Question

What is the total number of three digit numbers with unit digit $7$ and divisible by $11$?

• A. $6$
• B. $7$
• C. $8$
• D. $9$

Answer 1

Answer: (C)

$8$

Three digit numbers with unit digit $7$ and divisible by $11$

Divisibility rule of $11$

If the difference of the alternating sum of digits of a number is a multiple of $11$, then that number divisible by $11$.

$\underset{–}{x}\underset{–}{y}\underset{–}{7}$: Three digit number with unit's digit ${}^{\prime }{7}^{\prime }$.

x, y are digits from $0-9$, but $x\ne 0$(as xy$7$ three digit number).

xy$7$ divisible by $11$, so

$x-y+7=$Multiplies of $11$

$x-y+7=0$

$x+7=y$

$x=1$ or $2$

$x-y+7=11$

$x-4=y$

$x=4,5,6,7,8,9$

$x-y+7=22\Rightarrow x-y=15$

Not possible as $x-y$ difference of digits

So, possible numbers: $187,297,407,517,627,737,847,957$.