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Senior Manager  Joined: 18 Jul 2006
Posts: 407
Is a*b*c divisible by 32?  [#permalink]

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2
7 00:00

Difficulty:   75% (hard)

Question Stats: 57% (01:54) correct 43% (01:45) wrong based on 250 sessions

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Is a*b*c divisible by 32?

(1) a, b and c are consecutive even integers.

(2) a*c < 0

Originally posted by Juaz on 24 May 2007, 01:48.
Last edited by Juaz on 24 May 2007, 02:16, edited 1 time in total.
Manager  Joined: 22 May 2007
Posts: 88
Re: Is a*b*c divisible by 32?  [#permalink]

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addendum: a number is divisible by 8 if it can be divided 3 times by 2
Manager  Joined: 23 Mar 2007
Posts: 122
Re: Is a*b*c divisible by 32?  [#permalink]

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Answer has to be E .

1) lets say A=2 , B=4 and C=6 , then abc is not divisible by 32 . However if A=4 , B=6 and C=8 , abc is divisible by 32.So insufficient

2) a= 5 , c= -1 , b= 3 --> abc is not divisible by 32
a= 4 , c = -4 , b= 2 ---> abc is divisible by 32 . So insufficient

1 and 2 together
A= -2 , B=0 , C=2 , abc=0 so again insufficient.
Senior Manager  Joined: 18 Jul 2006
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Re: Is a*b*c divisible by 32?  [#permalink]

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OA is C, as 0 is divisible by 32.
Manager  Joined: 23 Mar 2007
Posts: 122
Re: Is a*b*c divisible by 32?  [#permalink]

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I doubt the OA. I am not sure if 0 is divisible by any number.Can anyone throw some light on this?
Director  Joined: 08 Jun 2005
Posts: 911
Re: Is a*b*c divisible by 32?  [#permalink]

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abhinava wrote:
I doubt the OA. I am not sure if 0 is divisible by any number.Can anyone throw some light on this?

http://mathforum.org/library/drmath/view/60913.html

I don't know if thats the GMAT official viewpoint. Manager  Joined: 19 Aug 2006
Posts: 171
Re: Is a*b*c divisible by 32?  [#permalink]

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Juaz wrote:
Is a*b*c is divisible by 32?

1. a,b and c are consecutive even integers.

2. a*c < 0

*Question edited.

OA is correct. Its C.

Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator.

Source:- http://en.wikipedia.org/wiki/0_(number #Extended_use_of_zero_in_mathematics
Manager  Joined: 04 May 2007
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Re: Is a*b*c divisible by 32?  [#permalink]

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Statement I: insufficient but helpful

Statement two says that a*c <0 so one of the numbers must be negative, all could be negative as well:

-8 * -6 * -4 = -192 which is divisible by 32 as per GMAT definition y=xq+r when q and r are unique integers and 0<=r<x ( -192=32*-6 + 0)

-6*-4*-2 =-48 which is not divisible by 32.

insufficient.

Taken together we have that they are consecutive, and that one is negative and the other is not. Because of the restriction of being consecutive and even we have only one possible set of numbers: -2,0,2.

abc =0. 0 is divisable by any integer except zero. so the answer was C.

tricky problem and I would have no doubt gotten this wrong on the test if i didn't have 10 minutes to sit and think about it
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GMAT 1: 530 Q39 V23 GMAT 2: 560 Q42 V26 GPA: 3.5
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Re: Is a*b*c divisible by 32?  [#permalink]

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Juaz wrote:
Is a*b*c is divisible by 32?

1. a,b and c are consecutive even integers.

2. a*c < 0

*Question edited.

What on earth question ?

Statements (1) and (2) combined are sufficient. From S1 + S2 it follows that either a or c is negative. As a , b, and C are consecutive even integers, one of these three numbers must be 0. Thus, abc=0 which is divisible by 32

and what on earth explanation ! Mind blown!!!   Current Student D
Joined: 12 Aug 2015
Posts: 2567
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Is a*b*c divisible by 32?  [#permalink]

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Try this abhimahna
Wait a second ..!!!!
Dont

What..!!!!!!
How
No
NO
NO
I have one question here =>
IF C is even and A is an integer then can A^C ever be negative.
Extremely poor quality Question.
And those explanations ????????

4 minutes wasted and that red flag popped out
Damn
Heartbreaking

Vyshak chetan2u Bunuel

Guys Am i missing something here or this is an """ABSURD QUESTION"""
_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58446
Re: Is a*b*c divisible by 32?  [#permalink]

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stonecold wrote:
Try this abhimahna
Wait a second ..!!!!
Dont

What..!!!!!!
How
No
NO
NO
I have one question here =>
IF C is even and A is an integer then can A^C ever be negative.
Extremely poor quality Question.
And those explanations ????????

4 minutes wasted and that red flag popped out
Damn
Heartbreaking

Vyshak chetan2u Bunuel

Guys Am i missing something here or this is an """ABSURD QUESTION"""

It's a multiplied by c, so a*c not a^c.
_________________
Current Student D
Joined: 12 Aug 2015
Posts: 2567
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: Is a*b*c divisible by 32?  [#permalink]

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Bunuel wrote:
stonecold wrote:
Try this abhimahna
Wait a second ..!!!!
Dont

What..!!!!!!
How
No
NO
NO
I have one question here =>
IF C is even and A is an integer then can A^C ever be negative.
Extremely poor quality Question.
And those explanations ????????

4 minutes wasted and that red flag popped out
Damn
Heartbreaking

Vyshak chetan2u Bunuel

Guys Am i missing something here or this is an """ABSURD QUESTION"""

It's a multiplied by c, so a*c not a^c.  ArgggghhhhH!!!!!!

Thank you Bunuel
I have a knack of making ridiculous mistakes every now and then.

Regards
Stone Cold
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Intern  B
Joined: 30 Mar 2017
Posts: 37
Location: United States (FL)
Is a*b*c divisible by 32?  [#permalink]

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Bunuel wrote:
stonecold wrote:
Try this abhimahna
Wait a second ..!!!!
Dont

What..!!!!!!
How
No
NO
NO
I have one question here =>
IF C is even and A is an integer then can A^C ever be negative.
Extremely poor quality Question.
And those explanations ????????

4 minutes wasted and that red flag popped out
Damn
Heartbreaking

Vyshak chetan2u Bunuel

Guys Am i missing something here or this is an """ABSURD QUESTION"""

It's a multiplied by c, so a*c not a^c.

EDIT: NEVER MIND - Realize that the consecutive even integers makes that issue I was thinking of not matter...

Hey Bunuel I got this right a while back but a problem I have now that I'm reviewing is that the problem doesn't say a<b<c. I'm nervous about getting hung up on stuff like this if this is how it will appear on the actual test. Should I expect ambiguities like this?
Current Student G
Joined: 07 Jan 2015
Posts: 64
Location: United States
GPA: 3.4
WE: Engineering (Manufacturing)
Re: Is a*b*c divisible by 32?  [#permalink]

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a*b*c needs to be$$\geq{32]$$ and divisble by 32.

1) States that a, b, c are consecutive even integer - it can be -2,2,4 or 2,4,6 (not divisible by 32) or 4,6,8 (divisible by 32) NOT sufficient
2) A*C<0 that means A is negative and C is positive or vice versa NOT sufficient

Combine both
A,C, B = -2,2,4 ( A*B*C is not divisible by 32) SUFFICIENT! C answer
Math Expert V
Joined: 02 Aug 2009
Posts: 7988
Re: Is a*b*c divisible by 32?  [#permalink]

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satsurfs wrote:
a*b*c needs to be$$\geq{32]$$ and divisble by 32.

1) States that a, b, c are consecutive even integer - it can be -2,2,4or 2,4,6 (not divisible by 32) or 4,6,8 (divisible by 32) NOT sufficient
2) A*C<0 that means A is negative and C is positive or vice versa NOT sufficient

Combine both
A,C, B = -2,2,4 ( A*B*C is not divisible by 32) SUFFICIENT! C answer

Hi..

you are correct with your method and answer but two errors..
[1) a*b*c needs to be$$\geq{32]$$..
Not necessary as 0 can also be one value of a*b*c
2) a,b,c are consecutive even integers
so -2,2,4 is wrong.. it will be -2,0,2

and hence product a*b*c= -2*0*2=0
and o is div by all numbers because 0*any integer = 0
_________________
Current Student G
Joined: 07 Jan 2015
Posts: 64
Location: United States
GPA: 3.4
WE: Engineering (Manufacturing)
Re: Is a*b*c divisible by 32?  [#permalink]

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Thanks for the follow up. However, I was told that 0 is neither even nor odd integer that is why I took 0 out.

chetan2u wrote:
satsurfs wrote:
a*b*c needs to be$$\geq{32]$$ and divisble by 32.

1) States that a, b, c are consecutive even integer - it can be -2,2,4or 2,4,6 (not divisible by 32) or 4,6,8 (divisible by 32) NOT sufficient
2) A*C<0 that means A is negative and C is positive or vice versa NOT sufficient

Combine both
A,C, B = -2,2,4 ( A*B*C is not divisible by 32) SUFFICIENT! C answer

Hi..

you are correct with your method and answer but two errors..
[1) a*b*c needs to be$$\geq{32]$$..
Not necessary as 0 can also be one value of a*b*c
2) a,b,c are consecutive even integers
so -2,2,4 is wrong.. it will be -2,0,2

and hence product a*b*c= -2*0*2=0
and o is div by all numbers because 0*any integer = 0
Intern  B
Joined: 09 Dec 2014
Posts: 37
Re: Is a*b*c divisible by 32?  [#permalink]

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The question is to find whether a*b*c is divisible by 32.

Statement 1: a, b and c are consecutive even integers.
We know 32=2^5. That is, to be divisible by 32 the numerator has to contain at least 2^5.

Case 1: Let's take values for a,b and c as 4,6 and 8 respectively.
4= 2^2
6= 2^1 *3
8=2^3
When we add all the powers of 2 and3 we get: (2^6 * 3^2)/2^5
This is divisible by 32. --> YES

Case 2: Let's take values for a,b and c as 2,4 and 6 respectively.
2=2^1
4=2^2
6=2^1 * 3^1
Which gives, (2^4 * 3^1)/2^5
This is not divisible by 32. --> NO
As we get both YES and NO from statement 1, this is not sufficient.

Statement 2: a*c < 0
We are just given a*c is negative and nothing else is given about these numbers.
Case 1: a,b and c can be -8,2 and 10 => (-8*2*10) is divisible by 32 --> YES
Case 2: a,b and c can be -3,1,5 => (-3*1*5) is not divisible by 32 --> NO
Thus statement 2 is insufficient.

Combining both, we have a,b and c are consecutive even integers and a*c<0.
This means, a<0, b is equal to 0 (0 is even and these are consecutive even numbers) and c>0. We don't have to pick numbers and check as anything multiplied by 0 is equal to 0. Also, 0 is a multiple of every number. Thus, 0 is a multiple of 32. Therefore, a*b*c is divisible by 32.

Thus answer is C.

Check this to know more about this property of 0: https://gmatclub.com/forum/is-0-zero-to ... 04179.html
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Ramya Re: Is a*b*c divisible by 32?   [#permalink] 30 Jul 2017, 05:53
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