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

Question

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

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.

DangerPenguin · Answer

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!

damham17 · Answer

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.

u1983 · Answer

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  .

exc4libur · Answer

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)

BrentGMATPrepNow · Answer

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

dianyang · Answer

(1) Statement 1: Just question, why 7 cannot be added? it also make the sum divisible by 4

Bunuel · Answer

Because statement (1) says the digit sum must be 4 times an integer, so it must be a multiple of 4. Here the digit sum is 19 + $. If $ = 7, the sum is 26, and 26 is not divisible by 4.

Hope it helps.

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

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