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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

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:

If x and y are positive integers such that the product of x [#permalink]

Show Tags

19 Sep 2010, 06:45

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

50% (02:20) correct
50% (01:08) wrong based on 38 sessions

HideShow timer Statistics

If x and y are positive integers such that the product of x and y is prime, what is the units’ digit of 7^x + 9^y ?

(1) 24 < y < 32 (2) x = 1

----- I get that just from the question stem itself, you know either x or y must be equal to 1, thus B cannot be the answer. I can't figure out how you can tell the units digit of 9 to the Y just from the statement one.

If x and y are positive integers such that the product of x and y is prime, what is the units’ digit of 7^x + 9^y ?

(1) 24 < y < 32 (2) x = 1

----- I get that just from the question stem itself, you know either x or y must be equal to 1, thus B cannot be the answer. I can't figure out how you can tell the units digit of 9 to the Y just from the statement one.

Help?

Since we know xy is a prime, it implies as you rightly pointed that one of them is 1.

(1) This implies y is not 1, hence x must be 1. Also, we know y must be a prime since xy is a prime. So y can only be 29 or 31. Either case, y is odd. What you need to note is that the units digit of 9^{Odd number} is always 9. So combining with x=1, I know the units digit of the number in question must be 7+9 or 6. Hence, sufficient

(2) Not sufficient, as I know nothing about y

So answer is (a)

Further explanation units digits of 9^x x=1 9 x=2 1 x=3 9 x=4 1 ... The pattern is easy to spot and imagine why it happens. As the last digit is always multiplied by 9, leaving either 1 or 9 itself
_________________

Hi! I see that noone answer your question yet. I won't discuss about (2) because you already gave the solution.

(1) We know that 24 < y < 32 hence x = 1 ! As a matter fact, if we want a product to be prime we need to multiply 1 by a prime number. As y is much greater than 1, x = 1. Besides, I just said that has to be a prime number. So y = 29 or 31! Now let's see how it goes for the unit digit of th power of 9 :

9^0 = 1 9^1 = 9 9^2 = 81 9^3 = 729 9^4 = ...1

so 9^k if k is odd gives the unit digit as 9.... As y = 29 or 31 (odd numbers), (2) is SUFFICIENT

interestingly i think but for the fact that 2 is a prime and an even prime at that, we are not able to answer based on (2). so we know x=1, so y has to be prime. all primes are odds (but for 2), if not for that, would we not be able to say 7 + 9^odd = ends in 6
_________________

when xy is some prime number, either x = 1 or y =1. 1. 24<y<32 ------> x =1 , y = 29 or 31 when y =29----> 7^1 + 9 ^ 29 = 7 + any number ending in 9 ----> unit digit 6 when y = 31 -----> 7^1 + 9 ^ 31 = 7 + any number ending in 9 ----> unit digit 6 1) is sufficient 2) not sufficient Ans is A
_________________

If you like my post, consider giving me some KUDOS !!!!! Like you I need them

one more thing to add here----- cyclicity of numbers is always good in GMAT to remember - any number ending with 0,1,5,6 raised to any power will have same unit digit as the number itself, cyclicity is 1 any number ending with 2,3,7,8 will have cyclicity 0f 4 for example 3^(n+1) will have same unit as 3^(n+5) or 3^(n+9) or so on.... where n >= 0 3 -> 9 -> 27 -> 81 ---- 243 -> 729 -> xxx7 -> xxx1 --- any number ending with 4,9 will have cyclicity of 2
_________________

If you like my post, consider giving me some KUDOS !!!!! Like you I need them

If x and y are positive integers such that the product of x and y is prime, what is the units’ digit of 7^x + 9^y ?

(1) 24 < y < 32 (2) x = 1

----- I get that just from the question stem itself, you know either x or y must be equal to 1, thus B cannot be the answer. I can't figure out how you can tell the units digit of 9 to the Y just from the statement one.

Help?

My approach was: 1. Y can be either 29 or 31. Now y^29 or y^31 will always end in 9 and watever the power of X is the units digit is going to be the same. So A.

2. X=1 is not enough for a conclusion.
_________________

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...