It is currently 15 Dec 2018, 21:39
My Tests

Close

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
Your Progress

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:
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4750
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1663 [0], given: 396

CAT Tests
abc is a three-digit number in which a is the hundreds digit [#permalink] New post 12 Aug 2018, 15:52
Expert's post
00:00

Question Stats:

50% (01:10) correct 50% (01:00) wrong based on 16 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

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4750
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1663 [0], given: 396

CAT Tests
Re: abc is a three-digit number in which a is the hundreds digit [#permalink] New post 17 Aug 2018, 16:33
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

Intern
Intern
Joined: 02 Dec 2018
Posts: 49
Followers: 0

Kudos [?]: 6 [0], given: 30

CAT Tests
Re: abc is a three-digit number in which a is the hundreds digit [#permalink] New post 02 Dec 2018, 08:50
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: 206
Followers: 3

Kudos [?]: 68 [0], given: 1

CAT Tests
Re: abc is a three-digit number in which a is the hundreds digit [#permalink] New post 02 Dec 2018, 19:33
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  


cron

GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

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®.