Hi carlos.lara.7,

We're asked for the missing DIGIT in the number 23, 957,X72.

1) The sum of the 8 digits is equal to 5 times an integer

The sum of the 7 digits that we know is 2+3+9+5+7+7+2 = 35. Once we include the missing digit, we'll have a sum that is divisible by 5... This means that the missing digit COULD be 0 (and the sum would be 35) OR it could be 5 (and the sum would be 40.
Fact 1 is INSUFFICIENT

2) The missing digit is equal to one of the digits in the number

This Fact limits the possibilities down to 2, 3, 5, 7 and 9, but does not tell us the exact value of the missing digit.
Fact 2 is INSUFFICIENT

Combined, we know the digit is...
Either 0 or 5
One of the digits 2, 3, 5, 7, 9

The only 'overlap' is the number 5.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

carlos.lara.7 wrote:What is the value of ?, if '?' represents a digit in the 8-digit number 23,957,?72?

(1) The sum of the 8 digits is equal to 5 times an integer

(2) The missing digit is equal to one of the digits in the number

You must know the divisibility rules for 2-9 digits.

• 1. "2": The last digit of the number should be even;
  2. "3": The sum of the digits of the number must be divisible by 3. This is also the rule for '9';
  3. "4": The last two digits of the number must be divisible by 4.
  4. "5": The last digit of the number is either 0 or 5. We are given this to test in the question.
  5. "6": Test the divisibility rule of both '2' and '3'. It must follow both the tests.
  6. "7": Though there are rules to test this, they would not save you time significantly, so it is better that you do not go for it.
  7. "8": The last three digits of the number must be divisible by 8.
  8. "9": The sum of the digits of the number must be divisible by 9. This is also the rule for '3'.

We have to find '?' in 23, 957, ?72.

S1: The sum of the digits, excluding "?" = 2+3+9+5+7+7+2 = 35. So, as per the rule of divisibility of 5, (35 + ?) should be divisible by 5. This implies that ? is either 0 or 5. No unique answer!

S2: '?' is one among 2, 3, 9, 5, 7. No unique answer!

S1 & S2: There is only one digit common between S1 and S2, and that is 5. So ? = 5. Unique answer!

OA: C

-Jay

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