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:
Re: If x and y are positive integers and n = 5^x + 7^(y + 15), what is the
[#permalink]
Show Tags
24 Oct 2014, 00:42
1
2
Bunuel wrote:
Tough and Tricky questions: Remainders.
If x and y are positive integers and n = 5^x + 7^(y + 15), what is the units digit of n?
(1) y = 2x – 15 (2) y^2 – 6y + 5 = 0
Sol:n = 5^x + 7^(y + 15)
Note that 5^ (any positive Integer) gives unit digit of 5...So we need to know only y to be able solve the problem..
Cylcity of 7 is 4
7^1=7 7^2=49 7^3=343 7^4=XXX1
7^5=XXXX7
St 1 says y=2x-15 or y+15=2x..thus we know power of 7 in the expression is even so unit digit for 7^(y+15) will be =9 or 1.. We have 2 answers possible for unit digit of n i.e 5+9=14(unit digit) or 5+1=6.
Not sufficient
St 2 says gives value of y=1,5 so we have either 7^16 or 7^20...for each expression unit digit is 1..
Sufficient
Ans B
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Re: If x and y are positive integers and n = 5^x + 7^(y + 15), what is the
[#permalink]
Show Tags
09 Aug 2017, 15:17
Hi.
I did this question and I don't understand why the answers ignore the units digit of 5^x.
if x is even, the units of 5^x is 0, but if x is odd, it is 5. The question is about the units of n, not 7^(y+15), and only with statement (2) you don't have information about x.
Re: If x and y are positive integers and n = 5^x + 7^(y + 15), what is the
[#permalink]
Show Tags
07 Nov 2017, 11:10
Edivar wrote:
Hi.
I did this question and I don't understand why the answers ignore the units digit of 5^x.
if x is even, the units of 5^x is 0, but if x is odd, it is 5. The question is about the units of n, not 7^(y+15), and only with statement (2) you don't have information about x.
If x is a positive integer, the units digit of \(5^x\) is always 5: 5^1 = 5, 5^2 = 25, 5^3 = 125, 5^4 = 625, ... I think you are mixing \(5^x\) (5 to the power of x) with \(5x\) (5 multiplied by x).
_________________
If x and y are positive integers and n = 5^x + 7^(y + 15), what is the
[#permalink]
Show Tags
18 Dec 2017, 01:51
Bunuel wrote:
Tough and Tricky questions: Remainders.
If x and y are positive integers and \(n = 5^x + 7^{(y + 15)}\), what is the units digit of n?
(1) \(y = 2x – 15\)
(2) \(y^2 – 6y + 5 = 0\)
Can you please tell me, what would be the answer if roots of quadratic equation were (2,1)? I believe, answer should be B. Even in this new case we can derive value for (n), however, unit digit for 7 will not match (as in the present case when roots are 5,1).
Re: If x and y are positive integers and n = 5^x + 7^(y + 15), what is the
[#permalink]
Show Tags
18 Dec 2017, 02:33
1
anubhavece wrote:
Bunuel wrote:
Tough and Tricky questions: Remainders.
If x and y are positive integers and \(n = 5^x + 7^{(y + 15)}\), what is the units digit of n?
(1) \(y = 2x – 15\)
(2) \(y^2 – 6y + 5 = 0\)
Can you please tell me, what would be the answer if roots of quadratic equation were (2,1)? I believe, answer should be B. Even in this new case we can derive value for (n), however, unit digit for 7 will not match (as in the present case when roots are 5,1).
hi..
In this case the statement II would read \(y^2-3y+2=0\) so when y = 1 or 2, the units digit will change.. in \(n = 5^x + 7^{(y + 15)}\).. 5^x will always give you 5 \(7^{(y+15)}\) will become 7^(16) or 7^(17) 7^16 = 7^(4*4+0) so will give you same units digit as 7^4 or 1 7^17 will give 7^(4*4+1) so will give same units digit as 7^1 or 7 so ans will be 5+1=6 OR 5+7=12 or 2 thus insuff
_________________
Re: If x and y are positive integers and n = 5^x + 7^(y + 15), what is the
[#permalink]
Show Tags
18 Dec 2017, 02:37
chetan2u wrote:
anubhavece wrote:
Bunuel wrote:
Tough and Tricky questions: Remainders.
If x and y are positive integers and \(n = 5^x + 7^{(y + 15)}\), what is the units digit of n?
(1) \(y = 2x – 15\)
(2) \(y^2 – 6y + 5 = 0\)
Can you please tell me, what would be the answer if roots of quadratic equation were (2,1)? I believe, answer should be B. Even in this new case we can derive value for (n), however, unit digit for 7 will not match (as in the present case when roots are 5,1).
hi..
In this case the statement II would read \(y^2-3y+2=0\) so when y = 1 or 2, the units digit will change.. in \(n = 5^x + 7^{(y + 15)}\).. 5^x will always give you 5 \(7^{(y+15)}\) will become 7^(16) or 7^(17) 7^16 = 7^(4*4+0) so will give you same units digit as 7^4 or 1 7^17 will give 7^(4*4+1) so will give same units digit as 7^1 or 7 so ans will be 5+1=6 OR 5+7=12 or 2 thus insuff
Ok Thanks a lot My Bad ..... I forgot that the purpose in DS is not just to find a answer but also remove ambiguity.
If x and y are positive integers and n = 5^x + 7^(y + 15), what is the
[#permalink]
Show Tags
18 Dec 2017, 06:23
Bunuel wrote:
Tough and Tricky questions: Remainders.
If x and y are positive integers and \(n = 5^x + 7^{(y + 15)}\), what is the units digit of n?
(1) \(y = 2x – 15\)
(2) \(y^2 – 6y + 5 = 0\)
Question : Unit Digit of n = ?
Given: \(n = 5^x + 7^{(y + 15)}\)
Point to Note: \(5^x\) will always have unit digit 5 for any positive integer value of x (as given) Hence, Calculating value of x is completely immaterial for us
All we need is the unit digit of \(7^{(y + 15)}\) to find the unit digit of n
Statement 1: \(y = 2x – 15\)
\(7^{(y + 15)}\) becomes \(7^{(2x)}\) for x = 1, \(7^{(2x)}\) will have unit digit = 9 for x = 2, \(7^{(2x)}\) will have unit digit = 1
NOT SUFFICIENT
Statement 2: \(y^2 – 6y + 5 = 0\)
i.e. y = 1 or 5
for y = 1, \(7^{(y+15)}\) will have unit digit = 1 for y = 5, \(7^{(y+15)}\) will have unit digit = 1
SUFFICIENT
Answer: option B
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
Re: If x and y are positive integers and n = 5^x + 7^(y + 15), what is the
[#permalink]
Show Tags
05 Oct 2018, 09:38
Bunuel wrote:
Tough and Tricky questions: Remainders.
If x and y are positive integers and \(n = 5^x + 7^{(y + 15)}\), what is the units digit of n?
(1) \(y = 2x – 15\)
(2) \(y^2 – 6y + 5 = 0\)
given that x and y are positive integers they are >0
\(5^1\) has a unit digit of 5 \(5^2\) has a unit digit of 5. This means that regardless of the exponential power of 5 it will always have a digit of 5, as long as the power is a positive integer.
So we are interested in knowing the y value.
Statement 1) does not provide us any information.
Insufficient
Statement 2) \(y^2 – 6y + 5 = 0\)
(y-5)(y-1) = 0 y = 1 or 5
The unit digit of powers of 7 are below. \(7^1\)=7 \(7^2 = 49\) \(7^3 = 343\) \(7^4 = 2401\)
This cycle repeats in multiples of 4, so 8,12,16,20 would have a unit digit of 1.
if y =1 then the power is 16, meaning it will have a units digit of 1 if y = 5 then the power is 20, meaning again it will have a digit of 1.
sufficient.
B is the answer.
gmatclubot
Re: If x and y are positive integers and n = 5^x + 7^(y + 15), what is the &nbs
[#permalink]
05 Oct 2018, 09:38
close
66% (01:36) correct 
