Jul 21 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes Jul 20 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jul 26 08:00 AM PDT  09:00 AM PDT The Competition Continues  Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Ends July 26th Jul 27 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC
Author 
Message 
TAGS:

Hide Tags

Retired Moderator
Joined: 22 Aug 2013
Posts: 1435
Location: India

A positive integer X is a six digit number of the form
[#permalink]
Show Tags
08 Aug 2018, 22:46
Question Stats:
46% (02:28) correct 54% (02:33) wrong based on 50 sessions
HideShow timer Statistics
A positive integer X is a six digit number of the form ababbb where a and b are distinct digits. What is the value of a? (1) X is divisible by 9. (2) X is divisible by each integer from 1 to 5. Posted from my mobile device
Official Answer and Stats are available only to registered users. Register/ Login.



Intern
Joined: 01 Feb 2018
Posts: 2

Re: A positive integer X is a six digit number of the form
[#permalink]
Show Tags
08 Aug 2018, 23:29
amanvermagmat wrote: A positive integer X is a six digit number of the form ababbb where a and b are distinct digits. What is the value of a?
(1) X is divisible by 9.
(2) X is divisible by each integer from 1 to 5.
Posted from my mobile device The answer shall be C... Sent from my SMJ210F using GMAT Club Forum mobile app



Intern
Joined: 08 Aug 2018
Posts: 40
Location: India
GPA: 4
WE: Engineering (Energy and Utilities)

A positive integer X is a six digit number of the form
[#permalink]
Show Tags
09 Aug 2018, 01:31
St1: Insufficient as it gives no clue about the number other than divisible by 9 St2: Only clue that 120 is a factor of the number and last digit or b is 0. Hence the number is a0a000. But no conclusion can be drawn from St2. Insufficient.
Together St1 & St2, you know that sum of a+a should be divisible by 9 and a=9 only solution that satisfies the equation.
Answer is C



VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)

Re: A positive integer X is a six digit number of the form
[#permalink]
Show Tags
09 Aug 2018, 02:51
amanvermagmat wrote: A positive integer X is a six digit number of the form ababbb where a and b are distinct digits. What is the value of a?
(1) X is divisible by 9.
(2) X is divisible by each integer from 1 to 5.
Posted from my mobile device Question stem: b=? St1: X is divisible by 9 When sum of all the digits of an integer is divisible by 9, then the integer is divisible by 9. 2a+4b=9k, where k>1 (\(a\neq0\)) a) a=1, b=4 b) a=9, b=0 So many (a.b) pairs possible. Insufficient. St2: X is divisible by each integer from 1 to 5. a) when the unit digit of any number is zero, then that number is divisible by at least 1,2 ,and 5. b) when the last two digits of a number is divisible by 4, then that number is divisible by 4. Since, here the last two digits are 'b'. So '00' is divisible by 4. c) when the sum of all the digits of an integer is divisible by 3, then the integer is divisible by 3. Now a can be 3 or 6 or 9. Or, six digit number is divisible by LCM(1,2,3,4,5)=120. So, unit digit has to be 0. Or, b=0. Insufficient. Combining, the only possibility of (a.b) is (9,0). Ans. (C)
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



VP
Joined: 09 Mar 2016
Posts: 1273

Re: A positive integer X is a six digit number of the form
[#permalink]
Show Tags
09 Aug 2018, 03:26
PKN wrote: amanvermagmat wrote: A positive integer X is a six digit number of the form ababbb where a and b are distinct digits. What is the value of a?
(1) X is divisible by 9.
(2) X is divisible by each integer from 1 to 5.
Posted from my mobile device Question stem: b=? St1: X is divisible by 9 When sum of all the digits of an integer is divisible by 9, then the integer is divisible by 9. 2a+4b=9k, where k>1 (\(a\neq0\)) a) a=1, b=4 b) a=9, b=0 So many (a.b) pairs possible. Insufficient. St2: X is divisible by each integer from 1 to 5. a) when the unit digit of any number is zero, then that number is divisible by at least 1,2 ,and 5. b) when the last two digits of a number is divisible by 4, then that number is divisible by 4. Since, here the last two digits are 'b'. So '00' is divisible by 4. c) when the sum of all the digits of an integer is divisible by 3, then the integer is divisible by 3. Now a can be 3 or 6 or 9. Or, six digit number is divisible by LCM(1,2,3,4,5)=120. So, unit digit has to be 0. Or, b=0. Insufficient. Combining, the only possibility of (a.b) is (9,0). Ans. (C) Hi PKN can you please elaborate on statement one, the highlihted part. i didnt get the logic behind it 2a+4b=9k is it some formula for checking divisibility St1: X is divisible by 9 When sum of all the digits of an integer is divisible by 9, then the integer is divisible by 9. 2a+4b=9k,where k>1 (\(a\neq0\)) a) a=1, b=4 b) a=9, b=0



VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)

A positive integer X is a six digit number of the form
[#permalink]
Show Tags
09 Aug 2018, 03:38
dave13 wrote: PKN wrote: amanvermagmat wrote: A positive integer X is a six digit number of the form ababbb where a and b are distinct digits. What is the value of a?
(1) X is divisible by 9.
(2) X is divisible by each integer from 1 to 5.
Posted from my mobile device Question stem: b=? St1: X is divisible by 9 When sum of all the digits of an integer is divisible by 9, then the integer is divisible by 9. 2a+4b=9k, where k>1 (\(a\neq0\)) a) a=1, b=4 b) a=9, b=0 So many (a.b) pairs possible. Insufficient. St2: X is divisible by each integer from 1 to 5. a) when the unit digit of any number is zero, then that number is divisible by at least 1,2 ,and 5. b) when the last two digits of a number is divisible by 4, then that number is divisible by 4. Since, here the last two digits are 'b'. So '00' is divisible by 4. c) when the sum of all the digits of an integer is divisible by 3, then the integer is divisible by 3. Now a can be 3 or 6 or 9. Or, six digit number is divisible by LCM(1,2,3,4,5)=120. So, unit digit has to be 0. Or, b=0. Insufficient. Combining, the only possibility of (a.b) is (9,0). Ans. (C) Hi PKN can you please elaborate on statement one, the highlihted part. i didnt get the logic behind it 2a+4b=9k is it some formula for checking divisibility St1: X is divisible by 9 When sum of all the digits of an integer is divisible by 9, then the integer is divisible by 9. 2a+4b=9k,where k>1 (\(a\neq0\)) a) a=1, b=4 b) a=9, b=0 Hi dave13, Question maker has given us a 6digit integer Given 6digit ababbb. St1 holds when sum of all the digits of the given integer is divisible by 9. What is the sum of the digits? Isn't it a+b+a+b+b+b=2a+4b If I say 'x' is divisible by 'y', then 'x' is a multiple of 'y'. Hope you agree. Here, 2a+4b has to be divisible by 9. So, (2a+4b) has to be a multiple of 9. Since we don't know the value of multiplying factor, I have assigned it as k. So, 2a+4b=multiple of 9=9*k Hope it clarifies your query. Waiting for further queries(if any).
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Intern
Joined: 16 Aug 2018
Posts: 28
Concentration: General Management, Strategy

Re: A positive integer X is a six digit number of the form
[#permalink]
Show Tags
17 Aug 2018, 07:48
my approach: (1)divisible by 9: 2*a+4*b=9m, m is an integer a b m 1 4 2 2 8 4 insufficient (2)consider 2,3,4,5 since there're 2 and 5, b must be 0; 3 zeros at the end also means it's divisible by 4 divisible by 3: 2*a divisible by 3 means a is a multiple of 3. a can be 3,6,9; insufficient 1+2: only 9 ensures x is divisble by 9. so a=9




Re: A positive integer X is a six digit number of the form
[#permalink]
17 Aug 2018, 07:48






