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# Is a*b*c divisible by 32?

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Director
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Is a*b*c divisible by 32? [#permalink]

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24 May 2007, 01:48
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Is a*b*c divisible by 32?

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

(2) a*c < 0
[Reveal] Spoiler: OA

Last edited by Juaz on 24 May 2007, 02:16, edited 1 time in total.

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Re: Is a*b*c divisible by 32? [#permalink]

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24 May 2007, 02:05

strategies:
1-Chose #s -best way

Last edited by UMB on 24 May 2007, 08:43, edited 1 time in total.

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Re: Is a*b*c divisible by 32? [#permalink]

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24 May 2007, 02:17
addendum: a number is divisible by 8 if it can be divided 3 times by 2

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Re: Is a*b*c divisible by 32? [#permalink]

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24 May 2007, 03:03
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.

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Re: Is a*b*c divisible by 32? [#permalink]

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24 May 2007, 11:04
OA is C, as 0 is divisible by 32.

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Re: Is a*b*c divisible by 32? [#permalink]

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25 May 2007, 02:39
I doubt the OA. I am not sure if 0 is divisible by any number.Can anyone throw some light on this?

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Re: Is a*b*c divisible by 32? [#permalink]

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25 May 2007, 03:33
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.

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Re: Is a*b*c divisible by 32? [#permalink]

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25 May 2007, 06:10
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

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Re: Is a*b*c divisible by 32? [#permalink]

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25 May 2007, 16:02

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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Re: Is a*b*c divisible by 32? [#permalink]

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21 Oct 2014, 08:14
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!!!

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Re: Is a*b*c divisible by 32? [#permalink]

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14 May 2016, 12:03
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Is a*b*c divisible by 32? [#permalink]

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24 Aug 2016, 03:00
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"""
_________________

Give me a hell yeah ...!!!!!

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Re: Is a*b*c divisible by 32? [#permalink]

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24 Aug 2016, 04:44
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.
_________________

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Re: Is a*b*c divisible by 32? [#permalink]

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24 Aug 2016, 08:10
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
_________________

Give me a hell yeah ...!!!!!

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Is a*b*c divisible by 32? [#permalink]

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26 Jul 2017, 03:15
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?

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Re: Is a*b*c divisible by 32? [#permalink]

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30 Jul 2017, 04:57
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

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Re: Is a*b*c divisible by 32? [#permalink]

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30 Jul 2017, 05:15
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..

[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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: Is a*b*c divisible by 32? [#permalink]

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30 Jul 2017, 05:36
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..

[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

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Re: Is a*b*c divisible by 32? [#permalink]

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30 Jul 2017, 05:53
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.

_________________

Thanks,
Ramya

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Re: Is a*b*c divisible by 32?   [#permalink] 30 Jul 2017, 05:53
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