Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60515

When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
02 Apr 2015, 06:09
Question Stats:
64% (02:39) correct 36% (02:32) wrong based on 515 sessions
HideShow timer Statistics
When positive integer n is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4 Kudos for a correct solution.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Math Expert
Joined: 02 Aug 2009
Posts: 8344

Re: When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
02 Apr 2015, 07:15
Bunuel wrote: When positive integer n is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
Kudos for a correct solution. the equation that can be formed is 13x+2=8y+5.. 13x3=8y... as we can see x can take only odd values as the RHS will always be even.. Also x can take values till 13 as 13*14>180.. now we have to substitue x as 1,3,5,7,9,11,13... once we find 7 fitting in , any other value need not be checked as every 4th value will give us answer so next value will be 15.. ans 1.. B
_________________




Manager
Joined: 06 Mar 2014
Posts: 220
Location: India
GMAT Date: 04302015

Re: When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
02 Apr 2015, 17:15
Bunuel wrote: When positive integer n is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
Kudos for a correct solution. \(N = 13q+2\) (possible values: 2,15,28,41,54,67,80, 93,106.... \(N = 8z+5\) (possible values: 5,13,21,29,37,45,53,61,69,77,85, 93 Therefore,\(N = (13*8)k+93\) \(N = 104k+93\) (possible values:93,197) Clearly only one value is possible that is less than 180. Answer:B




Retired Moderator
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 297

Re: When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
02 Apr 2015, 07:13
Bunuel wrote: When positive integer n is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
Kudos for a correct solution. n=13Q1+2 n=8Q2+5 13Q1+2=8Q2+5 13Q1=8Q2+3 When we list the multiples of 13, only when n=91 can we have a remainder of 3 when n is divided by 8. OR We will get a multiple of 13 only when Q2=11 Answer: B



Math Expert
Joined: 02 Aug 2009
Posts: 8344

Re: When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
02 Apr 2015, 07:17
AmoyV wrote: Bunuel wrote: When positive integer n is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
Kudos for a correct solution. n=13Q1+2 n=8Q2+5 13Q1+2=8Q2+5 13Q1=8Q2+3 When we list the multiples of 13, only when n=91 can we have a remainder of 3 when n is divided by 8. OR We will get a multiple of 13 only when Q2=11 Answer: B hi you do not have to check all multiples of 13.. the multiple has to be odd so Q1 has to be odd.. so check for only 1,3,5,7,9.. .. may save some time
_________________



Retired Moderator
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 297

Re: When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
02 Apr 2015, 07:59
chetan2u wrote: AmoyV wrote: Bunuel wrote: When positive integer n is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
Kudos for a correct solution. n=13Q1+2 n=8Q2+5 13Q1+2=8Q2+5 13Q1=8Q2+3 When we list the multiples of 13, only when n=91 can we have a remainder of 3 when n is divided by 8. OR We will get a multiple of 13 only when Q2=11 Answer: B hi you do not have to check all multiples of 13.. the multiple has to be odd so Q1 has to be odd.. so check for only 1,3,5,7,9.. .. may save some time Thanks for pointing that out.



Retired Moderator
Joined: 06 Jul 2014
Posts: 1214
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40

Re: When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
02 Apr 2015, 08:32
chetan2u wrote: AmoyV wrote: Bunuel wrote: When positive integer n is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
Kudos for a correct solution. n=13Q1+2 n=8Q2+5 13Q1+2=8Q2+5 13Q1=8Q2+3 When we list the multiples of 13, only when n=91 can we have a remainder of 3 when n is divided by 8. OR We will get a multiple of 13 only when Q2=11 Answer: B hi you do not have to check all multiples of 13.. the multiple has to be odd so Q1 has to be odd.. so check for only 1,3,5,7,9.. .. may save some time And we can save even more time: all numbers that will be multiple to 13 and 8+3 will be in periods 104 (13 * 8 = 104 ) so if our first number is 91 than next will be 91 + 104 = 195 and next 195 + 104 = 299 ans so on. And we know that we have diapason from 1 to 180 so 180  104 = 76 if we have one number that will be divisible on 13 and 8 + 3 and that number will be less that 76 than we have 2 numbers if we don't have such number before 76 than we have only one number in this diapason. for example we can solve the same task but change 8 + 3 on 8 + 4 the first number that will be divisible on 13 and 8 + 4 it's 52 this number before 76 so we have two numbers before 180 second number is 52 + 104 = 156 This is not very useful on this task but if we will have diapson not 1..180 but 1...800 for example it'll be very useful shortcut.
_________________



Manager
Joined: 26 May 2013
Posts: 91

Re: When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
03 Apr 2015, 10:07
chetan2u wrote: AmoyV wrote: Bunuel wrote: When positive integer n is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
Kudos for a correct solution. n=13Q1+2 n=8Q2+5 13Q1+2=8Q2+5 13Q1=8Q2+3 When we list the multiples of 13, only when n=91 can we have a remainder of 3 when n is divided by 8. OR We will get a multiple of 13 only when Q2=11 Answer: B hi you do not have to check all multiples of 13.. the multiple has to be odd so Q1 has to be odd.. so check for only 1,3,5,7,9.. .. may save some time That saves a ton of time. Is it because 8y+3 will always be odd ?



Math Expert
Joined: 02 Aug 2009
Posts: 8344

Re: When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
03 Apr 2015, 18:30
ak1802 wrote: chetan2u wrote: hi you do not have to check all multiples of 13.. the multiple has to be odd so Q1 has to be odd.. so check for only 1,3,5,7,9.. .. may save some time
That saves a ton of time. Is it because 8y+3 will always be odd ? hi ak1802, you are correct, 8y+3 will always be odd irrespective of the value of y... and that is why we check for odd values 1,3,5,7..
_________________



Director
Joined: 21 May 2013
Posts: 632

Re: When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
05 Apr 2015, 01:43
Bunuel wrote: When positive integer n is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
Kudos for a correct solution. The number should be of the form 13k+2 leaving a remainder of 5 when divided by 8. Calculating different mutilples of 13 i.e 13,26,39,52,65,78,91 Only 91 satisfies i.e 91+2=93 and 93 leaves a remainder of 5 when divided by 8. Answer=B



Math Expert
Joined: 02 Sep 2009
Posts: 60515

Re: When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
06 Apr 2015, 06:33
Bunuel wrote: When positive integer n is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
Kudos for a correct solution. MAGOOSH OFFICIAL SOLUTION:The LCM of 8 and 13 is 104. Hence there cannot be more than 2 such values less than 180. Options (D) and (E) are out of the window for sure. The number n should be of the following two forms: n = 8a + 5 n = 13b + 2 In a given bunch of numbers, there will be many more numbers of the form (8a + 5) and fewer of the form (13b + 2) so let’s start with a number of the form (13b + 2). If b = 0, n = 2. Is it of the form (8a + 5)? No. n/8 gives a remainder of 2, not 5. If b = 1, n = 15. Is it of the form (8a + 5)? No. n/8 gives a remainder of 7, not 5. If b = 2, n = 28. Is it of the form (8a + 5)? No. n/8 gives a remainder of 4, not 5. If b = 3, n = 41. Is it of the form (8a + 5)? No. n/8 gives a remainder of 1, not 5. If b = 4, n = 54. Is it of the form (8a + 5)? No. n/8 gives a remainder of 6, not 5. If b = 5, n = 67. Is it of the form (8a + 5)? No. n/8 gives a remainder of 3, not 5. If b = 6, n = 80. Is it of the form (8a + 5)? No. n/8 gives a remainder of 0, not 5. If b = 7, n = 93. Is it of the form (8a + 5)? Yes! n/8 gives a remainder of 5. The smallest value of n is 93. The next value of n = 93 + 104 = 197 i.e. greater than 180. Hence there is just one value of n less than 180. Answer: B.
_________________



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4863
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
24 Apr 2016, 01:36
Bunuel wrote: When positive integer n is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
Kudos for a correct solution. Possible Values of n will be FOR SET 13 ={ 15 , 28 , 41 , 54 , 67 , 80 , 93 , 106 , 119 , 132, 145, 158 , 171 } FOR SET 8 = { 13 , 21 , 29 , 37 , 45 , 53, 61 , 69 , 77, 85 ............. Go no further } For set 8 there is a patter to observe the numbers are all ODD numbers , but for set 13 the alternate numbers are Odd Numbers.... So, now check the odd numbers in set 13 which when divided by 8 leaves remainder 5 { Here start from 93 as you have already checked numbers upto 85 and no number is common } 93/8 = 11*8 + 5 { This is our number } Check further ( only the odd numbers ) you cant find any ODD number.... Hence we have only the number 93 which is common to both SET 13 and SET 8 , so this is our number !!Answer will be only one possible number and that is 93
_________________



VP
Joined: 07 Dec 2014
Posts: 1227

When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
Updated on: 29 Nov 2017, 20:05
When positive integer n is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
n=13q+2 n=8p+5 13q+2=8p+5➡ 13q3=8p the least value of q that will make 13q3 a multiple of 8=7 13*7+2=93 93 is least value of n next highest value of n=93+13*8=197, which is>180 thus, 93 is the only value of n<180 B
Originally posted by gracie on 31 Aug 2016, 17:12.
Last edited by gracie on 29 Nov 2017, 20:05, edited 2 times in total.



Current Student
Joined: 12 Aug 2015
Posts: 2550

Re: When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
04 Dec 2016, 02:38
Great Question. Here is what i did => n=13k+2 n=8k+5 combining the two equations above we can say that n=104k+93 n=> 93,93+104,93+2*104,... Clearly there is only one value of n<180. Hence B
_________________



Intern
Joined: 20 Jun 2016
Posts: 4
Location: United States (MA)
Concentration: Finance, Technology
GPA: 3.25

When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
29 Nov 2017, 01:00
I kind of noticed a minor shortcut with after reading the Divisibility Applied to Remainders post Quote: Now, let’s come back to our original question. We have a number n which when divided by 3 gives a remainder 1 and when divided by 7 gives a remainder 5. We can say the number is of the form:
n = 3a + 1 and n = 7b + 5
...
Can we say that the remainder in both the cases is (2) since we need another 2 to make complete groups of 3 and 7? When n is divided by 3 and the remainder obtained is 1, it is the same as saying the remainder is 2. n is 1 more than a multiple of 3 which means it is 2 less than the next multiple of 3. Therefore, we can say n = 3x – 2 and n = 7y – 2.
Now this is exactly like the situation we discussed above. When we divide n by 21, remainder will be 2 Taking the same principle we see that 13a + 2 = 8b + 5 However, if we add 2 to b, we're now an additional 11 units away from (8b + 5), as 5  (8*2) = 11 Similarly, if we take add 1 to a, we're now an additional 11 units away from (13a + 2), as 2  (13*1) = 11 So (13[a+1]  11) = (8[b+2]  11) or (13x  11) = (8y  11). The LCM(13, 8) is 104, so amongst the potential values of n it must follow the form (104q  11). Since n is a positive integer, q must be > 0 With q=1, n=93 With q=2, n=197: greater than our upper limit for the problem, leaving only 1 number that fits the question's criteria.



Manager
Joined: 30 Mar 2017
Posts: 114

When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
Updated on: 23 Jun 2018, 12:51
Trying over 5 numbers until finding the one that works seems inefficient. Here's what I did...
From the given info, we have these 2 equations: (1) n = 13x + 2 (2) n = 8y + 5
Note that the above are equivalent to: (1*) n = 13x  11 (2*) n = 8y  3
Thus, we have  13x  11 = 8y  3  13x = 8y + 8  13x = 8(y+1) So,  (y+1) has to be a multiple of 13, and  x has to be a multiple of 8
The smallest multiple of 13 is 13 (obviously), so if we substitute y = 12 into (2*), then we get n = 93, which is the smallest value of n. Similarly, if we substitute x = 8 into (1*), then we get the same answer, n = 93.
You can calculate the LCM of 8 and 13 (which is 104), and see that the next value of n is 197 (93 + 104). Or, since we found the smallest value of n by using x = 8 or y = 12, we can find the next value by using x = 16 (the next multiple of 8) or y = 25 (which would make y+1 the next multiple of 13). If we substitute x = 16 into (1*), we get n = 197. Similarly, if we substitute y = 25 into (2*), we get the same n = 197.
Originally posted by aserghe1 on 30 Dec 2017, 17:20.
Last edited by aserghe1 on 23 Jun 2018, 12:51, edited 1 time in total.



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2806

Re: When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
02 May 2018, 10:31
Bunuel wrote: When positive integer n is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4 We can create the equation: n = 13Q + 2 So n can be 2, 15, 28, 41, 54, 67, 80, 93, ... and n = 8Q + 5 So n can be 5, 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93, … We see that the first number that satisfies both conditions is 93. To find the other numbers, we can keep adding the LCM of 13 and 8, which is 13 x 8 = 104. Therefore, the next value that satisfies both conditions is 93 + 104 = 197. However, 197 is already greater than 180, so we only have one value, namely 93, that is less than 180 and satisfies both conditions. Answer: B
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



VP
Joined: 07 Dec 2014
Posts: 1227

When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
02 May 2018, 11:36
Bunuel wrote: When positive integer n is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4 assume a difference of 1 between quotients (n5)/8(n2)/13=1 ➡5n49=104 this doesn't work, but it tells us that 5n49 is a multiple of 104 with a units digit of 6 104*4=416 5n49=416 n=93, the least value of n next least value of n=93+13*8=197, which is>180 1 B



VP
Joined: 09 Mar 2016
Posts: 1225

Re: When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
08 Jun 2018, 12:22
Bunuel wrote: Bunuel wrote: When positive integer n is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
Kudos for a correct solution. MAGOOSH OFFICIAL SOLUTION:The LCM of 8 and 13 is 104. Hence there cannot be more than 2 such values less than 180. Options (D) and (E) are out of the window for sure. The number n should be of the following two forms: n = 8a + 5 n = 13b + 2 In a given bunch of numbers, there will be many more numbers of the form (8a + 5) and fewer of the form (13b + 2) so let’s start with a number of the form (13b + 2). If b = 0, n = 2. Is it of the form (8a + 5)? No. n/8 gives a remainder of 2, not 5. If b = 1, n = 15. Is it of the form (8a + 5)? No. n/8 gives a remainder of 7, not 5. If b = 2, n = 28. Is it of the form (8a + 5)? No. n/8 gives a remainder of 4, not 5. If b = 3, n = 41. Is it of the form (8a + 5)? No. n/8 gives a remainder of 1, not 5. If b = 4, n = 54. Is it of the form (8a + 5)? No. n/8 gives a remainder of 6, not 5. If b = 5, n = 67. Is it of the form (8a + 5)? No. n/8 gives a remainder of 3, not 5. If b = 6, n = 80. Is it of the form (8a + 5)? No. n/8 gives a remainder of 0, not 5. If b = 7, n = 93. Is it of the form (8a + 5)? Yes! n/8 gives a remainder of 5. The smallest value of n is 93. The next value of n = 93 + 104 = 197 i.e. greater than 180. Hence there is just one value of n less than 180. Answer: B. pushpitkc hello the method above is quite time consuming:) can you please suggest a shortcut to solve it ? many thanks



Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3294
Location: India
GPA: 3.12

Re: When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
Show Tags
08 Jun 2018, 12:47
dave13 wrote: Bunuel wrote: Bunuel wrote: When positive integer n is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
Kudos for a correct solution. MAGOOSH OFFICIAL SOLUTION:The LCM of 8 and 13 is 104. Hence there cannot be more than 2 such values less than 180. Options (D) and (E) are out of the window for sure. The number n should be of the following two forms: n = 8a + 5 n = 13b + 2 In a given bunch of numbers, there will be many more numbers of the form (8a + 5) and fewer of the form (13b + 2) so let’s start with a number of the form (13b + 2). If b = 0, n = 2. Is it of the form (8a + 5)? No. n/8 gives a remainder of 2, not 5. If b = 1, n = 15. Is it of the form (8a + 5)? No. n/8 gives a remainder of 7, not 5. If b = 2, n = 28. Is it of the form (8a + 5)? No. n/8 gives a remainder of 4, not 5. If b = 3, n = 41. Is it of the form (8a + 5)? No. n/8 gives a remainder of 1, not 5. If b = 4, n = 54. Is it of the form (8a + 5)? No. n/8 gives a remainder of 6, not 5. If b = 5, n = 67. Is it of the form (8a + 5)? No. n/8 gives a remainder of 3, not 5. If b = 6, n = 80. Is it of the form (8a + 5)? No. n/8 gives a remainder of 0, not 5. If b = 7, n = 93. Is it of the form (8a + 5)? Yes! n/8 gives a remainder of 5. The smallest value of n is 93. The next value of n = 93 + 104 = 197 i.e. greater than 180. Hence there is just one value of n less than 180. Answer: B. pushpitkc hello the method above is quite time consuming:) can you please suggest a shortcut to solve it ? many thanks Hey dave13Since n when divided by 13 gives us a remainder of 2, we can say that n = 13x + 2 n = 13x + 2. Now, n can take values 2, 15, 28, 41, 54, 67, 80, 93, ... Since n when divided by 8 gives us a remainder of 5, we can say that n = 8x + 5 n = 8x + 5. Now, n can take values 5, 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93, … As you see, 93 is the very first common number in both the lists. The next number will be when LCM(8,13) = 104 is added to 93. Only when n = 93+104 = 197, will both the lists(13x + 2),(8x + 5) have the same number. Hope this helps you!
_________________
You've got what it takes, but it will take everything you've got




Re: When positive integer n is divided by 13, the remainder is 2. When n
[#permalink]
08 Jun 2018, 12:47



Go to page
1 2
Next
[ 24 posts ]



