December 10, 2018 December 10, 2018 10:00 PM PST 11:00 PM PST Practice the one most important Quant section  Integer properties, and rapidly improve your skills. December 11, 2018 December 11, 2018 09:00 PM EST 10:00 PM EST Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 475
Location: United Kingdom
Concentration: International Business, Strategy
GPA: 2.9
WE: Information Technology (Consulting)

What is the threedigit number abc, given that a, b, and c
[#permalink]
Show Tags
Updated on: 23 May 2013, 03:47
Question Stats:
63% (02:41) correct 37% (02:39) wrong based on 589 sessions
HideShow timer Statistics
What is the threedigit number abc, given that a, b, and c are the positive single digits that make up the number? (1) a = 1.5b and b = 1.5c (2) a = 1.5x + b and b = x + c, where x represents a positive single digit As the OA is not given, for me the answer will be E and this is how I got it. Please let me know if I am right or wrong.
Statement 1 > Insufficient because b and c can take any single value.
Statement 2 > Insufficient as again b and c can take any values.
Combining the two statements
a = 1.5x + b and b = x + c (From Statement 2) a = 1.5b and b = 1.5c (From Statement 1)
Substituting 1 in 2
we get b = 3x and x = 0.5 c. again b and c can take any value and therefore my answer is E.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Best Regards, E.
MGMAT 1 > 530 MGMAT 2> 640 MGMAT 3 > 610 GMAT ==> 730
Originally posted by enigma123 on 31 Jan 2012, 17:59.
Last edited by Bunuel on 23 May 2013, 03:47, edited 2 times in total.
Added the OA




Math Expert
Joined: 02 Sep 2009
Posts: 51067

Re: +ve single digits
[#permalink]
Show Tags
31 Jan 2012, 18:23
What is the threedigit number abc, given that a, b, and c are the positive single digits that make up the number?(1) a = 1.5b and b = 1.5c > a/b=3/2=9/6 and b/c=3/2=6/4 > a/b/c=9/6/4 and as a, b, and c are the positive single digits, then a=9, b=6 and c=4 > abc=964. Sufficient. (2) a = 1.5x + b and b = x + c, where x represents a positive single digit > multiple values are possible, for example: if x=2 then a=3+b and b=2+c > abc can 631 (for c=1) be or 742 (for c=2). Not sufficient. Answer: A.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Manager
Joined: 20 Jun 2012
Posts: 82
Location: United States
Concentration: Finance, Operations

Re: What is the threedigit number abc, given that a, b, and c
[#permalink]
Show Tags
30 Sep 2013, 10:58
enigma123 wrote: What is the threedigit number abc, given that a, b, and c are the positive single digits that make up the number?
(1) a = 1.5b and b = 1.5c (2) a = 1.5x + b and b = x + c, where x represents a positive single digit
1) a=1.5b ...........................1 b=1.5c ...........................2 the number is 100a +10b +c = n c=c b=1.5c , put value of b in given equation no.1 a=2.25c n = 225c+25c+c = 241c .. we know c is an integer and in this case it can take four values from 1 to 4 .. for values greater than 4, "n" will become 5 digit number. now a=2.25c .. we know a is also an integer .. from the possible values of c we have i.e. 1,2,3,4 .. only 4 will make a an integer .. hence, a = 2.25*4=9 b = 1.5*4=6 c = 4 n = 964 2) well, this one is easy just put values in 100a+10b+c .. you'll get 260x+110c .. too many possibilities
_________________
Forget Kudos ... be an altruist



Intern
Joined: 30 Apr 2010
Posts: 20

Re: What is the threedigit number abc, given that a, b, and c
[#permalink]
Show Tags
16 Oct 2013, 05:26
(1) a = 1.5b b = 1.5c a = 2.25c
a must equal an integer and the only way this is satisfied is if c = 4 (2.25 * 4 = 9)
b = 1.5c = 1.5(4) = 6 a = 1.5b = 1.5(6) = 9
all checks out and no other possibilities so (1) is sufficient.
(2) Too many possibilities. a = 1.5x + b and b = x + c a = 1.5x + x + c = 2.5x + c a = 2.5x + c > many possible values for 'a' and 'c'. Not sufficient.
Answer: A



Intern
Joined: 16 Mar 2014
Posts: 16
GMAT Date: 08182015

Re: What is the threedigit number abc, given that a, b, and c
[#permalink]
Show Tags
06 Oct 2015, 13:15
Bunuel wrote: What is the threedigit number abc, given that a, b, and c are the positive single digits that make up the number?
(1) a = 1.5b and b = 1.5c > a/b=3/2=9/6 and b/c=3/2=6/4 > a/b/c=9/6/4 and as a, b, and c are the positive single digits, then a=9, b=6 and c=4 > abc=964. Sufficient.
(2) a = 1.5x + b and b = x + c, where x represents a positive single digit > multiple values are possible, for example: if x=2 then a=3+b and b=2+c > abc can 631 (for c=1) be or 742 (for c=2). Not sufficient.
Answer: A. Here is another way to solve this question. Question Stem: abc with a, b, c are the positive single digits > abc = 100a + 10b + c (1) a = 3b/2 b = 3c/2 => abc = 241c and a = 9c/4 > c must be 4 to make a a positive single digit. => abc = 241 x 4 = 964 > Sufficient. (2) a = 3x/2; b = x + c => abc = 260x + 111c. Many possible for x and c > Not sufficient. Answer: A



Intern
Joined: 18 Jul 2016
Posts: 9

Re: What is the threedigit number abc, given that a, b, and c
[#permalink]
Show Tags
21 Sep 2016, 10:42
Another way to look at it is 1. a=3/2 b and b=3/2 c and all the digits are obviously positive integers. => both b and c are multiples of 2 => c=2^n , where n is an integer and n>1 => c=4 gives b=6 and a=9 , while c=8 gives b=12(invalid). hence number is 964. SUFFICIENT
2. a=3/2x+b, b=x+c All that we can infer is x is definitely even. There is no constraint on c. Multiple options possible Hence INSUFFICIENT



Board of Directors
Joined: 17 Jul 2014
Posts: 2625
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: What is the threedigit number abc, given that a, b, and c
[#permalink]
Show Tags
01 Nov 2016, 05:51
enigma123 wrote: What is the threedigit number abc, given that a, b, and c are the positive single digits that make up the number?
(1) a = 1.5b and b = 1.5c (2) a = 1.5x + b and b = x + c, where x represents a positive single digit
I took some extra time to test additional values...to make sure B is not sufficient... 1. a=1.5b, b=1.5c only option that works  c=4, b=6, a=8. sufficient. 2. a=1.5x +b > b=x+c => a=2.5x+c now...we know for sure that x must be an even number... suppose x=0 a=b=c > it's possible, the question stem does not state that digits are different. suppose x=2. a=5+c b=2+c c can be 1 > a=6, b=3 c can be 2 > a=7, b=4. so already 3 different options...definitely B alone is not sufficient. answer is A.



NonHuman User
Joined: 09 Sep 2013
Posts: 9088

Re: What is the threedigit number abc, given that a, b, and c
[#permalink]
Show Tags
05 Jan 2018, 22:46
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: What is the threedigit number abc, given that a, b, and c &nbs
[#permalink]
05 Jan 2018, 22:46






