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271. How many 3-digit numbers begin with a prime digit and e

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271. How many 3-digit numbers begin with a prime digit and e [#permalink] New post   11 Mar 2011, 12:53
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271. How many 3-digit numbers begin with a prime digit and end with another prime digit?
(A) 16
(B) 32
(C) 80
(D) 120
(E) 160

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Re: 271. How many 3-digit numbers begin with a prime digit and e [#permalink] New post   11 Mar 2011, 13:00
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banksy wrote:
271. How many 3-digit numbers begin with a prime digit and end with another prime digit?
(A) 16
(B) 32
(C) 80
(D) 120
(E) 160


Unit place and hundredth place digit can be any of 2,3,5 and 7 and tenth place digit can be any of 0 to 9 , so \(4*10*4 = 160\)
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Re: 271. How many 3-digit numbers begin with a prime digit and e [#permalink] New post   11 Mar 2011, 13:04
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beyondgmatscore wrote:
banksy wrote:
271. How many 3-digit numbers begin with a prime digit and end with another prime digit?
(A) 16
(B) 32
(C) 80
(D) 120
(E) 160


Unit place and hundredth place digit can be any of 2,3,5 and 7 and tenth place digit can be any of 0 to 9 , so \(4*10*4 = 160\)


The wording of this question is quite ambiguous because one can think that "another prime digit" means different from the one used for the hundreds digit and in this case the answer would be 4*10*3=120.

Answer: D.
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Re: 271. How many 3-digit numbers begin with a prime digit and e [#permalink] New post   11 Mar 2011, 13:19
It is indeed ambiguous. I just took "another" to mean one more prime number and not as a "different" prime number, but I see how it can be interpreted either ways.
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Re: 271. How many 3-digit numbers begin with a prime digit and e [#permalink] New post   12 Mar 2011, 12:34
Question clearly states , the 3 digit number starts with one prime number and ends with another prime number

2,3,5,7 are possible primes here.


ones ending with 2 can be have 30 combinations ( ending with 3 = 10, ending with 5 =10, ending with 7 =10, middle digit can be anything from 0 to 9)

similarly we can have 30 combinations for each of 3 , 5, 7 .

so 30*4 =120.

Answer is D
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Re: 271. How many 3-digit numbers begin with a prime digit and e [#permalink] New post   13 Mar 2011, 06:02
If you were to break down how you are to read this question and what are the first things that should come to mind, after reading the answers, ive gotten a little lost. I understand that that primes should be 2,3,5,7. But after that im lost, please treat this as an idiots guide:)
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Re: 271. How many 3-digit numbers begin with a prime digit and e [#permalink] New post   13 Mar 2011, 06:09
scbguy wrote:
If you were to break down how you are to read this question and what are the first things that should come to mind, after reading the answers, ive gotten a little lost. I understand that that primes should be 2,3,5,7. But after that im lost, please treat this as an idiots guide:)


First digit can be 2,3,5,7
Second digit can be 0,1,2,3,4,5,6,7,8,9
Third digit can be 2,3,5,7

So; by the slot method, first and 3rd digit both have 4 choices and the 2nd one, 10
Total = 4*10*4= 160.

Apparently, that's not actually meant in the question. It means to say that the first digit is a prime number and the 3rd digit is a different prime number(different from one used in the hundred's place)

Thus;
Hundreds place: 4 choices
Tens place: 10 choices
Units place> 3 choices

4*10*3 = 120 three digits numbers that start with a prime number and end with a different prime number.
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Re: 271. How many 3-digit numbers begin with a prime digit and e [#permalink] New post   25 Apr 2022, 08:18
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Re: 271. How many 3-digit numbers begin with a prime digit and e [#permalink]
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