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

Oldest

Best Reply

Author

Message

TAGS:

Intern

Joined: 14 Oct 2012

Posts: 21

Followers: 0

Kudos [?]: 1 [0], given: 21

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

24 Nov 2012, 13:21

00:00

Question Stats:

65% (01:43) correct

34% (00:59) wrong

based on 23 sessions

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

[Reveal] Spoiler: OA

Last edited by Bunuel on 25 Nov 2012, 05:51, edited 2 times in total.

Renamed the topic and edited the question.

Manager

Joined: 06 Jun 2010

Posts: 162

Followers: 2

Kudos [?]: 14 [0], given: 151

Re: Can anyone help with this? [#permalink]

24 Nov 2012, 13:40

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

Director

Joined: 02 Jul 2012

Posts: 790

Location: India

Concentration: Strategy

Schools: Ross '16, McCombs '16, Kenan-Flagler '16, McDonough '16, Boston U '16, Jones '16, Olin '16

GMAT 1: 740 Q49 V42

GPA: 3.8

WE: Engineering (Energy and Utilities)

Followers: 19

Kudos [?]: 277 [0], given: 45

Re: Can anyone help with this? [#permalink]

24 Nov 2012, 22:34

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.

Answer is hence E.

Kudos Please... If my post helped.
_________________

Kudos Please... If my post helped.

Thanks To The Almighty - My GMAT Debrief
My Own CR Question 1|My Own CR Question 2|My Own DS Question 1|My Own DS Question 2|
My Own PS Question 1

GMAT Club team member

Joined: 02 Sep 2009

Posts: 12099

Followers: 1876

Kudos [?]: 10096 [0], given: 959

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

25 Nov 2012, 06:06

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.

Answer: A.

Hope it's clear.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rules #3 and 5.
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!, 11 New DS set. NEW!!!

What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

Re: If x and y are positive integers such that the product of x [#permalink] 25 Nov 2012, 06:06

		Similar topics	Author	Replies	Last post
Similar Topics:		If x and y are positive integers such that the product of x	Hermione	4	01 Nov 2006, 11:58
		If x and y are positive integers such that the product of x	Capthan	7	23 Jul 2008, 07:22
		If x and y are positive integers , is the product xy even	krishan	2	29 Jan 2009, 05:47
	2	If x and y are positive integers such that the product of x	shuj00	13	19 Feb 2010, 12:02
		If x and y are positive integers such that the product of x	Atrain13gm	8	19 Sep 2010, 06:45

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

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

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

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

Main navigation

GMAT Resources

Partners

MBA Resources