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

It is currently 22 Feb 2019, 04:26

Close

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
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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT RC Webinar

     February 23, 2019

     February 23, 2019

     07:00 AM PST

     09:00 AM PST

    Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
  • FREE Quant Workshop by e-GMAT!

     February 24, 2019

     February 24, 2019

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

If a and b are prime numbers, such that a > b, which of the following

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53066
If a and b are prime numbers, such that a > b, which of the following  [#permalink]

Show Tags

New post 21 Sep 2017, 06:16
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

55% (01:24) correct 45% (01:22) wrong based on 131 sessions

HideShow timer Statistics

If a and b are prime numbers, such that a > b, which of the following cannot be true?

A. a+b is prime.
B. ab is odd.
C. a(a-b) is odd.
D. a-b is prime.
E. a^b is even.

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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. ,11 Mixed Questions, 12 Fresh Meat

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., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2491
If a and b are prime numbers, such that a > b, which of the following  [#permalink]

Show Tags

New post 21 Sep 2017, 07:03
Bunuel wrote:
If a and b are prime numbers, such that a > b, which of the following cannot be true?

A. a+b is prime.
B. ab is odd.
C. a(a-b) is odd.
D. a-b is prime.
E. a^b is even.

Answer E. \(a\) must be odd. All primes except 2 are odd. And \(a\) must be greater than \(b\). Thus the only even prime, 2, cannot be \(a\).

An odd base raised to any integral power (even or odd) -- is odd. The expression \(a^{b}\) cannot be even.

Because \(a > b\), the only even power, 2, cannot be "a." There are no prime numbers smaller than 2.

So \(a\) is odd. Its minimum possible value is 3, and all primes greater than 3 are odd.

Rule: An odd base raised to any integer power is always odd. (It is probably easier simply to remember that odd times odd equals odd, and extend that principle.)

Whether an odd number is raised to a power of 2, 3, 4, 5, or 51, the result is odd * odd (* odd * odd . . .) for as many powers as there are. The exponent's even or odd sign is irrelevant. Examples:

If \(a = 3, b = 2\), then \(3^2 = 9\), and odd * odd = odd

If \(a = 5, b = 3\), then \(5^3 = 5 * 5 * 5 = 125\)

Other answer choices can be disproved. Which of following cannot be true?

A. \(a+b\) is prime.
If \(a = 3, b = 2\), \((3 + 2) = 5\). 5 is prime. It can be true. REJECT

B. \(ab\) is odd.
If \(a = 5, b = 3\), \((ab) = 15\), which is odd. Can be true. REJECT

C. \(a(a-b)\) is odd.
If \(a = 3, b = 2\): \((3)(3-2) = (3)(1) = 3\), which is odd. Can be true. REJECT

D. \(a-b\) is prime.
If \(a = 5, b = 3\), \((5 - 3) = 2\), which is prime. Can be true. REJECT

ANSWER E
_________________

To live is the rarest thing in the world.
Most people just exist.

Oscar Wilde

CR & LSAT Forum Moderator
User avatar
D
Status: He came. He saw. He conquered. -- Studying for the LSAT -- Corruptus in Extremis
Joined: 31 Jul 2017
Posts: 473
Location: United States
Concentration: Finance, Economics
Reviews Badge
Re: If a and b are prime numbers, such that a > b, which of the following  [#permalink]

Show Tags

New post 21 Sep 2017, 08:02
3^2 = 9; 5^3 = 125; 7^2 = 49

The list goes on, but just a little evidence to show E is the correct answer.

By POE:

If a and b are prime numbers, such that a > b, which of the following cannot be true?

A. a+b is prime. 5+2 = 7 Prime
B. ab is odd. 5*7 = 35 Odd
C. a(a-b) is odd. 3(3-2) = 3 Odd
D. a-b is prime. 7-5 = 2 Prime
E. a^b is even. Answer
_________________

D-Day: November 18th, 2017

Need a laugh and a break? Go here: https://gmatclub.com/forum/mental-break-funny-videos-270269.html

Need a CR tutor? PM me!

Intern
Intern
avatar
Joined: 14 Sep 2017
Posts: 5
Re: If a and b are prime numbers, such that a > b, which of the following  [#permalink]

Show Tags

New post 23 Sep 2017, 09:01
genxer123 wrote:
Bunuel wrote:
If a and b are prime numbers, such that a > b, which of the following cannot be true?

A. a+b is prime.
B. ab is odd.
C. a(a-b) is odd.
D. a-b is prime.
E. a^b is even.

Answer E. \(a\) must be odd. All primes except 2 are odd. And \(a\) must be greater than \(b\). Thus the only even prime, 2, cannot be \(a\).

An odd base raised to any integral power (even or odd) -- is odd. The expression \(a^{b}\) cannot be even.

Because \(a > b\), the only even power, 2, cannot be "a." There are no prime numbers smaller than 2.

So \(a\) is odd. Its minimum possible value is 3, and all primes greater than 3 are odd.

Rule: An odd base raised to any integer power is always odd. (It is probably easier simply to remember that odd times odd equals odd, and extend that principle.)

Whether an odd number is raised to a power of 2, 3, 4, 5, or 51, the result is odd * odd (* odd * odd . . .) for as many powers as there are. The exponent's even or odd sign is irrelevant. Examples:

If \(a = 3, b = 2\), then \(3^2 = 9\), and odd * odd = odd

If \(a = 5, b = 3\), then \(5^3 = 5 * 5 * 5 = 125\)

Other answer choices can be disproved. Which of following cannot be true?

A. \(a+b\) is prime.
If \(a = 3, b = 2\), \((3 + 2) = 5\). 5 is prime. It can be true. REJECT

B. \(ab\) is odd.
If \(a = 5, b = 3\), \((ab) = 15\), which is odd. Can be true. REJECT

C. \(a(a-b)\) is odd.
If \(a = 3, b = 2\): \((3)(3-2) = (3)(1) = 3\), which is odd. Can be true. REJECT

D. \(a-b\) is prime.
If \(a = 5, b = 3\), \((5 - 3) = 2\), which is prime. Can be true. REJECT

ANSWER E
But 2^5=32. Then E can be true.
CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3446
Location: Canada
If a and b are prime numbers, such that a > b, which of the following  [#permalink]

Show Tags

New post 23 Sep 2017, 09:06
Top Contributor
Rupanjel wrote:
But 2^5=32. Then E can be true.


Be careful.
In your counter-example (2^5), you have a = 2 and b = 5. This breaks the given condition that a > b

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com
Image

Intern
Intern
avatar
Joined: 14 Sep 2017
Posts: 5
Re: If a and b are prime numbers, such that a > b, which of the following  [#permalink]

Show Tags

New post 23 Sep 2017, 09:22
GMATPrepNow wrote:
Rupanjel wrote:
But 2^5=32. Then E can be true.


Be careful.
In your counter-example (2^5), you have a = 2 and b = 5. This breaks the given condition that a > b

Cheers,
Brent

oh yeah...my bad :(
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4955
Location: United States (CA)
Re: If a and b are prime numbers, such that a > b, which of the following  [#permalink]

Show Tags

New post 25 Sep 2017, 15:36
Bunuel wrote:
If a and b are prime numbers, such that a > b, which of the following cannot be true?

A. a+b is prime.
B. ab is odd.
C. a(a-b) is odd.
D. a-b is prime.
E. a^b is even.


Recall that all the prime numbers other than 2 are odd. Since a > b, a must be odd (even if b = 2). Thus, a^b must be odd since any odd number raised to a power is odd. So, a^b can’t be even.

Answer: E
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9887
Premium Member
Re: If a and b are prime numbers, such that a > b, which of the following  [#permalink]

Show Tags

New post 16 Oct 2018, 23:36
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: If a and b are prime numbers, such that a > b, which of the following   [#permalink] 16 Oct 2018, 23:36
Display posts from previous: Sort by

If a and b are prime numbers, such that a > b, which of the following

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.