GMAT Changed on April 16th - Read about the latest changes here

 It is currently 26 May 2018, 06:46

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1245
Is a^3 + b^2 + 4 divisible by 6? [#permalink]

### Show Tags

31 Jan 2018, 06:01
Expert's post
1
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

58% (02:07) correct 42% (01:59) wrong based on 43 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

_________________

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

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1245
Re: Is a^3 + b^2 + 4 divisible by 6? [#permalink]

### Show Tags

31 Jan 2018, 06:02
Reserving this space to post the official solution.
_________________

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

SVP
Joined: 26 Mar 2013
Posts: 1645
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

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: 342
Location: Malaysia
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?   [#permalink] 31 Jan 2018, 07:15
Display posts from previous: Sort by