December 13, 2018 December 13, 2018 08:00 AM PST 09:00 AM PST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL. December 14, 2018 December 14, 2018 09:00 AM PST 10:00 AM PST 10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51121

abc is a threedigit number in which a is the hundreds digit, b is the
[#permalink]
Show Tags
13 Aug 2018, 04:06
Question Stats:
49% (01:22) correct 51% (01:32) wrong based on 53 sessions
HideShow timer Statistics



Manager
Joined: 10 May 2018
Posts: 126
Concentration: Finance, Sustainability

Re: abc is a threedigit number in which a is the hundreds digit, b is the
[#permalink]
Show Tags
13 Aug 2018, 06:20
Great question! Is the answer (B), one? Bunuel wrote: abc is a threedigit 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 threedigit numbers abc does the function &(abc)& yield a prime number?
(A) Zero (B) One (C) Two (D) Three (E) Nine Waiting for the OA.
_________________



Director
Joined: 20 Feb 2015
Posts: 796
Concentration: Strategy, General Management

Re: abc is a threedigit number in which a is the hundreds digit, b is the
[#permalink]
Show Tags
13 Aug 2018, 06:33
Bunuel wrote: abc is a threedigit 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 threedigit 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 .



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2291

Re: abc is a threedigit number in which a is the hundreds digit, b is the
[#permalink]
Show Tags
13 Aug 2018, 07:15
Solution Given:• abc is a threedigit number • \(&(abc)& = (2^a) * (3^b) * (5^c)\)
To find:• The number of threedigit 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 threedigit 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. Answer: B
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2  Remainders1  Remainders2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



Intern
Joined: 04 May 2014
Posts: 45
Concentration: Strategy, Operations

Re: abc is a threedigit number in which a is the hundreds digit, b is the
[#permalink]
Show Tags
13 Aug 2018, 13:03
Bunuel wrote: abc is a threedigit 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 threedigit numbers abc does the function &(abc)& yield a prime number?
(A) Zero (B) One (C) Two (D) Three (E) Nine Good question.. Initially i misread 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. Answer=B




Re: abc is a threedigit number in which a is the hundreds digit, b is the &nbs
[#permalink]
13 Aug 2018, 13:03






