Last visit was: 08 Jul 2025, 23:59 It is currently 08 Jul 2025, 23:59
Close
GMAT Club Daily Prep
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.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 8 July 2025
Posts: 102,597
Own Kudos:
Given Kudos: 97,452
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,597
Kudos: 739,643
 [47]
4
Kudos
Add Kudos
43
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
WoundedTiger
Joined: 25 Apr 2012
Last visit: 25 Sep 2024
Posts: 523
Own Kudos:
2,479
 [8]
Given Kudos: 740
Location: India
GPA: 3.21
WE:Business Development (Other)
Products:
Posts: 523
Kudos: 2,479
 [8]
6
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
General Discussion
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 8 July 2025
Posts: 102,597
Own Kudos:
739,643
 [3]
Given Kudos: 97,452
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,597
Kudos: 739,643
 [3]
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
thefibonacci
Joined: 22 Jan 2014
Last visit: 30 Jan 2019
Posts: 130
Own Kudos:
260
 [4]
Given Kudos: 212
WE:Project Management (Computer Hardware)
Posts: 130
Kudos: 260
 [4]
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel

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

B.

n = 5^x + 7^(y+15)
5^x always ends in 5.
so n = 5 + 7^(y+15)

1) y = 2x-15
=> y+15 = 2x
so (y+15) is always even
but 7^2x can end in 9 or 1
so insufficient.

2) y^2 - 6y + 5 = 0
y = 1 or 5
=> y+15 = 16, 20 (which always ends in 1)
so sufficient.
avatar
Edivar
Joined: 08 Aug 2017
Last visit: 31 Oct 2017
Posts: 1
Posts: 1
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 8 July 2025
Posts: 102,597
Own Kudos:
Given Kudos: 97,452
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,597
Kudos: 739,643
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Edivar
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).
avatar
anubhavece
Joined: 30 Aug 2017
Last visit: 16 Jun 2020
Posts: 5
Own Kudos:
Given Kudos: 171
Posts: 5
Kudos: 1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

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).
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 08 Jul 2025
Posts: 11,296
Own Kudos:
41,621
 [1]
Given Kudos: 333
Status:Math and DI Expert
Products:
Expert
Expert reply
Posts: 11,296
Kudos: 41,621
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
anubhavece
Bunuel

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
avatar
anubhavece
Joined: 30 Aug 2017
Last visit: 16 Jun 2020
Posts: 5
Own Kudos:
Given Kudos: 171
Posts: 5
Kudos: 1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
anubhavece
Bunuel

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.
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 08 Jul 2025
Posts: 6,371
Own Kudos:
15,564
 [2]
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,371
Kudos: 15,564
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel

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
User avatar
Salsanousi
Joined: 19 Oct 2013
Last visit: 29 Dec 2020
Posts: 399
Own Kudos:
Given Kudos: 117
Location: Kuwait
GPA: 3.2
WE:Engineering (Real Estate)
Posts: 399
Kudos: 344
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

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.
User avatar
Basshead
Joined: 09 Jan 2020
Last visit: 07 Feb 2024
Posts: 927
Own Kudos:
Given Kudos: 432
Location: United States
Posts: 927
Kudos: 286
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If x and y are positive integers and \(n = 5^x + 7^{(y + 15)}\), what is the units digit of n?

Quick notes:
5 to any power = units digit of 5.
Cyclicity of 7 = 7, 9, 3, 1

To determine the units digit of n, we need to determine the value of y+15. Lets look at the choices:


(1) \(y = 2x – 15\)

We have no idea what x is -- Insufficient.

(2) \(y^2 – 6y + 5 = 0\)

y = 5, 1

y + 15 = 16 or 20.

Since y has a cyclicity of 4, y raised to any multiple of 4 will give us a units digit of 1.

Statement 2 is sufficient.

Answer is B.
User avatar
nivivacious
Joined: 10 Mar 2015
Last visit: 18 Aug 2024
Posts: 243
Own Kudos:
Given Kudos: 175
Location: India
Concentration: Strategy, Marketing
GPA: 3.5
WE:Advertising (Advertising and PR)
Posts: 243
Kudos: 282
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

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) \(y^2 – 6y + 5 = 0\)

Trick here is not to fall into C trap
5^anything = 5
Hence finding x is not important

y^2 – 6y + 5 = 0
We get solutions as 5 and 1
for both, the unit digit ie 7^20 and 7^16 is the same ie 9
Hence B
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,360
Own Kudos:
Posts: 37,360
Kudos: 1,010
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderator:
Math Expert
102597 posts