Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 17 Jul 2019, 10:33 ### 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, b is the

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 56276
abc is a three-digit number in which a is the hundreds digit, b is the  [#permalink]

### Show Tags

1
2 00:00

Difficulty:   55% (hard)

Question Stats: 49% (01:47) correct 51% (01:53) wrong based on 64 sessions

### HideShow 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

_________________
Manager  G
Joined: 10 May 2018
Posts: 123
Concentration: Finance, Sustainability
Re: abc is a three-digit number in which a is the hundreds digit, b is the  [#permalink]

### Show Tags

Great question!
Bunuel wrote:
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

Waiting for the OA. _________________
Stuck in the 600-700 score bracket? I welcome you to read my four-step course of action to a modest score.
I also invite you to critique and help me find flaws in my modus operandi. Thanks!
Director  G
Joined: 20 Feb 2015
Posts: 790
Concentration: Strategy, General Management
Re: abc is a three-digit number in which a is the hundreds digit, b is the  [#permalink]

### Show Tags

Bunuel wrote:
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

since 2 ,3,5 are fixed
The required result is only possible when we have a 2 or a 3 or a 5 as the final value
The only possible value is
100
for which we get 2 as the result

Imo B

please correct me if I am wrong .
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 2942
Re: abc is a three-digit number in which a is the hundreds digit, b is the  [#permalink]

### Show Tags

Solution

Given:
• abc is a three-digit number
• $$&(abc)& = (2^a) * (3^b) * (5^c)$$

To find:
• The number of three-digit numbers, abc, for which &(abc)& yields a prime number

Approach and Working:
• For, $$&(abc)& = (2^a) * (3^b) * (5^c)$$, to be a prime number, the possible cases are,
o a = 1 and b = c = 0, or
o a = b = 0 and c = 1, or
o a = c = 0 and b =1
o In any other case, &abc& cannot be a prime number
o And, for abc to be a three-digit number, 'a' cannot be 0

Therefore, the only possible case is when a = 1 and b = c =0

Hence, the correct answer is option B.

_________________
Intern  B
Joined: 04 May 2014
Posts: 45
Concentration: Strategy, Operations
Re: abc is a three-digit number in which a is the hundreds digit, b is the  [#permalink]

### Show Tags

Bunuel wrote:
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

Good question.. Initially i mis-read the question. I thought we have to find three digit prime number being generated by taking different values of a, b, c. But the question is about yielding a prime number which may be of 1 digit / 2 digits / 3 digits etc.
My logic- Since the expression (2^a)(3^b)(5^c) contains 2, 3 & 5 in product form, the number getting generated out of any value of a, b, c will always be divisible by 2 or 3 or 5. So, that number cant be prime.

2 , 3 & 5 all are prime numbers. So, if we end up in finding a value of a, b. c such that it yields either 2, 3 or 5 then our purpose is served. We can do that in three ways
1) a= 0, b=1, c=0, this gives product of abc as 3 but "abc" becomes a two digit number (10) as a =0 (remember question asks for three digit value for abc)
2) a=1, b = 0, c= 0, this gives product of abc as 2 and also results in "abc"as a three digit number (100)
3) a=0, b=0, c=1, this gives product of abc as as 5, but "abc" becomes one digit number (1) as a =0, b=0
Any other value will not result in a prime number

Hence, a=1, b = 0, c= 0 satisfies both the requirements of three digit number (abc) and product a*b*c = prime number. Re: abc is a three-digit number in which a is the hundreds digit, b is the   [#permalink] 13 Aug 2018, 14:03
Display posts from previous: Sort by

# abc is a three-digit number in which a is the hundreds digit, b is the  