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Intern  Joined: 14 Apr 2016
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If a, b, c, d, and e are integers and cde = 0, is d = 0 ?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 73% (01:19) correct 27% (01:07) wrong based on 423 sessions

### HideShow timer Statistics If a, b, c, d, and e are integers and cde = 0, is d = 0 ?

(1) abc = 30
(2) ace = 0

Spoiler: :: Steps
I got the question right, but is my reasoning correct?

If cde = 0, then c, d or e must equal 0.

(1) Tells us that abc = 30. No information about d.
But we can say that c is different than 0.
Insufficient.

(2) Tells us that ace = 0. No information about d.
But we can say that a, c or e must equal 0.
Insufficient.

Combining both statements: the prompt tells us that c, d or e = 0. (1) That c is not 0, so d or e must equal 0. (2) Based on statement 1, c can't be 0, so a or e is 0.
If cde = 0, is d = 0 ? Since d or e could equal 0, both statements combined are still insufficient. Answer E.

Originally posted by mipek on 01 Oct 2016, 12:53.
Last edited by mipek on 02 Oct 2016, 10:34, edited 1 time in total.
Current Student Joined: 08 Jun 2013
Posts: 33
Re: If a, b, c, d, and e are integers and cde = 0, is d = 0 ?  [#permalink]

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mipek
Your reasoning is absolutely on point. That is the simplest and straight forward approach to solve this question.
Math Expert V
Joined: 02 Aug 2009
Posts: 7763
Re: If a, b, c, d, and e are integers and cde = 0, is d = 0 ?  [#permalink]

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2
1
mipek wrote:
If a, b, c, d, and e are integers and cde = 0, is d = 0 ?

(1) abc = 30
(2) ace = 0

I got the question right, but is my reasoning correct?

If cde = 0, then c, d or e must equal 0.

(1) Tells us that abc = 30. No information about d.
But we can say that c is different than 0.
Insufficient.

(2) Tells us that ace = 0. No information about d.
But we can say that a, c or e must equal 0.
Insufficient.

Combining both statements: the prompt tells us that c, d or e = 0. (1) That c is not 0, so d or e must equal 0. (2) Based on statement 1, c can't be 0, so a or e is 0.
If cde = 0, is d = 0 ? Since d or e could equal 0, both statements combined are still insufficient. Answer E.

Hi
The procedure is correct but a flaw while you combine the two statements..e is surely 0
II tells you either or all of a,c and E are 0 ..BUT a and c are surely NOT 0, so E is zero..

Now cde is 0, so either of three or some or all are 0.. BUT c is not 0, and e is 0..
Still cannot say anything about d.. it can be any number
Insufg
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Intern  Joined: 14 Apr 2016
Posts: 8
Re: If a, b, c, d, and e are integers and cde = 0, is d = 0 ?  [#permalink]

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chetan2u wrote:

Hi
The procedure is correct but a flaw while you combine the two statements..e is surely 0
II tells you either or all of a,c and E are 0 ..BUT a and c are surely NOT 0, so E is zero..

Now cde is 0, so either of three or some or all are 0.. BUT c is not 0, and e is 0..
Still cannot say anything about d.. it can be any number
Insufg

chetan2u,

Saying that in statement II a and c are surely NOT 0; would mean that you took some information from statement I with you, which is not permissible unless you are combining both statements.

Am I missing something?
Math Expert V
Joined: 02 Aug 2009
Posts: 7763
Re: If a, b, c, d, and e are integers and cde = 0, is d = 0 ?  [#permalink]

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mipek wrote:
chetan2u wrote:

Hi
The procedure is correct but a flaw while you combine the two statements..e is surely 0
II tells you either or all of a,c and E are 0 ..BUT a and c are surely NOT 0, so E is zero..

Now cde is 0, so either of three or some or all are 0.. BUT c is not 0, and e is 0..
Still cannot say anything about d.. it can be any number
Insufg

chetan2u,

Saying that in statement II a and c are surely NOT 0; would mean that you took some information from statement I with you, which is not permissible unless you are combining both statements.

Am I missing something?

Hi
You are correct. I have written that I have taken both statements together
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Intern  B
Joined: 11 Jan 2015
Posts: 33
Re: If a, b, c, d, and e are integers and cde = 0, is d = 0 ?  [#permalink]

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Combining both statements: abc + ace = 30 + 0 --> ac(b+e)=30 --> So to evaluate the stem we only know that c is not 0 --> insufficient
Intern  B
Joined: 18 Jan 2017
Posts: 35
Re: If a, b, c, d, and e are integers and cde = 0, is d = 0 ?  [#permalink]

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1
abc = 30

So, we know that a, b and c are not 0

but it is given that ace = 0

Since a and c are not 0, clearly e = 0

cde=0

We know c is not 0, we know e=0, but still nothing about d.
Intern  Joined: 11 Jun 2011
Posts: 3
Location: India
Schools: IMD Jan'18, IIMA
GMAT 1: 680 Q49 V34 GPA: 4
Re: If a, b, c, d, and e are integers and cde = 0, is d = 0 ?  [#permalink]

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malavika1 wrote:
abc = 30

So, we know that a, b and c are not 0

but it is given that ace = 0

Since a and c are not 0, clearly e = 0

cde=0

We know c is not 0, we know e=0, but still nothing about d.

But since we know that a, c, d, e are all different integers then if e must be ZERO, then d must be non zero, so answer is C. What is wrong in this logic?
Intern  B
Joined: 12 May 2017
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If a, b, c, d, and e are integers and cde = 0, is d = 0 ?  [#permalink]

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Quote:
But since we know that a, c, d, e are all different integers then if e must be ZERO, then d must be non zero, so answer is C. What is wrong in this logic?

Who says they are different integers? The info in the question stem only says they are integers.

IF the question stem contained a part which said that the integers were unique, then yes, you would be right and the answer was C.

BUT, that's not the case, so d could be more then 0. So the answer must be E.
Intern  B
Joined: 18 Jan 2017
Posts: 35
Re: If a, b, c, d, and e are integers and cde = 0, is d = 0 ?  [#permalink]

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MaximD wrote:
IF the question stem contained a part which said that the integers were unique, then yes, you would be right and the answer was C.

I feel that if the question stem had mentioned that that the integers were unique, then the answer would have been B.

Then we would have:

cde = 0
ace = 0

Subtracting,

(d-a)ce = 0

d - a cannot be zero, because then d = a (but that's not possible since integers were unique).

So, ce = 0

This means that either c or e is zero.

So, d has to be non-zero.
Intern  B
Joined: 18 Jan 2017
Posts: 35
Re: If a, b, c, d, and e are integers and cde = 0, is d = 0 ?  [#permalink]

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Can someone confirm if my analysis above is correct?
Intern  B
Joined: 01 May 2017
Posts: 10
Re: If a, b, c, d, and e are integers and cde = 0, is d = 0 ?  [#permalink]

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I originally chose C because I assumed that the integers had to be unique. It seems strange to denote them as different variables if they can be the same integer....
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Re: If a, b, c, d, and e are integers and cde = 0, is d = 0 ?  [#permalink]

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f a, b, c, d, and e are integers and cde = 0, is d = 0 ?

(1) abc = 30
(2) ace = 0

for 1)
abc=30 does imply c is not 0 but what about e not sufficient

2)
ace=0 not sufficeint anyone from 3 can be 0 not suffcient

both imply e=0 but what about d , it can be 0 or not

both statements not sufficient .

option E

Thanks Re: If a, b, c, d, and e are integers and cde = 0, is d = 0 ?   [#permalink] 22 Aug 2018, 13:08
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