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

It is currently 19 Sep 2018, 02:13

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

Is b even? (1) a/b is even (2) (a+1)b is even

  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: 49251
Is b even? (1) a/b is even (2) (a+1)b is even  [#permalink]

Show Tags

New post 04 Apr 2018, 23:46
1
2
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

42% (01:36) correct 58% (01:10) wrong based on 65 sessions

HideShow timer Statistics

examPAL Representative
User avatar
S
Joined: 07 Dec 2017
Posts: 591
Is b even? (1) a/b is even (2) (a+1)b is even  [#permalink]

Show Tags

New post Updated on: 05 Apr 2018, 01:27
Bunuel wrote:
Is b even?

(1) a/b is even

(2) (a+1)b is even


This is a bit of a trick question as we're not explicitly told that a,b are integers.
As such, since we're only given general information about the product and quotient of a and b, (E) will be our answer.
For example in (1) if we set b=1/2 than a/b = 2a which is even for any integer a and in (2) we can keep using fractions such as a=2 and b=2/3. Similarly, when combining, we can find fractions that work in both cases such as a=3 and b=1/2

If we assume that a,b are integers, then a more standard solution would be:

As we're asked about number-properties (even/odd) we'll look for a theoretical solution (one without calculation).
This is a Logical approach.

(1) If a/b is even then it is divisible by 2. Since a/b is a factor of a, this means that a is divisible by 2. It tells us nothing about b, however. (For example, consider a = 20, b=2 or a=20, b=5)
Insufficient.

(2) If a product is even, then at least one of its factors is even. So, at least one of (a+1) and b are even. As we don't know which one, we cannot answer.
Insufficient.

Combined: From (1) we know that a is even meaning that a+1 is odd. Therefore, by (2), b must be even.
Sufficient!

In this case (C) is our answer.
_________________

Image
Image
Sign up for 7-day free trial

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.


Originally posted by DavidTutorexamPAL on 05 Apr 2018, 00:45.
Last edited by DavidTutorexamPAL on 05 Apr 2018, 01:27, edited 1 time in total.
DS Forum Moderator
User avatar
D
Joined: 27 Oct 2017
Posts: 714
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: Is b even? (1) a/b is even (2) (a+1)b is even  [#permalink]

Show Tags

New post 05 Apr 2018, 00:46
1
(1) a/b is even
Not sufficient. (A,B) can be (6,2) or (6,3) or even non integers.
(2) (a+1)b is even
B can be even or odd or non integers. (a,b) can be (1,2) or (1,1)
Not sufficient.

after combing st1 &2 , multiplying st1&2 , we get a(a+1) is even integer. That means a is an integer.
Now if a is integer, then as per statement 2, b is also a integer as (a+1)*b is an even integer.
Now if both a and b are integers, and a/b is even, a is even integer.
Now using a as even integer, (a+1) is odd integer, hence b is even integer as (a+1)*b is even.

Sufficient.

answer c
_________________

Win GMAT CLUB Tests - Weekly Quant Quiz Contest
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

DS Forum Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1343
Location: India
Premium Member
Re: Is b even? (1) a/b is even (2) (a+1)b is even  [#permalink]

Show Tags

New post 05 Apr 2018, 01:05
Bunuel wrote:
Is b even?

(1) a/b is even

(2) (a+1)b is even


I think the answer should be E.

We are not given that a/b are integers, so they can take fractional/decimal values also.

Lets take an example of a=3, b=1.5. Here a/b = 3/1.5 = 2, which is even. And (a+1)b = 4*1.5 = 6, which is also even.

Now lets take an example of a=8, b=2. Here a/b = 8/2 = 4, which is even. And (a+1)b = 9*2 = 18, which is also even.

Looking at the above two cases, b can be even, or it can take a decimal value also. So even after combining the statements are not sufficient. Hence E
examPAL Representative
User avatar
S
Joined: 07 Dec 2017
Posts: 591
Re: Is b even? (1) a/b is even (2) (a+1)b is even  [#permalink]

Show Tags

New post 05 Apr 2018, 01:09
amanvermagmat wrote:
Bunuel wrote:
Is b even?

(1) a/b is even

(2) (a+1)b is even


I think the answer should be E.

We are not given that a/b are integers, so they can take fractional/decimal values also.

Lets take an example of a=3, b=1.5. Here a/b = 3/1.5 = 2, which is even. And (a+1)b = 4*1.5 = 6, which is also even.

Now lets take an example of a=8, b=2. Here a/b = 8/2 = 4, which is even. And (a+1)b = 9*2 = 18, which is also even.

Looking at the above two cases, b can be even, or it can take a decimal value also. So even after combining the statements are not sufficient. Hence E


Good point. But then the question becomes kind of pointless, doesn't it? (as if they aren't integers you can do whatever you like)
_________________

Image
Image
Sign up for 7-day free trial

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.

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49251
Re: Is b even? (1) a/b is even (2) (a+1)b is even  [#permalink]

Show Tags

New post 05 Apr 2018, 01:14
DavidTutorexamPAL wrote:
amanvermagmat wrote:
Bunuel wrote:
Is b even?

(1) a/b is even

(2) (a+1)b is even


I think the answer should be E.

We are not given that a/b are integers, so they can take fractional/decimal values also.

Lets take an example of a=3, b=1.5. Here a/b = 3/1.5 = 2, which is even. And (a+1)b = 4*1.5 = 6, which is also even.

Now lets take an example of a=8, b=2. Here a/b = 8/2 = 4, which is even. And (a+1)b = 9*2 = 18, which is also even.

Looking at the above two cases, b can be even, or it can take a decimal value also. So even after combining the statements are not sufficient. Hence E


Good point. But then the question becomes kind of pointless, doesn't it? (as if they aren't integers you can do whatever you like)


Yes, in its current form the answer must be E. C would be correct if the question were "Is integer b 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

DS Forum Moderator
User avatar
D
Joined: 27 Oct 2017
Posts: 714
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: Is b even? (1) a/b is even (2) (a+1)b is even  [#permalink]

Show Tags

New post 05 Apr 2018, 02:40
One of the trickiest question Sir...

You are awesome
Bunuel wrote:
amanvermagmat wrote:
Is b even?

(1) a/b is even

(2) (a+1)b is even


I think the answer should be E.

We are not given that a/b are integers, so they can take fractional/decimal values also.

Lets take an example of a=3, b=1.5. Here a/b = 3/1.5 = 2, which is even. And (a+1)b = 4*1.5 = 6, which is also even.

Now lets take an example of a=8, b=2. Here a/b = 8/2 = 4, which is even. And (a+1)b = 9*2 = 18, which is also even.

Looking at the above two cases, b can be even, or it can take a decimal value also. So even after combining the statements are not sufficient. Hence E


Good point. But then the question becomes kind of pointless, doesn't it? (as if they aren't integers you can do whatever you like)[/quote]

Yes, in its current form the answer must be E. C would be correct if the question were "Is integer b even?".[/quote]
_________________

Win GMAT CLUB Tests - Weekly Quant Quiz Contest
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Intern
Intern
avatar
B
Joined: 16 Aug 2018
Posts: 29
Concentration: General Management, Strategy
Schools: Guanghua"21 (A)
GMAT 1: 700 Q49 V36
Re: Is b even? (1) a/b is even (2) (a+1)b is even  [#permalink]

Show Tags

New post 23 Aug 2018, 19:40
DavidTutorexamPAL wrote:
amanvermagmat wrote:
Bunuel wrote:
Is b even?

(1) a/b is even

(2) (a+1)b is even


I think the answer should be E.

We are not given that a/b are integers, so they can take fractional/decimal values also.

Lets take an example of a=3, b=1.5. Here a/b = 3/1.5 = 2, which is even. And (a+1)b = 4*1.5 = 6, which is also even.

Now lets take an example of a=8, b=2. Here a/b = 8/2 = 4, which is even. And (a+1)b = 9*2 = 18, which is also even.

Looking at the above two cases, b can be even, or it can take a decimal value also. So even after combining the statements are not sufficient. Hence E


Good point. But then the question becomes kind of pointless, doesn't it? (as if they aren't integers you can do whatever you like)


agree. i've seen a lot of questions like this in gmatclub. quite tricky. but most likely you won't see it in real gmat tests.
when it comes to odd/even, gmat prompt always states numbers are integers. otherwise, it'll be pointless. good question but pretty much out of scope.
Re: Is b even? (1) a/b is even (2) (a+1)b is even &nbs [#permalink] 23 Aug 2018, 19:40
Display posts from previous: Sort by

Is b even? (1) a/b is even (2) (a+1)b is even

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

Events & Promotions

PREV
NEXT


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®.