Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to pre-think assumptions and solve the most challenging questions in less than 2 minutes.
Re: What is the value of the two-digit positive integer n?
[#permalink]
Show Tags
18 Mar 2013, 03:05
20
9
alex1233 wrote:
What is the value of the two-digit positive integer n?
(1) When n is divided by 5, the remainder is equal to the tens digit of n.
(2) When n is divided by 9, the remainder is equal to the tens digit of n.
Any help on this one would be much appreciated! Thanks
Let's take each statement at a time.
(1) When n is divided by 5, the remainder is equal to the tens digit of n. Think of a two digit number which is divisible by 5 - say 15. The remainder should be 1 so say n = 16. Think of another number which is divisible by 5 - say 25. The remainder should be 2 so say n = 27 There will be more such numbers so we can see that this is certainly not sufficient.
(2) When n is divided by 9, the remainder is equal to the tens digit of n. Think of a two digit number which is divisible by 9 - say 18. The remainder should be 1 so say n = 19. Think of another number which is divisible by 9 - say 27. The remainder should be 2 so say n = 29 There will be more such numbers so we can see that this is certainly not sufficient.
What do we do when we consider both statements together? We need to think of a number divisible by both 5 and 9, say 45 (their LCM). The remainder should be 4 so add 4 to 45 to get n = 49 Think of another number divisible by both which will be the next multiple of 45 i.e. 90. The remainder should be 9 but when we divide a number by 5, the remainder cannot be greater than 4. So n cannot be 99. Hence, there is only one such two digit number i.e. n = 49.
Answer (C)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Re: What is the value of the two-digit positive integer n?
[#permalink]
Show Tags
18 Mar 2013, 12:21
clearly statement 1 leads to many options and same to statement 2
now taking both the statements together.
it should be a no. which is common multiple of both 5 and 9 and also is 2 digit no. which has 10th place digit as reminder... we have 9x5=45 so for reminder to be 4 the no. should be 49, which gives us reminder as 4. no other no. satisfies all the criteria mentioned in question.
clearly option C is answer
_________________
giving kudos is the best thing you can do for me..
Re: What is the value of the two-digit positive integer n?
[#permalink]
Show Tags
27 Jun 2013, 06:38
2
alex1233 wrote:
What is the value of the two-digit positive integer n?
(1) When n is divided by 5, the remainder is equal to the tens digit of n.
(2) When n is divided by 9, the remainder is equal to the tens digit of n.
Any help on this one would be much appreciated! Thanks
we really dont need any calculation in this question. This is quite conceptual. we know remainder of any number when divided by 5 can only be 1,2,3 or 4.
Its given remainder equals to tens digit. we'll take the four remainders one by one.
1 >> we know tens digit should be 1 so number could only be 11 OR 16. 2 >> we know tens digit should be 2 so number could only be 22 OR 27 3 >> we know tens digit should be 3 so number could only be 33 OR 38. 4 >> we know tens digit should be 4 so number could only be 44 OR 49.
we cant get an answer from st. 1.
we can do same reasoning for st. 2 1 >> 10,19 2 >> 20,29 3 >> 30,39 4 >> 40,49 .... so on .. also no point going forward. we found a match from st. 1(and in st. 1 we wrote all the possible outcomes, so possibility of another such no. is zero) .. the no. is 49.
Re: What is the value of the two-digit positive integer n?
[#permalink]
Show Tags
15 Feb 2014, 16:30
VeritasPrepKarishma wrote:
alex1233 wrote:
What is the value of the two-digit positive integer n?
(1) When n is divided by 5, the remainder is equal to the tens digit of n.
(2) When n is divided by 9, the remainder is equal to the tens digit of n.
Any help on this one would be much appreciated! Thanks
Let's take each statement at a time.
(1) When n is divided by 5, the remainder is equal to the tens digit of n. Think of a two digit number which is divisible by 5 - say 15. The remainder should be 1 so say n = 16. Think of another number which is divisible by 5 - say 25. The remainder should be 2 so say n = 27 There will be more such numbers so we can see that this is certainly not sufficient.
(2) When n is divided by 9, the remainder is equal to the tens digit of n. Think of a two digit number which is divisible by 9 - say 18. The remainder should be 1 so say n = 19. Think of another number which is divisible by 9 - say 27. The remainder should be 2 so say n = 29 There will be more such numbers so we can see that this is certainly not sufficient.
What do we do when we consider both statements together? We need to think of a number divisible by both 5 and 9, say 45 (their LCM). The remainder should be 4 so add 4 to 45 to get n = 49 Think of another number divisible by both which will be the next multiple of 45 i.e. 90. The remainder should be 9 but when we divide a number by 5, the remainder cannot be greater than 4. So n cannot be 99. Hence, there is only one such two digit number i.e. n = 49.
Answer (C)
Hi Karishma,
I'm a bit stucked with both statements together. How do you know that the remainder has to be 4 and not 1,2 or 3?
Re: What is the value of the two-digit positive integer n?
[#permalink]
Show Tags
16 Feb 2014, 20:55
1
jlgdr wrote:
VeritasPrepKarishma wrote:
alex1233 wrote:
What is the value of the two-digit positive integer n?
(1) When n is divided by 5, the remainder is equal to the tens digit of n.
(2) When n is divided by 9, the remainder is equal to the tens digit of n.
Any help on this one would be much appreciated! Thanks
Let's take each statement at a time.
(1) When n is divided by 5, the remainder is equal to the tens digit of n. Think of a two digit number which is divisible by 5 - say 15. The remainder should be 1 so say n = 16. Think of another number which is divisible by 5 - say 25. The remainder should be 2 so say n = 27 There will be more such numbers so we can see that this is certainly not sufficient.
(2) When n is divided by 9, the remainder is equal to the tens digit of n. Think of a two digit number which is divisible by 9 - say 18. The remainder should be 1 so say n = 19. Think of another number which is divisible by 9 - say 27. The remainder should be 2 so say n = 29 There will be more such numbers so we can see that this is certainly not sufficient.
What do we do when we consider both statements together? We need to think of a number divisible by both 5 and 9, say 45 (their LCM). The remainder should be 4 so add 4 to 45 to get n = 49 Think of another number divisible by both which will be the next multiple of 45 i.e. 90. The remainder should be 9 but when we divide a number by 5, the remainder cannot be greater than 4. So n cannot be 99. Hence, there is only one such two digit number i.e. n = 49.
Answer (C)
Hi Karishma,
I'm a bit stucked with both statements together. How do you know that the remainder has to be 4 and not 1,2 or 3?
Could you please elaborate on this?
Many thanks! Cheers J
The tens digit of 45 is 4. 45 is the first positive two digit number which is divisible by both 5 and 9. So when n is divided by 5 or 9, the remainder should be 4 so n should be 49. The remainder will be 4 which is the tens digit of 49.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Re: What is the value of the two-digit positive integer n?
[#permalink]
Show Tags
23 Feb 2017, 04:56
PROMPT ANALYSIS N is a 2 digit number
SUPERSET The value of n could be in the range 10 to 99
TRANSLATION In order to find the value of n, we need: 1# Exact value of n 2# equations to find the value of n.
STATEMENT ANALYSIS St 1: we can say that n could be 11, 22, 33, 44. INSUFFICIENT. Hence option a and d eliminated. St 2: we can say that n could be 19, 29, 39, 49, 59, 69, 79, 89. INSUFFICIENT. Hence option b eliminated.
St 1 & St 2: there is no number in common which can follow both the statements. INSUFFICIENT.
Re: What is the value of the two-digit positive integer n?
[#permalink]
Show Tags
21 Dec 2018, 20:58
VeritasKarishma wrote:
alex1233 wrote:
What is the value of the two-digit positive integer n?
(1) When n is divided by 5, the remainder is equal to the tens digit of n.
(2) When n is divided by 9, the remainder is equal to the tens digit of n.
Any help on this one would be much appreciated! Thanks
Let's take each statement at a time.
(1) When n is divided by 5, the remainder is equal to the tens digit of n. Think of a two digit number which is divisible by 5 - say 15. The remainder should be 1 so say n = 16. Think of another number which is divisible by 5 - say 25. The remainder should be 2 so say n = 27 There will be more such numbers so we can see that this is certainly not sufficient.
(2) When n is divided by 9, the remainder is equal to the tens digit of n. Think of a two digit number which is divisible by 9 - say 18. The remainder should be 1 so say n = 19. Think of another number which is divisible by 9 - say 27. The remainder should be 2 so say n = 29 There will be more such numbers so we can see that this is certainly not sufficient.
What do we do when we consider both statements together? We need to think of a number divisible by both 5 and 9, say 45 (their LCM). The remainder should be 4 so add 4 to 45 to get n = 49 Think of another number divisible by both which will be the next multiple of 45 i.e. 90. The remainder should be 9 but when we divide a number by 5, the remainder cannot be greater than 4. So n cannot be 99. Hence, there is only one such two digit number i.e. n = 49.
Answer (C)
Quote:
can you elaborate as to how 99 cannot be the number. I did not understand that part
When you divide a number by any divisor say D, the remainder MUST be less than D. Say if you divide a number by 5, can the remainder be 7? No. Then 5 will go another time in it and the remainder will be 2. So remainders can be 0/1/2/3/4 only.
Since N when divided by 5 gives remainder which is tens digit of N, the tens digit of N must be one of 0/1/2/3/4 only. So it cannot be 9 and hence 99 cannot be N.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
What is the value of the two-digit positive integer n?
[#permalink]
Show Tags
22 Dec 2018, 15:05
VeritasKarishma wrote:
alex1233 wrote:
What is the value of the two-digit positive integer n?
(1) When n is divided by 5, the remainder is equal to the tens digit of n.
(2) When n is divided by 9, the remainder is equal to the tens digit of n.
Any help on this one would be much appreciated! Thanks
Let's take each statement at a time.
(1) When n is divided by 5, the remainder is equal to the tens digit of n. Think of a two digit number which is divisible by 5 - say 15. The remainder should be 1 so say n = 16. Think of another number which is divisible by 5 - say 25. The remainder should be 2 so say n = 27 There will be more such numbers so we can see that this is certainly not sufficient.
(2) When n is divided by 9, the remainder is equal to the tens digit of n. Think of a two digit number which is divisible by 9 - say 18. The remainder should be 1 so say n = 19. Think of another number which is divisible by 9 - say 27. The remainder should be 2 so say n = 29 There will be more such numbers so we can see that this is certainly not sufficient.
What do we do when we consider both statements together? We need to think of a number divisible by both 5 and 9, say 45 (their LCM). The remainder should be 4 so add 4 to 45 to get n = 49 Think of another number divisible by both which will be the next multiple of 45 i.e. 90. The remainder should be 9 but when we divide a number by 5, the remainder cannot be greater than 4. So n cannot be 99. Hence, there is only one such two digit number i.e. n = 49.
Answer (C)
VeritasKarishma I didn't understand why remainder cannot be greater than 4. If our new divisor is 45, then shouldn't remainder be < 45? I mean, we aren't dividing 99 by 5, we are dividing 99 by 45 (LCM of 9 and 5), right? In that case, we still get a remainder of 9, which is the tens digit of n = 99.
I'm sure there's a gap in my understanding, but unable to analyse what it is exactly.
_________________
We learn permanently when we teach, We grow infinitely when we share.
Re: What is the value of the two-digit positive integer n?
[#permalink]
Show Tags
27 Feb 2019, 10:16
Conceptual solution
(1) n=5q+d; 10d+u=5q+d; u=5q-9d; d=5q/9-u/9. We know d=(1,2,3 or4). Not sufficient.
(2) n=9p+d; 10d+u=9p+d; u=9(p-d). --> u=0 or 9. d=p-u/9. Not sufficient.
(1)+(2) test u=0: by (1), then d=5*(Q/9). Q/9 must be integer. d cannot be multiple of 5 (can't be 0, can't be 5). u can't be 0 -> u=9. by (2), d=p-1; d=(5/9)*q-1 --> p=5/9q; d=5q/9-1. d must be bigger than 0, lower than 5. -> q/9 must be equal to 1 --> 5q/9=5. d=5-1=4.
49. (C)
gmatclubot
Re: What is the value of the two-digit positive integer n?
[#permalink]
27 Feb 2019, 10:16
close
60% (02:35) correct 
