   11 Dec 2014, 07:08
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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


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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.
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C
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DangerPenguin
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Re: If $ represents a digit in the 7-digit number 3,62$,215, what is the [#permalink] New post   11 Dec 2014, 10:02
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To be divisible by 4, the sum of digits must be divisible by 2 twice. Without integer $, the sum of digits is 19.

statement 1: insufficient
19 + ? = a number that is divisible by 4
$ could be 1, 5, or 9. not enough info

statement 2: insufficient
$ could be 0, 4, 7, 8, 9

statement 1+2: sufficient
Together, we know that $ must be 9!

Answer C!
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Re: If $ represents a digit in the 7-digit number 3,62$,215, what is the [#permalink] New post   12 Dec 2014, 17:35
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Statement 1:

What $ would make the sum a multiple of 4?
$ could be 1, 5, or 9

As such, S1 is insufficient.

Statement 2:
This results in the possibility of 0, 4, 7, 8, and 9.

As such, S2 is insufficient.

Combined (S1 and S2):

9 would the be number. As such, the answer choice is C.
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If $ represents a digit in the 7-digit number 3,62$,215, what is the [#permalink] New post   23 Nov 2018, 10:11
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adkikani wrote:
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] New post   12 Sep 2019, 09:33
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adkikani wrote:
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.

Answer (C)
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Re: If $ represents a digit in the 7-digit number 3,62$,215, what is the [#permalink] New post   22 Mar 2022, 10:03
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Bunuel wrote:

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
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Re: If $ represents a digit in the 7-digit number 3,62$,215, what is the [#permalink] New post   27 Mar 2023, 00:23
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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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