If N is a positive three-digit number that is greater than 200, and each digit of N is a factor of N itself, what is the value of N?
(1) The tens digit of N is 5.
(2) The units digit of N is 5.
Could an expert please walk me through how you would eliminate choices quickly? The place I got this question from said the answer is A
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DS Number property question
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Hi nbalow,
This question is thick with Number Property rules and Arithmetic patterns (knowing the Rule of 3 and the Rule of 9 would be helpful when working through this prompt).
We're told that N is a positive 3-digit number greater than 200 AND that each DIGIT of N is a FACTOR of N. We're asked for the value of N.
Fact 1: The tens digit is 5
From this Fact, we have.....
_5_ as our 3-digit number.
Since 5 MUST be a factor of this number, we would be restricted to numbers that END in 5 or 0. However, 0 is NOT a factor of ANY number, so the 3-digit number CANNOT end in 0. This leaves us with...
_55
Since we now have an odd number, the first digit CANNOT be even (since even numbers cannot divide evenly into odd numbers). We're also told that the number must be greater than 200, so there are only 4 options to consider:
355, 555, 755, 955
3 does not divide into 355
7 does not divide into 755
9 does not divide into 955
The only number that fits this description is 555.
Fact 1 is SUFFICIENT
Fact 2: The units digit of N is 5
From this Fact, we have.....
_ _5 as our 3-digit number.
From our prior work in Fact 1, we know that 555 is a possible value and that the other two digits MUST be odd.
315 is evenly divisible by 3 and 1 and 5, so this is another possible value for N.
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
This question is thick with Number Property rules and Arithmetic patterns (knowing the Rule of 3 and the Rule of 9 would be helpful when working through this prompt).
We're told that N is a positive 3-digit number greater than 200 AND that each DIGIT of N is a FACTOR of N. We're asked for the value of N.
Fact 1: The tens digit is 5
From this Fact, we have.....
_5_ as our 3-digit number.
Since 5 MUST be a factor of this number, we would be restricted to numbers that END in 5 or 0. However, 0 is NOT a factor of ANY number, so the 3-digit number CANNOT end in 0. This leaves us with...
_55
Since we now have an odd number, the first digit CANNOT be even (since even numbers cannot divide evenly into odd numbers). We're also told that the number must be greater than 200, so there are only 4 options to consider:
355, 555, 755, 955
3 does not divide into 355
7 does not divide into 755
9 does not divide into 955
The only number that fits this description is 555.
Fact 1 is SUFFICIENT
Fact 2: The units digit of N is 5
From this Fact, we have.....
_ _5 as our 3-digit number.
From our prior work in Fact 1, we know that 555 is a possible value and that the other two digits MUST be odd.
315 is evenly divisible by 3 and 1 and 5, so this is another possible value for N.
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
