November 22, 2018 November 22, 2018 10:00 PM PST 11:00 PM PST Mark your calendars  All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA) November 24, 2018 November 24, 2018 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
Author 
Message 
TAGS:

Hide Tags

Manager
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 139
Location: India
Concentration: Finance, International Business
WE: Information Technology (Investment Banking)

If the integers a and n are greater than 1 and the product
[#permalink]
Show Tags
Updated on: 16 Aug 2015, 15:11
Question Stats:
55% (01:02) correct 45% (00:55) wrong based on 1153 sessions
HideShow timer Statistics
If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, what is the value of a? (1) a^n = 64 (2) n = 6
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by subhajeet on 11 May 2012, 05:35.
Last edited by Bunuel on 16 Aug 2015, 15:11, edited 1 time in total.
Edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 50730

Re: If the integers a and n are greater than 1 and the product
[#permalink]
Show Tags
11 May 2012, 05:38
subhajeet wrote: If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, what is the value of a? (1) a^n = 64
(2) n = 6
Can anyone help me with this question. How is B the correct answer. Prime factorization would be the best way to attack such kind of questions. Given: \(a^n*k=8!=2^7*3^2*5*7\). Question: \(a=?\) (1) \(a^n=64=2^6=4^3=8^2\), so \(a\) could be 2, 4, or 8. Not sufficient. (2) \(n=6\) > the only integer (more than 1), which is a factor of 8!, and has the power of 6 (at least) is 2, hence \(a=2\). Sufficient. Answer: B.
_________________
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




Senior Manager
Joined: 13 Aug 2012
Posts: 431
Concentration: Marketing, Finance
GPA: 3.23

Re: If the integers a and n are greater than 1 and the product
[#permalink]
Show Tags
21 Jan 2013, 22:36
This one is a fun question (a good practice of our understanding of factors)! Analyze the given first before delving into the statements. \(8*6*7*5*4*3*2*1 = a^n * R\) Statement (1): a^n = 64 \(8*6*7*5*4*3*2*1 = 64 * R\) 64 could be 2^6 or 8^2. In 8!, it contains at least 6 factors of 2. In 8!, it also contains 2 factors of 8. Thus, a could be 2 or 8. Thus, INSUFFICIENT. Statement (2): n = 6 Let us analyze 8! = 8*7*6*5*4*3*2*1. How many prime factors have at least 6 factors in 8!. Let us start with a = 2. YES! Let us then try a=3. NO! We are certain that 2 has the most number of factors in 8! and it has at least 6. SUFFICIENT. a = 2 AnsweR: B
_________________
Impossible is nothing to God.




Manager
Joined: 02 Jun 2011
Posts: 130

Re: If the integers a and n are greater than 1 and the product
[#permalink]
Show Tags
14 May 2012, 01:41
Bunuel wrote: subhajeet wrote: If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, what is the value of a? (1) a^n = 64
(2) n = 6
Can anyone help me with this question. How is B the correct answer. Prime factorization would be the best way to attack such kind of questions. Given: \(a^n*k=8!=2^7*3^2*5*7\). Q: \(a=?\) (1) \(a^n=64=2^6=4^3=8^2\), so \(a\) can be 2, 4, or 8. Not sufficient. (2) \(n=6\) > the only integer (more than 1), which is the factor of 8!, and has the power of 6 (at least) is 2, hence \(a=2\). Sufficient. Answer: B. Dear Bunuel, OA is B but why B? Kindly tell the source from where you get all these number properties/Prime no. properties? If its your Brain then only the explaination for the above will do ! All DS are on Number Properties and i am doing silly mistakes. i opted 'C' Thanx



Math Expert
Joined: 02 Sep 2009
Posts: 50730

Re: If the integers a and n are greater than 1 and the product
[#permalink]
Show Tags
14 May 2012, 01:48
kashishh wrote: Bunuel wrote: subhajeet wrote: If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, what is the value of a? (1) a^n = 64
(2) n = 6
Can anyone help me with this question. How is B the correct answer. Prime factorization would be the best way to attack such kind of questions. Given: \(a^n*k=8!=2^7*3^2*5*7\). Q: \(a=?\) (1) \(a^n=64=2^6=4^3=8^2\), so \(a\) can be 2, 4, or 8. Not sufficient. (2) \(n=6\) > the only integer (more than 1), which is the factor of 8!, and has the power of 6 (at least) is 2, hence \(a=2\). Sufficient. Answer: B. Dear Bunuel, OA is B but why B? Kindly tell the source from where you get all these number properties/Prime no. properties? If its your Brain then only the explaination for the above will do ! All DS are on Number Properties and i am doing silly mistakes. i opted 'C' Thanx Check Number Theory chapter of Math Book: mathnumbertheory88376.htmlHope 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



Manager
Joined: 18 Oct 2011
Posts: 87
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01302013
GPA: 3.3

Re: If the integers a and n are greater than 1 and the product
[#permalink]
Show Tags
22 Jan 2013, 12:22
product of the first 8 integers is: (2^8)(3^2)(5)(7)
Statement 1: a^n = 64. this means a could equal 2,4, or 8 because we don't know what n is. Not sufficient. Statement 2: if n = 6 the only possible value for a is 2 as the product of the first 8 integers does not include any other number raised to the 6th power. Sufficient



Intern
Status: Break IT
Joined: 12 Jun 2011
Posts: 3
Location: USA
Schools: ISB
WE 1: 4

Re: If the integers a and n are greater than 1 and the product
[#permalink]
Show Tags
09 May 2013, 17:15
i have a question here, what if n = 2 or 3? would the answer be E? or C?



Math Expert
Joined: 02 Sep 2009
Posts: 50730

Re: If the integers a and n are greater than 1 and the product
[#permalink]
Show Tags
10 May 2013, 00:17



Manager
Joined: 01 Nov 2016
Posts: 66
Concentration: Technology, Operations

Re: If the integers a and n are greater than 1 and the product
[#permalink]
Show Tags
24 Oct 2017, 19:30
I don't think this question is written well. I get this part: Quote: If the integers a and n are greater than 1 So there are two integers, a and n. They are both greater than 1, Got it. The problem is I don't get this part: Quote: and the product of the first 8 positive integers is a multiple of a^n The product of the first 8 positive integers OF WHAT? What are we multiplying? a and n together? Is there a set we are looking at?



Math Expert
Joined: 02 Sep 2009
Posts: 50730

Re: If the integers a and n are greater than 1 and the product
[#permalink]
Show Tags
24 Oct 2017, 22:29



Manager
Joined: 01 Nov 2016
Posts: 66
Concentration: Technology, Operations

If the integers a and n are greater than 1 and the product
[#permalink]
Show Tags
26 Oct 2017, 12:29
Bunuel wrote: joondez wrote: I don't think this question is written well. I get this part: Quote: If the integers a and n are greater than 1 So there are two integers, a and n. They are both greater than 1, Got it. The problem is I don't get this part: Quote: and the product of the first 8 positive integers is a multiple of a^n The product of the first 8 positive integers OF WHAT? What are we multiplying? a and n together? Is there a set we are looking at? The product of the first 8 positive integers is 1*2*3*4*5*6*7*8. Check completer solution here: https://gmatclub.com/forum/iftheinteg ... l#p1084330In that case the question should be: Quote: If the integers a and n are greater than 1 and the product of the first 8 positive integers of all real numbers is a multiple of a^n, what is the value of a?
(1) a^n = 64
(2) n = 6



Math Expert
Joined: 02 Sep 2009
Posts: 50730

Re: If the integers a and n are greater than 1 and the product
[#permalink]
Show Tags
26 Oct 2017, 20:36
joondez wrote: In that case the question should be: Quote: If the integers a and n are greater than 1 and the product of the first 8 positive integers of all real numbers is a multiple of a^n, what is the value of a?
(1) a^n = 64
(2) n = 6 The question is correct as it is. The first 8 positive integers are 1, 2, 3, 4, 5, 6, 7, and 8. What does "of all real numbers" has to do here? Also, notice that this is an official question from GMAT Prep, so it's as correct as it gets.
_________________
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: 01 Nov 2016
Posts: 66
Concentration: Technology, Operations

Re: If the integers a and n are greater than 1 and the product
[#permalink]
Show Tags
27 Oct 2017, 09:05
When the question asked for the first 8 positive numbers, it was clearly describing a set. However, it wasn't clear to me what set they were describing. I spent time wondering if they were describing a set of "a" multiple, "n" multiples, or "a^n" multiples. There are many other GMAT questions were the wording is extremely specific but for this question you had to assume that we were looking at all real numbers, which is not always the case for other GMAT questions. So to me this is a very poorly worded question. You are very good at GMAT questions so you may have been able to recognize the question pattern right away, but for someone who is unable to make assumptions based on the question maker's mind, this question was not solvable. And the fact that this is a GMATPrep question does not make it infallible, in fact I have done other GMATPrep questions where even you yourself have stated that they made a mistake



Math Expert
Joined: 02 Sep 2009
Posts: 50730

Re: If the integers a and n are greater than 1 and the product
[#permalink]
Show Tags
27 Oct 2017, 09:09
joondez wrote: When the question asked for the first 8 positive numbers, it was clearly describing a set. However, it wasn't clear to me what set they were describing. I spent time wondering if they were describing a set of "a" multiple, "n" multiples, or "a^n" multiples. There are many other GMAT questions were the wording is extremely specific but for this question you had to assume that we were looking at all real numbers, which is not always the case for other GMAT questions. So to me this is a very poorly worded question. You are very good at GMAT questions so you may have been able to recognize the question pattern right away, but for someone who is unable to make assumptions based on the question maker's mind, this question was not solvable. And the fact that this is a GMATPrep question does not make it infallible, in fact I have done other GMATPrep questions where even you yourself have stated that they made a mistake Sorry but this does not make sense. "The product of the first 8 positive integers" cannot possible mean anything but 1*2*3*4*5*6*7*8.
_________________
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



Director
Joined: 14 Dec 2017
Posts: 512

Re: If the integers a and n are greater than 1 and the product
[#permalink]
Show Tags
12 Jun 2018, 03:23
subhajeet wrote: If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, what is the value of a? (1) a^n = 64
(2) n = 6 Given \(a, n > 1\), \(8! = a^n * K\) so we have \(2^7 * 3^2 * 5 * 7 = a^n * K\).......(i) Statement 1: \(a^n = 64\), hence , we have \(a^n = 2^6\) or \(8^2\) or \(4^3\), therefore \((2^6) * 2 * 3^2 * 5 * 7 = a^n * K\), \(a = 2, n = 6\) \((8^2) * 2 * 3^2 * 5 * 7 = a^n * K\), \(a = 8 , n = 2\) Hence, Statement 1 is Not Sufficient. Statement 2: \(n = 6\), hence we have from (i), that on factorization of \(8!\) the only integer greater than 1 & can accommodate \(6\) as its power is \(a = 2\). Hence, Statement 2 is Sufficient. Answer B. Thanks, GyM
_________________
New to GMAT Club  https://gmatclub.com/forum/newtogmatclubneedhelp271131.html#p2098335



Intern
Joined: 11 Jul 2018
Posts: 2

Re: If the integers a and n are greater than 1 and the product
[#permalink]
Show Tags
28 Aug 2018, 08:46
BunuelWe know that a^n is a factor of 8!. Hence you wrote, a^n (k) =8!=2^7 * 3^2 * 5 * 7 & according to st 2 as n = 6 we said that 2 in the only factor of 8! with power >=6. But my question is, what about the multiple "k"? What is for example, k=3^4 In that case, in a^n, the power of 3 will also be=6.



Manager
Joined: 06 Nov 2016
Posts: 61
Location: Viet Nam
Concentration: Strategy, International Business
GPA: 3.54

Re: If the integers a and n are greater than 1 and the product
[#permalink]
Show Tags
28 Aug 2018, 09:40
Bunuel wrote: subhajeet wrote: If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, what is the value of a? (1) a^n = 64
(2) n = 6
Can anyone help me with this question. How is B the correct answer. Prime factorization would be the best way to attack such kind of questions. Given: \(a^n*k=8!=2^7*3^2*5*7\). Question: \(a=?\) (1) \(a^n=64=2^6=4^3=8^2\), so \(a\) could be 2, 4, or 8. Not sufficient. (2) \(n=6\) > the only integer (more than 1), which is a factor of 8!, and has the power of 6 (at least) is 2, hence \(a=2\). Sufficient. Answer: B. Beautiful. I did the same way to solve this question, though it took me awhile to realize that prime factorization is the quickest way ?
_________________
（＾人＾）
GMATCLUB Search for tags
GMAC © Official Guides  The Master Directory + Links
Question Directory by Topic & Difficulty Problem Solving  Data Sufficiency  Sentence Correction  Critical Reasoning  Reading Comprehension
ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Intern
Joined: 30 Sep 2018
Posts: 2

Re: If the integers a and n are greater than 1 and the product
[#permalink]
Show Tags
31 Oct 2018, 14:53
Bunuel what about the multiple k is, for example, k=3^4 In that case, in a^n, the power of 3 will also be=6.



Director
Joined: 11 Feb 2015
Posts: 572

Re: If the integers a and n are greater than 1 and the product
[#permalink]
Show Tags
18 Nov 2018, 07:27
Doing the prime factorisation of 8! was the key to get this question right. Once you do so then you realise that only when a=2 then n could be 6. Very nice official question!!
_________________
"Please hit +1 Kudos if you like this post"
_________________ Manish
"Only I can change my life. No one can do it for me"




Re: If the integers a and n are greater than 1 and the product &nbs
[#permalink]
18 Nov 2018, 07:27






