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:

It should be 7^x and not 7X. If we consider 7X,solution would be E whereas if it is 7^x,solution is A. 1 states that y is between 24 and 32.As we know,product xy is prime.This is only possible if X is 1. Considering Y as 29 gives us 9^29 and thus that leads us to its units digit as 1.Now 7^x+9^y = 1. Similarly,Y = 31 gives us the same outcome.Sufficient

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

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

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not. (B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not. (C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. (D) EACH statement ALONE is sufficient to answer the question. (E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.

I do not agree with the OA. Answer should be E.

From the question statement, we can see that one of the numbers is 1 and the other is a prime.

1)We get x=1, y can be 29 or 31. If it is 29, units digit of expression is 8. If it is 31, units digit of expression is 6. Insufficient.

2) Obviously insufficient. As illustrated from statement 1.

Answer is hence E.

Kudos Please... If my post helped.
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

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?

Since x and y are positive integers, then in order the product of x and y to be prime, either of them must be 1 another must be a prime number.

(1) 24 < y < 32 --> y is not equal to 1, thus y must be a prime number and x must be equal to 1. Only primes between 24 and 32 are 29 and 31, so y is either 29 or 31. Now, the units digit of 9^odd is 9, thus the units’ digit of 7^1 + 9^odd is 7+9=6. Sufficient.

(2) x = 1 --> y can be ANY prime number. If x=1 and y=2, then the units’ digit of 7^x + 9^y is 8, but if x=1 and y is any other prime then the the units’ digit of 7^x + 9^y is 6. Not sufficient.

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

Show Tags

27 Jan 2014, 14:14

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.
_________________

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

Show Tags

01 Feb 2014, 04:34

1

This post received KUDOS

Since x*y is prime one of them must be 1 and other must be prime.

Stmt1: 28<y<32. Therefore x has to be 1. and y must be 29 or 31. Now 9 raised to odd power always has 9 in units digit. What is this final units digit? 7+9 = 6. SUFF. Stmt2: x=1. y could be any prime under the sun. NOT SUFF.
_________________

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

Show Tags

28 May 2014, 05:46

First things first. Xy is a prime number can only be true when either x or y is a prime number and the other is equal yo 1. Now, Statement 1 tells us that y is a prime number in that range thus y (29,31) and x of course 1. Now When 9 is raised to an odd number the units digit is always 9 therefore Statement 1 is sufficient.

Statement 2 tells us that x=1, but Y could be any prime number so it is insufficient.

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

Show Tags

04 Sep 2014, 00:34

First, remember that a prime has only 2 factors: 1 and itself. Thus, if x * y = prime, either x or y is 1 and the other is prime. Now, look at the cyclicity of 7 and 9. 7^1 = 7, 7² = 49, 7³ = 343, 7^4 = 2401 --> next will be units digit of 7 again. Cyclicity is 4. For 9 the rule is : If 9 is raised to an odd power, the units digit will be 9, if its raised to an even power the units digit will be 1.

(1) 24 < y < 32 --> y is not 1, hence X has to be 1. Units digit of 7^1 = 7. Now the only two primes in the given interval are 29 and 31, both of which are odd. Hence units digit of 9^y will be 9. Hence units digit of the sum is 0. SUFF.

(2) x = 1. This tells us again that 7^1 = 7 BUT y can now be 2 (which is the only EVEN prime) OR any other ODD prime. Thus the units digit of 9^y can either be 1 or 9. Insufficient.

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

Show Tags

28 May 2016, 08:47

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.
_________________