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

It is currently 20 Oct 2018, 08:03

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

If a and b are integers such that a + b = 5, which of the following is

  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: 50005
If a and b are integers such that a + b = 5, which of the following is  [#permalink]

Show Tags

New post 13 Mar 2018, 01:12
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

73% (00:59) correct 27% (00:58) wrong based on 117 sessions

HideShow timer Statistics

If a and b are integers such that a + b = 5, which of the following is true?

I. The product of a and b is odd.
II. If a is odd, b is even.
III. If a is negative, b is positive.

A. I only
B. II only
C. I and II
D. II and III
E. I, II and III

_________________

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

examPAL Representative
User avatar
G
Joined: 07 Dec 2017
Posts: 721
Re: If a and b are integers such that a + b = 5, which of the following is  [#permalink]

Show Tags

New post 13 Mar 2018, 01:24
Bunuel wrote:
If a and b are integers such that a + b = 5, which of the following is true?

I. The product of a and b is odd.
II. If a is odd, b is even.
III. If a is negative, b is positive.

A. I only
B. II only
C. I and II
D. II and III
E. I, II and III


Since our numbers our very small, we'll try picking different numbers instead of solving explicitly.
This is an Alternative approach.

We'll try easy value for a,b: first 0,5 then 1,4 and if we need another than 2,3 or -1, 6.
I. 0*5=0 so this is false.
II. if a = 5 then b = 0, so it is even. if a = 1 then b = 4, so it is even. If a = 3 then b = 2 so it is even.
Even if we're not sure why the statement is true, after 3 examples we should feel OK guessing that it is true.
(Additionally, trying these examples will hopefully have reminded us that odd - odd = even. This is the proof that II is true)
III. a = -1 --> b = 6. a = -2, b = 7.
At this point it should be clear that we've hit on a trend: making a smaller will only make b larger so it is definitely positive.

All in all, I is False, II is true, III is true
(D) is our answer.
_________________

Image
Sign up for 7-day free trial
Image

I am a CR Expert - Ask Me ANYTHING about CR
I am a DS Expert - Ask Me ANYTHING about DS


Watch free GMAT tutorials in Math, Verbal, IR, and AWA.

GMAT test takers: Watch now the GMAC interview with the people who write the GMAT test!
We discussed the chances of improving a GMAT score; how important the first questions on the test are; what to do if you don’t have enough time to complete a whole section; and more.

You can watch all the action from the interview here.

Manager
Manager
User avatar
S
Joined: 13 Feb 2018
Posts: 135
CAT Tests
Re: If a and b are integers such that a + b = 5, which of the following is  [#permalink]

Show Tags

New post 13 Mar 2018, 01:28
From a+b=5 we can assume that a and b have opposite even/odd nature

I The product of a and b is odd --> As we know a and b have opposite even/odd nature so their multiple MUST be even --> FALSE
II If a is odd, b is even --> As we know a and b have opposite even/odd nature so if a is odd then b MUST be even --> TRUE
III If a is negative, b is positive -- > if a is negative b Must be positive and moreover |a|=b+5 --> TRUE

So my choice is D
Intern
Intern
avatar
B
Joined: 07 Jan 2018
Posts: 11
If a and b are integers.....  [#permalink]

Show Tags

New post 26 Sep 2018, 10:18
If a and b are integers such that a+b=5, which of the following MUST be true?
I. The product of a and b is odd.
II. If a is odd, b is even
III. If a is negative, b is positive

(A) I only
(B) II only
(C) I and II only
(D) II III only
(E) I,II and III

Please explain with all the possibilities (plugging in numbers?

Posted from my mobile device
Director
Director
User avatar
G
Joined: 31 Oct 2013
Posts: 651
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If a and b are integers.....  [#permalink]

Show Tags

New post 26 Sep 2018, 10:25
1
mittu wrote:
If a and b are integers such that a+b=5, which of the following MUST be true?
I. The product of a and b is odd.
II. If a is odd, b is even
III. If a is negative, b is positive

(A) I only
(B) II only
(C) I and II only
(D) II III only
(E) I,II and III

Please explain with all the possibilities (plugging in numbers?

Posted from my mobile device



a + b = 5

odd = even + odd...........

thus product can't be odd as even*odd = even.

If a is odd b has to even. fact.

*** 5 is positive value thus if one is negative another has to be positive.

Thus D is the best answer.

Hope it helps.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50005
Re: If a and b are integers such that a + b = 5, which of the following is  [#permalink]

Show Tags

New post 26 Sep 2018, 12:17
mittu wrote:
If a and b are integers such that a+b=5, which of the following MUST be true?
I. The product of a and b is odd.
II. If a is odd, b is even
III. If a is negative, b is positive

(A) I only
(B) II only
(C) I and II only
(D) II III only
(E) I,II and III

Please explain with all the possibilities (plugging in numbers?

Posted from my mobile device


Merging topics.

Please search before posting and name topics properly. Check rules here: https://gmatclub.com/forum/rules-for-po ... 33935.html Thank you.
_________________

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

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3896
Location: United States (CA)
Re: If a and b are integers such that a + b = 5, which of the following is  [#permalink]

Show Tags

New post 02 Oct 2018, 19:20
Bunuel wrote:
If a and b are integers such that a + b = 5, which of the following is true?

I. The product of a and b is odd.
II. If a is odd, b is even.
III. If a is negative, b is positive.

A. I only
B. II only
C. I and II
D. II and III
E. I, II and III


Since a + b = 5, either a is odd and b is even and vice versa, so II is true.

Thus, the product of a and b is even, so I is not true.

Finally if a is negative, then b would have to be positive to get a positive sum, so III is true.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

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

CEO
CEO
User avatar
P
Joined: 08 Jul 2010
Posts: 2560
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: If a and b are integers such that a + b = 5, which of the following is  [#permalink]

Show Tags

New post 03 Oct 2018, 01:36
Bunuel wrote:
If a and b are integers such that a + b = 5, which of the following is true?

I. The product of a and b is odd.
II. If a is odd, b is even.
III. If a is negative, b is positive.

A. I only
B. II only
C. I and II
D. II and III
E. I, II and III


a + b = 5
i.e. (a,b) may be (0,5) (1,4) (2,3) etc.

I. The product of a and b is odd. is NOT true for (2,3)
II. If a is odd, b is even. MUST be true as only sum of even and odd will result in an odd outcome
III. If a is negative, b is positive. MUST be true because if one of the values is negative then for resultant sum to be positive the other value must be positive

Answer: Option D
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Intern
Intern
avatar
Joined: 10 Sep 2018
Posts: 2
GMAT ToolKit User
Re: If a and b are integers such that a + b = 5, which of the following is  [#permalink]

Show Tags

New post 03 Oct 2018, 01:42
+1 for D

Product of a and b is not necessarily odd. Consider -1 and 6
Posted from my mobile device
GMAT Club Bot
Re: If a and b are integers such that a + b = 5, which of the following is &nbs [#permalink] 03 Oct 2018, 01:42
Display posts from previous: Sort by

If a and b are integers such that a + b = 5, which of the following is

  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®.