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555-605 Level|   Number Properties|         
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HKD1710
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How many three-digit numerals begin With a digit that represents a pri 12 Nov 2018, 10:26
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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25% (medium)

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76% (01:17) correct 24% (01:42) wrong based on 1462 sessions

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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
 
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C
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nkin
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How many three-digit numerals begin With a digit that represents a pri 12 Nov 2018, 10:41
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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
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How many three-digit numerals begin With a digit that represents a pri 13 Nov 2018, 02:22
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HKD1710
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
 

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 :grin:

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 :lol:

\(4*10*4 = 160\)


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! :?­
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How many three-digit numerals begin With a digit that represents a pri 13 Nov 2018, 05:09
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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
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How many three-digit numerals begin With a digit that represents a pri 24 Nov 2018, 03:57
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Gladiator59
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
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.
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How many three-digit numerals begin With a digit that represents a pri 08 Jun 2019, 03:50
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aghosh54
Gladiator59
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
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.


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.
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How many three-digit numerals begin With a digit that represents a pri Updated on: 17 May 2021, 08:27
Originally posted by BrentGMATPrepNow on 12 Feb 2020, 16:59.
Last edited by BrentGMATPrepNow on 17 May 2021, 08:27, edited 1 time in total.
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HKD1710
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

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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How many three-digit numerals begin With a digit that represents a pri 25 Sep 2020, 14:13
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HKD1710
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

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
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How many three-digit numerals begin With a digit that represents a pri 28 Dec 2020, 11:34
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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
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How many three-digit numerals begin With a digit that represents a pri 18 Feb 2022, 08:31
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HKD1710
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
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.­
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How many three-digit numerals begin With a digit that represents a pri 20 Nov 2024, 07:41
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here is my solution:
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