How many three-digit numerals begin With a digit that represents a pri

Question

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

nkin · Accepted Answer

Let number be X X X. First and last spots can be taken by 2, 3, 5, 7, so 4 numbers for each spot. Middle spot can be taken by any of the 10 digits.

So, my guess is 4*10*4 = 160 is the answer.

Option C

dave13 · Answer

The Fundamental Counting Principle (also called the counting rule) is a way to figure out the number of outcomes in a probability problem. Basically, you multiply the events together to get the total number of outcomes. The formula is: If you have an event “a” and another event “b” then all the different outcomes for the events is a * b. "AND" means multiplication

Source: https://www.statisticshowto.datascience ... principle/ So,

Stage 1. 4 numbers ( 2, 3, 5, 7) Stage 2. 10 numbers ( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) Stage 3. 4 numbers (2, 3, 5, 7) Stage 4. Kill that annoying fly that is buzzing around your office

4*10*4 = 160 pushpitkc , how are you there ?

i have one question to clear my confusions when do i need to use slot method ? i also was thinking like this: 4 numbers in 4! ways 10 numbers in 10! ways 4 numbers in 4! ways! 4!*10!*4!

Gladiator59 · Answer

dave13  if I may chip in my two cents,

You have to use factorial to list out the possibke permutations in an order.

Here you are just selecting numbers ( digits of a three digit number with constraints)

So your answer is almost correct albeit the factorial sign.

4 ways to choose a prime.

The three digit number will begin and end with a prime and the middle digit will have 10 options.

Hence, 4*10*4 = 160

Does this make sense?

Best,
Gladi

aghosh54 · Answer

No ways to select the first no is 4
no of ways to select middle no is 10
Why is the no ways to select the third no is 4 and not 3? If we select 4, are not we repeating same combination?
Please clarify.

Shrey9 · Answer

yes we are repeating it, 
but thats okay, according to the condition...
Start with a prime digit, and end with a prime digit, doesn't say, "it can't have repeating prime digits"
then, the answer will be 4*10*3 = 120
 I guess so

here the answer is fine, 4*10*4 = 160.

BrentGMATPrepNow · Answer

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.

RELATED VIDEO 
 https://www.youtube.com/watch?v=w5d5bvCRyd4

ScottTargetTestPrep · Answer

Solution:
 
Since 2, 3, 5, and 7 are the only single digit primes, there are 4 choices for the hundreds digit and 4 choices for the units digit. However, since there is no restriction for the tens digit, there are 10 choices. Therefore, there are 4 x 10 x 4 = 160 such 3-digit numbers.

Answer: C

CEdward · Answer

Had to use recognize a pattern to figure this one out. 
The only hundreds digits that would qualify are 2, 3, 5, 7.
202, 212, 222, 232, 242, 252, 262, 272, 282, 292. <----10 digits. These digits can also end in 3, 5, or 7. In total, there are 40 digits in the two-hundred series that satisfies the condition.

Repeat the same thing for the other three series.
40 x 4 = 160

kungfury42 · Answer

Choices for the 1st position = {2, 3, 5, 7} = 4
Choices for the 2nd position = {0, 1, 2, ... 10} = 10
Choices for the 3rd position = {2, 3, 5, 7} = 4

Total numbers possible = 4*10*4 = 160

Option C.

3mrecan · Answer

here is my solution:

bumpbot · Answer

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How many three-digit numerals begin With a digit that represents a pri

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How many three-digit numerals begin With a digit that represents a pri

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