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

Question

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

beyondgmatscore · Answer

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

Bunuel · Answer

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.

beyondgmatscore · Answer

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.

Spidy001 · Answer

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

scbguy · Answer

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:)

fluke · Answer

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.

bumpbot · Answer

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

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