GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Sep 2019, 16:28

### 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

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

# If x and y are positive integers and n = 5^x + 7^(y + 15), what is the

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58117
If x and y are positive integers and n = 5^x + 7^(y + 15), what is the  [#permalink]

### Show Tags

23 Oct 2014, 01:02
3
16
00:00

Difficulty:

55% (hard)

Question Stats:

68% (02:11) correct 32% (02:32) wrong based on 765 sessions

### HideShow timer Statistics

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) $$y^2 – 6y + 5 = 0$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 58117
Re: If x and y are positive integers and n = 5^x + 7^(y + 15), what is the  [#permalink]

### Show Tags

23 Oct 2014, 01:03
1
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

Check Units digits, exponents, remainders problems directory in our Special Questions Directory.
_________________
Director
Joined: 25 Apr 2012
Posts: 666
Location: India
GPA: 3.21
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.”
Manager
Joined: 22 Jan 2014
Posts: 171
WE: Project Management (Computer Hardware)
Re: If x and y are positive integers and n = 5^x + 7^(y + 15), what is the  [#permalink]

### Show Tags

24 Oct 2014, 05:36
1
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

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.
_________________
Illegitimi non carborundum.
Math Expert
Joined: 02 Aug 2009
Posts: 7831
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
_________________
Intern
Joined: 08 Aug 2017
Posts: 1
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.
Math Expert
Joined: 02 Sep 2009
Posts: 58117
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).
_________________
Intern
Joined: 30 Aug 2017
Posts: 5
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).
Intern
Joined: 30 Aug 2017
Posts: 5
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.
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2972
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
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

_________________
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

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Director
Joined: 19 Oct 2013
Posts: 524
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
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.

Re: If x and y are positive integers and n = 5^x + 7^(y + 15), what is the   [#permalink] 05 Oct 2018, 09:38
Display posts from previous: Sort by