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

 It is currently 23 Oct 2018, 20:25

### 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

# Is a^3 + b^2 + 4 divisible by 6?

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

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2069
Is a^3 + b^2 + 4 divisible by 6?  [#permalink]

### Show Tags

31 Jan 2018, 06:01
00:00

Difficulty:

75% (hard)

Question Stats:

58% (02:28) correct 43% (02:23) wrong based on 51 sessions

### HideShow timer Statistics

Q.)
Is $$a^3 + b^2 + 4$$ divisible by 6?

(I) b is odd
(II) $$\frac{5a}{b}$$ is even

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient

Regards,
Saquib
Quant Expert
e-GMAT

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2069
Re: Is a^3 + b^2 + 4 divisible by 6?  [#permalink]

### Show Tags

31 Jan 2018, 06:02
SVP
Joined: 26 Mar 2013
Posts: 1842
Re: Is a^3 + b^2 + 4 divisible by 6?  [#permalink]

### Show Tags

31 Jan 2018, 06:36
Is $$a^3 + b^2 + 4$$ divisible by 6?

(I) b is odd

No info about a

Let's take exmaple

a =1, b= 1...........$$\frac{6}{6}$$ = 1 ............Answer to question is Yes

a =2, b= 1...........$$\frac{13}{6}$$ is Not integer ............Answer to question is No

Insufficient

(II) $$\frac{5a}{b}$$ is even

Let's analyze first:

Case 1:

$$\frac{even}{even}$$ = even

This means a = even & b =even.......This means we can have either number divisible by 6

Let a=4, b =10.......$$\frac{20}{10}$$=2... Apply in question, we get 168, which is even and its sum is divisible by 3....so it is divisible by 6......Answer is Yes

We can choose a = 8 and b =10........Answer is No

I could say insufficient. But I want to examine case 2

Case 2:

This means a = even & b =odd ( for example a = 2, b =5)

This means directly.......(even)^3 + (odd)^2 + 4 =odd which can't be divisible by 6....Answer is No (please note that exponent does NOT change nature of integer if odd or even)

combining 1 & 2

It is clear we have case 2 ans straight forward answer will be always NO

Sufficuent

Senior Manager
Joined: 31 Jul 2017
Posts: 477
Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Is a^3 + b^2 + 4 divisible by 6?  [#permalink]

### Show Tags

31 Jan 2018, 07:15
EgmatQuantExpert wrote:
Q.)
Is $$a^3 + b^2 + 4$$ divisible by 6?

(I) b is odd
(II) $$\frac{5a}{b}$$ is even

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient

Regards,
Saquib
Quant Expert
e-GMAT

Statement I: Take $$a =1, b = 1$$
$$a^3 + b^2 + 4$$ is divisible by 6.

Take $$a = 2, b = 1$$
$$a^3 + b^2 + 4$$ is not divisible by 6. So, Insufficient.

Statement II:
Take $$a = 0, b =$$ $$\sqrt{2}$$
$$a^3 + b^2 + 4$$ is divisible by 6.

Take $$a = 1, b = 1/2$$
$$a^3 + b^2 + 4$$ is not divisible by 6.

By Combining both we get,

$$b = odd, a =even$$

So, Option C.
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

Is a^3 + b^2 + 4 divisible by 6? &nbs [#permalink] 31 Jan 2018, 07:15
Display posts from previous: Sort by

# Is a^3 + b^2 + 4 divisible by 6?

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

 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®.