Lucy’s Secret Number puzzle

You are at a party and overhear a conversation between Lucy and her friend.

In the conversation, Lucy mentions she has a secret number that is less than 100.

She also confesses the following information:

"The number is uniquely describable by the answers to the following four questions:"

   Q1) Is the number divisible by two?
   Q2) Is the number divisible by three?
   Q3) Is the number divisible by five?
   Q4) Is the number divisible by seven?

She then proceeds to whisper the answers to these questions to her friend. Unfortunately, because of the ambient noise at the party, you only hear the answer to one of the questions. However, knowing just this one answer allows you to determine Lucy’s secret number.

Questions

Which question and answer did you overhear?
If the answer to this question is “Yes”, what is Lucy’s secret number?

Divisible
7	5	3	2	Solutions
N	N	N	N	1, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
N	N	N	Y	2, 4, 8, 16, 22, 26, 32, 34, 38, 44, 46, 52, 58, 62, 64, 68, 74, 76, 82, 86, 88, 92, 94
N	N	Y	N	3, 9, 27, 33, 39, 51, 57, 69, 81, 87, 93, 99
N	N	Y	Y	6, 12, 18, 24, 36, 48, 54, 66, 72, 78, 96
N	Y	N	N	5, 25, 55, 65, 85, 95
N	Y	N	Y	10, 20, 40, 50, 80, 100
N	Y	Y	N	15, 45, 75
N	Y	Y	Y	30, 60, 90
Y	N	N	N	7, 49, 77, 91
Y	N	N	Y	14, 28, 56, 98
Y	N	Y	N	21, 63
Y	N	Y	Y	42, 84
Y	Y	N	N	35
Y	Y	N	Y	70

Lucy’s Secret Number puzzle

Questions

Solution