BTGModeratorVI wrote: ↑Sat Feb 15, 2020 2:50 pm
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
Source: Official Guide
Answer:
C
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. For more information about the FCP, watch this free video:
https://www.gmatprepnow.com/module/gmat- ... /video/775
You can also watch a demonstration of the FCP in action:
https://www.gmatprepnow.com/module/gmat ... /video/776
Then you can try solving the following questions:
EASY
-
https://www.beatthegmat.com/what-should- ... 67256.html
-
https://www.beatthegmat.com/counting-pro ... 44302.html
-
https://www.beatthegmat.com/picking-a-5- ... 73110.html
-
https://www.beatthegmat.com/permutation- ... 57412.html
-
https://www.beatthegmat.com/simple-one-t270061.html
MEDIUM
-
https://www.beatthegmat.com/combinatoric ... 73194.html
-
https://www.beatthegmat.com/arabian-hors ... 50703.html
-
https://www.beatthegmat.com/sub-sets-pro ... 73337.html
-
https://www.beatthegmat.com/combinatoric ... 73180.html
-
https://www.beatthegmat.com/digits-numbers-t270127.html
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https://www.beatthegmat.com/doubt-on-sep ... 71047.html
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https://www.beatthegmat.com/combinatoric ... 67079.html
DIFFICULT
-
https://www.beatthegmat.com/wonderful-p- ... 71001.html
-
https://www.beatthegmat.com/permutation- ... 73915.html
-
https://www.beatthegmat.com/permutation-t122873.html
-
https://www.beatthegmat.com/no-two-ladie ... 75661.html
-
https://www.beatthegmat.com/combinations-t123249.html
Cheers,
Brent
