GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
abc is a three-digit number in which a is the hundreds digit
[#permalink]
12 Aug 2018, 15:52
12 Aug 2018, 15:52
1
Expert Reply
6
Bookmarks
00:00
Question Stats:
46% (01:29) correct
53% (01:29) wrong based on 92 sessions
Hide Show timer Statistics
abc is a three-digit number in which a is the hundreds digit, b is the tens digit, and c is the units digit. Let \(&(abc)& = (2^a)(3^b)(5^c)\). For example, \(&(203)& = (2^2)(3^0)(5^3) = 500\). For how many three-digit numbers abc does the function &(abc)& yield a prime number?
(A) Zero
(B) One
(C) Two
(D) Three
(E) Nine
(A) Zero
(B) One
(C) Two
(D) Three
(E) Nine
Re: abc is a three-digit number in which a is the hundreds digit
[#permalink]
17 Aug 2018, 16:33
17 Aug 2018, 16:33
3
Expert Reply
1
Bookmarks
Explanation
Since a prime number has only two factors, 1 and itself, \((2^a)(3^b)(5^c)\) cannot be prime unless the digits a, b, and c are such that two of the digits are 0 and the third is 1.
For instance, \((2^0)(3^1)(5^0) = (1)(3)(1) = 3\) is prime.
Thus, the only three values of abc that would result in a prime number & (abc)& are 100, 010, and 001. However, only one of those three numbers (100) is a three-digit number.
Since a prime number has only two factors, 1 and itself, \((2^a)(3^b)(5^c)\) cannot be prime unless the digits a, b, and c are such that two of the digits are 0 and the third is 1.
For instance, \((2^0)(3^1)(5^0) = (1)(3)(1) = 3\) is prime.
Thus, the only three values of abc that would result in a prime number & (abc)& are 100, 010, and 001. However, only one of those three numbers (100) is a three-digit number.
Re: abc is a three-digit number in which a is the hundreds digit
[#permalink]
Updated on: 04 Dec 2018, 18:54
Updated on: 04 Dec 2018, 18:54
Edit: Nevermind, silly mistake.
Originally posted by QuantumWonder on 02 Dec 2018, 08:50.
Last edited by QuantumWonder on 04 Dec 2018, 18:54, edited 2 times in total.
Last edited by QuantumWonder on 04 Dec 2018, 18:54, edited 2 times in total.
