 It is currently 30 Sep 2020, 19:21 ### GMAT 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

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### 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  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS: Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2934  , given: 394

abc is a three-digit number in which a is the hundreds digit [#permalink]
1
KUDOS
Expert's post 00:00

Question Stats: 54% (01:23) correct 45% (01:18) wrong based on 46 sessions
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
[Reveal] Spoiler: OA

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2934  , given: 394

Re: abc is a three-digit number in which a is the hundreds digit [#permalink]
1
KUDOS
Expert's post
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.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Manager Joined: 02 Dec 2018
Posts: 74
Followers: 0

Kudos [?]: 14 , given: 60

Re: abc is a three-digit number in which a is the hundreds digit [#permalink]
Edit: Nevermind, silly mistake.

Last edited by QuantumWonder on 04 Dec 2018, 18:54, edited 2 times in total.
Supreme Moderator
Joined: 01 Nov 2017
Posts: 371
Followers: 10

Kudos [?]: 177 , given: 4

Re: abc is a three-digit number in which a is the hundreds digit [#permalink]
Expert's post
QuantumWonder wrote:
I am really confused. The function &abc& being 1,0,0 yields &100&=2^2*3^0*5^0 = 4. 4 is not a prime number. What am I misinterpreting?

hi
&abc& = $$2^a3^b5^c$$..
so here &abc& = &100&= $$2^13^05^0=2$$ and 2 is prime..
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html Re: abc is a three-digit number in which a is the hundreds digit   [#permalink] 02 Dec 2018, 19:33
Display posts from previous: Sort by

# abc is a three-digit number in which a is the hundreds digit  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.