Problem Solving

BTGModeratorVI wrote: ↑

Mon Sep 14, 2020 8:48 am

How many three-digit numerals begin with a digit that represents a prime number and end with a digit that represents a prime number?

(A) 16
(B) 80
(C) 160
(D) 180
(E) 240

Answer: C
Source: Official guide

Take the task of creating three-digit numerals and break it into stages.

Stage 1: Select a digit for the hundreds position
This digit can be 2, 3, 5, or 7
So, we can complete stage 1 in 4 ways

Stage 2: Select a digit for the tens position
This digit can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
So we can complete the stage in in 10 ways

Stage 3: Select a digit for the units position
This digit can be 2, 3, 5, or 7
So, we can complete this stage in 4 ways

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create three-digit numerals) in (4)(10)(4) ways (= 160 ways)

Answer: C

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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