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

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

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New post 31 Jan 2018, 06:01
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A
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C
D
E

Difficulty:

  65% (hard)

Question Stats:

60% (01:59) correct 40% (01:59) wrong based on 45 sessions

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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

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Re: Is a^3 + b^2 + 4 divisible by 6?  [#permalink]

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New post 31 Jan 2018, 06:02
Reserving this space to post the official solution. :)
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Re: Is a^3 + b^2 + 4 divisible by 6?  [#permalink]

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New post 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

Answer: C
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Is a^3 + b^2 + 4 divisible by 6?  [#permalink]

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New post 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.
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Is a^3 + b^2 + 4 divisible by 6? &nbs [#permalink] 31 Jan 2018, 07:15
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