Subesha wrote down Davina's phone number in her math binder. Later that day, while correcting her homework, Subesha accidentally erased the last two digits of the phone number, leaving 893-44__. Subesha tries to call Davina by dialing phone numbers starting with 893-44. What is the least number of phone calls that she has to make to be guaranteed to reach Davina's house?
(A) 100
(B) 90
(C) 10
(D) 1000
(E) 20

## Grade 7
Subesha wrote down Davina's phone number in her math binder. Later that day, while correcting her homework, Subesha accidentally erased the last two digits of the phone number, leaving 893-44__. Subesha tries to call Davina by dialing phone numbers starting with 893-44. What is the least number of phone calls that she has to make to be guaranteed to reach Davina's house?
(A) 100
(B) 90
(C) 10
(D) 1000
(E) 20

## Solution

Davina could have a telephone number between and including 893-4400 and 893-4499. Since there are 100 numbers between and including these two numbers, this is precisely the number of calls that Subesha would have to make to be assured that she would reach Davina's house. An alternate way of seeing this is to realize that Davina's number is of the form 893 -44 $\underline{a} \underline{b}$, where there are 10 possibilities for $a$ and for each of these possibilities, there are 10 possibilities for $b$. Thus there are $10 ¥ 10=100$ different possibilities in total.

ANSWER: (A)