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

 It is currently 19 Jun 2019, 00:07 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If x and y are positive integers such that the product of x

Author Message
TAGS:

Hide Tags

Intern  Joined: 14 Oct 2012
Posts: 21
If x and y are positive integers such that the product of x  [#permalink]

Show Tags

4
5 00:00

Difficulty:   65% (hard)

Question Stats: 57% (01:49) correct 43% (01:46) wrong based on 218 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

Originally posted by saikiranx on 24 Nov 2012, 13:21.
Last edited by Bunuel on 25 Nov 2012, 05:51, edited 2 times in total.
Renamed the topic and edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 55681
Re: If x and y are positive integers such that the product of x  [#permalink]

Show Tags

2
4
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.

Hope it's clear.

_________________
General Discussion
Manager  Joined: 06 Jun 2010
Posts: 153
Re: Can anyone help with this?  [#permalink]

Show Tags

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

2 just gives us value of X.Insufficient.

Thus,ans is A
VP  Joined: 02 Jul 2012
Posts: 1153
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42 GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: Can anyone help with this?  [#permalink]

Show Tags

saikiranx wrote:
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.

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

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types
Manager  Joined: 25 Oct 2013
Posts: 143
Re: If x and y are positive integers such that the product of x  [#permalink]

Show Tags

1
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.
_________________
Click on Kudos if you liked the post!

Practice makes Perfect.
SVP  Joined: 06 Sep 2013
Posts: 1651
Concentration: Finance
Re: If x and y are positive integers such that the product of x  [#permalink]

Show Tags

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.

Therefore A is the correct answer

Cheers
J
Manager  Joined: 21 Oct 2013
Posts: 181
Location: Germany
GMAT 1: 660 Q45 V36 GPA: 3.51
If x and y are positive integers such that the product of x  [#permalink]

Show Tags

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.

Hope its all clear!
Non-Human User Joined: 09 Sep 2013
Posts: 11396
Re: If x and y are positive integers such that the product of x  [#permalink]

Show Tags

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] 27 Dec 2017, 00:55
Display posts from previous: Sort by

If x and y are positive integers such that the product of x  