Question

A lucky year is one in which at least one date, when written in form day / month / year, has the following property. The product of the month times the day equals the last two digits of the year. For example, $1956$ is a lucky year because it has the date $7/8/56$ where $7\times 8=56$, but $1962$ is not a lucky year as $62=62\times 1$ or $31\times 2$, where $31/2/1962$ is not a valid date. From $1900$ and $2018$ how many years are not lucky (not including $1900$ and $2018$)?

• A. $44$
• B. $4$
• C. $21$
• D. $33$

Answer 1

The correct option is C $21$

Month $\times$ Date $=\{1,2,3,.....,99\}$

Month $\Rightarrow \{1,2,3,....,12\}$

Date $\Rightarrow \{1,2,3,.....,31\}$

Years which are not lucky

$1937,1941,1943,1947,1953,1958,1959,1961,1962,1967,1971,1973,1974,1979,1982,1983,1986,1989,1994,1997,2000$.

Total$=21$ years.