Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 11 Oct 2012
Posts: 13
GMAT Date: 12192012
WE: Analyst (Energy and Utilities)

Is b/3 an integer? [#permalink]
Show Tags
Updated on: 26 Nov 2012, 03:16
Question Stats:
42% (00:54) correct 59% (00:53) wrong based on 400 sessions
HideShow timer Statistics
Is b/3 an integer? (1) (b^2−9)/3 is an integer. (2) p and p + 1 are prime factors of b. All,
I am having trouble with even seemingly easy questions in DS and can't see my way out. Would you please advise? I picked A, but it is quite the opposite (B).
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by valerjo79 on 26 Nov 2012, 03:11.
Last edited by Bunuel on 26 Nov 2012, 03:16, edited 1 time in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 47039

Re: Is b/3 an integer? [#permalink]
Show Tags
26 Nov 2012, 03:25




Intern
Joined: 11 Oct 2012
Posts: 13
GMAT Date: 12192012
WE: Analyst (Energy and Utilities)

Re: Is b/3 an integer? [#permalink]
Show Tags
26 Nov 2012, 04:10
Thanks Bunuel! Apologies for not following the rules, will do so next time. M



Intern
Joined: 03 Oct 2011
Posts: 16

Is b/3 an integer? [#permalink]
Show Tags
03 Nov 2014, 20:25
Bunuel wrote: Is b/3 an integer?(1) (b^2−9)/3 is an integer. Given that \(\frac{b^29}{3}=integer\) > \(\frac{b^2}{3}3=integer\) > \(\frac{b^2}{3}=integer\). Now, if \(b=0\), then \(\frac{b}{3}=0=integer\) but if \(b=\sqrt{3}\), then \(\frac{b}{3}\neq{integer}\). Not sufficient. (2) p and p + 1 are prime factors of b. Since both \(p\) and \(p+1\) are primes, then \(p=2\) and \(p+1=3\). Thus we have that \(b\) is a multiple of 3. Sufficient. Answer: B. P.S. Please read carefully and follow: rulesforpostingpleasereadthisbeforeposting133935.html Pay attention to the rule #3: the name of the topic (subject field) MUST be the first 40 characters (~the first two sentences) of the question. For (1) Can Someone or Bunuel explain why \(\frac{b^29}{3}=integer\) cannot > \(\frac{(b3)(b+3)}{3}=integer\) So that we can then assume that since b, b3 and b+3 share factors, (1) is sufficient



Intern
Joined: 10 Apr 2008
Posts: 25
Location: India
WE: Consulting (Computer Software)

Is b/3 an integer? [#permalink]
Show Tags
04 Nov 2014, 04:06
Bunuel, can you please explain why cannot we factor b^2  9 to (b3)(b+3)? I marked D because I thought option A is sufficient. Please help! Ameya



Math Expert
Joined: 02 Sep 2009
Posts: 47039

Re: Is b/3 an integer? [#permalink]
Show Tags
04 Nov 2014, 04:58



Intern
Joined: 10 Jan 2014
Posts: 9

Re: Is b/3 an integer? [#permalink]
Show Tags
04 Nov 2014, 07:45
valerjo79 wrote: Is b/3 an integer? (1) (b^2−9)/3 is an integer. (2) p and p + 1 are prime factors of b. All,
I am having trouble with even seemingly easy questions in DS and can't see my way out. Would you please advise? I picked A, but it is quite the opposite (B). I have a fundamental error here. The question asks Is b/3 an int? So basically it is asking if I can answer as Yes or No. So with (1) I get the answer as No with (2) I get as Yes So shouldn't the answer be D then because I can say yes or no in both (1) & (2)



Math Expert
Joined: 02 Sep 2009
Posts: 47039

Re: Is b/3 an integer? [#permalink]
Show Tags
04 Nov 2014, 07:51
anki2762 wrote: valerjo79 wrote: Is b/3 an integer? (1) (b^2−9)/3 is an integer. (2) p and p + 1 are prime factors of b. All,
I am having trouble with even seemingly easy questions in DS and can't see my way out. Would you please advise? I picked A, but it is quite the opposite (B). I have a fundamental error here. The question asks Is b/3 an int? So basically it is asking if I can answer as Yes or No. So with (1) I get the answer as No with (2) I get as Yes So shouldn't the answer be D then because I can say yes or no in both (1) & (2) In a Yes/No Data Sufficiency question, each statement is sufficient if the answer is “always yes” or “always no” while a statement is insufficient if the answer is "sometimes yes" and "sometimes no".For (1) the answer is "sometimes yes" and "sometimes no". If \(b = 0\), then the answer is YES but of \(b = \sqrt{3}\), the answer is NO. Also, on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. So, we cannot have a NO answer from one statement and YES answer from another. Hope it's clear.
_________________
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



Intern
Joined: 03 Oct 2011
Posts: 16

Re: Is b/3 an integer? [#permalink]
Show Tags
04 Nov 2014, 17:49
Bunuel wrote: anki2762 wrote: valerjo79 wrote: Is b/3 an integer? (1) (b^2−9)/3 is an integer. (2) p and p + 1 are prime factors of b. All,
I am having trouble with even seemingly easy questions in DS and can't see my way out. Would you please advise? I picked A, but it is quite the opposite (B). I have a fundamental error here. The question asks Is b/3 an int? So basically it is asking if I can answer as Yes or No. So with (1) I get the answer as No with (2) I get as Yes So shouldn't the answer be D then because I can say yes or no in both (1) & (2) In a Yes/No Data Sufficiency question, each statement is sufficient if the answer is “always yes” or “always no” while a statement is insufficient if the answer is "sometimes yes" and "sometimes no".For (1) the answer is "sometimes yes" and "sometimes no". If \(b = 0\), then the answer is YES but of \(b = \sqrt{3}\), the answer is NO. Also, on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. So, we cannot have a NO answer from one statement and YES answer from another. Hope it's clear. I hate to keep coming back to this but for \(\frac{(b3)(b+3)}{3}\), if b is \(sqrt(3)\) the result is 2 which is an integer I really do not understand how we cannot conclude that if at least one of \(b3\) and \(b+3\) is a factor of 3, then both of them must be factors of 3 and consequently, \(b\) must also be a factor of 3. Can someone please show me where I'm wrong?



Math Expert
Joined: 02 Sep 2009
Posts: 47039

Re: Is b/3 an integer? [#permalink]
Show Tags
05 Nov 2014, 04:52
gooner wrote: Bunuel wrote: anki2762 wrote: In a Yes/No Data Sufficiency question, each statement is sufficient if the answer is “always yes” or “always no” while a statement is insufficient if the answer is "sometimes yes" and "sometimes no".
For (1) the answer is "sometimes yes" and "sometimes no". If \(b = 0\), then the answer is YES but of \(b = \sqrt{3}\), the answer is NO.
Also, on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. So, we cannot have a NO answer from one statement and YES answer from another.
Hope it's clear.
I hate to keep coming back to this but for \(\frac{(b3)(b+3)}{3}\), if b is \(sqrt(3)\) the result is 2 which is an integer I really do not understand how we cannot conclude that if at least one of \(b3\) and \(b+3\) is a factor of 3, then both of them must be factors of 3 and consequently, \(b\) must also be a factor of 3. Can someone please show me where I'm wrong? Dear gooner, The question asks whether b/3 an integer. Now, for \(b = \sqrt{3}\) is \(\frac{\sqrt{3}}{3}\) an integer?
_________________
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



Intern
Joined: 14 Apr 2016
Posts: 4
Location: India
GPA: 3.9

Re: Is b/3 an integer? [#permalink]
Show Tags
13 Jul 2016, 12:39
Hi Bunuel,
Can we say for a number such as [12][/3], the prime factors are 2 and 3. If yes, then Statement B doesn't give us a unique solution.
Thanks in advance.



Math Expert
Joined: 02 Sep 2009
Posts: 47039

Re: Is b/3 an integer? [#permalink]
Show Tags
13 Jul 2016, 12:45



Intern
Joined: 14 Apr 2016
Posts: 4
Location: India
GPA: 3.9

Is b/3 an integer? [#permalink]
Show Tags
13 Jul 2016, 12:51
Sorry a typo error, I meant for number 12*3^1/2



Math Expert
Joined: 02 Sep 2009
Posts: 47039

Re: Is b/3 an integer? [#permalink]
Show Tags
14 Jul 2016, 01:01



CEO
Joined: 12 Sep 2015
Posts: 2633
Location: Canada

Re: Is b/3 an integer? [#permalink]
Show Tags
12 Sep 2017, 13:29
valerjo79 wrote: Is b/3 an integer?
(1) (b^2−9)/3 is an integer. (2) p and p + 1 are prime factors of b. ] Target question: Is b/3 an integer? Statement 1: (b² − 9)/3 is an integer There are several values of b that satisfy statement 1. Here are two: Case a: b = 6. Here, (b² − 9)/3 = (6² − 9)/3 = (36 − 9)/3 = 27/3 = 9, and 9 is an integer. In this case, b/3 = 6/3 = 2. So, b/3 IS an integerCase b: b = √18. Here, (b² − 9)/3 = (√18² − 9)/3 = (18 − 9)/3 = 9/3 = 3, and 3 is an integer. In this case, b/3 = (√18)/3 = (3√2)/3 = √2 (. So, b/3 is NOT an integerSince we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: p and p + 1 are prime factors of b Notice that p and p+1 are CONSECUTIVE integers Since p and p+1 are CONSECUTIVE integers, we know that one of the numbers must be odd and one must be even. Since 2 is the ONLY even integer, we can conclude that p = 2 and p+1 = 3 Since p and p+1 are factors of b, we can see that b is divisible by 2 and by 3. If b is divisible by 3, then b/3 must be an integer Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: Cheers, Brent
_________________
Brent Hanneson – Founder of gmatprepnow.com



Intern
Joined: 21 Jan 2017
Posts: 26

Is b/3 an integer? [#permalink]
Show Tags
10 Jul 2018, 01:28
Bunuel wrote: Is b/3 an integer?(1) (b^2−9)/3 is an integer. Given that \(\frac{b^29}{3}=integer\) > \(\frac{b^2}{3}3=integer\) > \(\frac{b^2}{3}=integer\). Now, if \(b=0\), then \(\frac{b}{3}=0=integer\) but if \(b=\sqrt{3}\), then \(\frac{b}{3}\neq{integer}\). Not sufficient. (2) p and p + 1 are prime factors of b. Since both \(p\) and \(p+1\) are primes, then \(p=2\) and \(p+1=3\). Thus we have that \(b\) is a multiple of 3. Sufficient. Answer: B. P.S. Please read carefully and follow: http://gmatclub.com/forum/rulesforpos ... 33935.html Pay attention to the rule #3: the name of the topic (subject field) MUST be the first 40 characters (~the first two sentences) of the question. Hi Bunuel, Why can't we take b as 6 \(\sqrt{12}\) ?? we have 2 and 3 as prime factors here as well. Please explain. Thanks, Uma



Math Expert
Joined: 02 Aug 2009
Posts: 6223

Is b/3 an integer? [#permalink]
Show Tags
10 Jul 2018, 01:48
umabharatigudipalli wrote: Bunuel wrote: Is b/3 an integer?(1) (b^2−9)/3 is an integer. Given that \(\frac{b^29}{3}=integer\) > \(\frac{b^2}{3}3=integer\) > \(\frac{b^2}{3}=integer\). Now, if \(b=0\), then \(\frac{b}{3}=0=integer\) but if \(b=\sqrt{3}\), then \(\frac{b}{3}\neq{integer}\). Not sufficient. (2) p and p + 1 are prime factors of b. Since both \(p\) and \(p+1\) are primes, then \(p=2\) and \(p+1=3\). Thus we have that \(b\) is a multiple of 3. Sufficient. Answer: B. P.S. Please read carefully and follow: http://gmatclub.com/forum/rulesforpos ... 33935.html Pay attention to the rule #3: the name of the topic (subject field) MUST be the first 40 characters (~the first two sentences) of the question. Hi Bunuel, Why can't we take b as 6 \(\sqrt{12}\) ?? we have 2 and 3 as prime factors here as well. Please explain. Thanks, Uma Uma, when we talk of factors, ONLY integers can have factors \(6\sqrt{12}=6*\sqrt{4*3}=12\sqrt{3}=12*1.732...\) and this is NOT an integer.. you cannot take 6 in isolation as other part \(\sqrt{12}\) is not an integer.. example \(6*0.5\), this will not have 2 and 3 as prime factors because 6*0.5=3, so only 3 hope it helps
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Math Expert
Joined: 02 Sep 2009
Posts: 47039

Re: Is b/3 an integer? [#permalink]
Show Tags
10 Jul 2018, 01:55
chetan2u wrote: umabharatigudipalli wrote: Bunuel wrote: Is b/3 an integer?(1) (b^2−9)/3 is an integer. Given that \(\frac{b^29}{3}=integer\) > \(\frac{b^2}{3}3=integer\) > \(\frac{b^2}{3}=integer\). Now, if \(b=0\), then \(\frac{b}{3}=0=integer\) but if \(b=\sqrt{3}\), then \(\frac{b}{3}\neq{integer}\). Not sufficient. (2) p and p + 1 are prime factors of b. Since both \(p\) and \(p+1\) are primes, then \(p=2\) and \(p+1=3\). Thus we have that \(b\) is a multiple of 3. Sufficient. Answer: B. P.S. Please read carefully and follow: http://gmatclub.com/forum/rulesforpos ... 33935.html Pay attention to the rule #3: the name of the topic (subject field) MUST be the first 40 characters (~the first two sentences) of the question. Hi Bunuel, Why can't we take b as 6 \(\sqrt{12}\) ?? we have 2 and 3 as prime factors here as well. Please explain. Thanks, Uma Uma, when we talk of factors, ONLY integers can have factors \(6\sqrt{12}=6*\sqrt{4*3}=12\sqrt{3}=12*1.732...\) and this is NOT an integer.. you cannot take 6 in isolation as other part \(\sqrt{12}\) is not an integer.. example \(6*0.5\), this will not have 2 and 3 as prime factors because 6*0.5=3, so only 3 hope it helps On the GMAT when we are told that \(a\) is divisible by \(b\) (or which is the same: "\(a\) is multiple of \(b\)", or "\(b\) is a factor of \(a\)"), we can say that:1. \(a\) is an integer; 2. \(b\) is an integer; 3. \(\frac{a}{b}=integer\). Hope it helps.
_________________
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




Re: Is b/3 an integer?
[#permalink]
10 Jul 2018, 01:55






