If a, b, c, d, and e are integers and cde = 0, is d = 0 ? (1) abc = 3

Question

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

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

GMATinsight · Answer

cde = 0 i.e AT-LEAST one of c, d, ande is ZERO

Question: Is d = ?

STatement 1 : abc = 30

i.e. none of a, b and c are zero
but d may be zero or e may be zero hence

NOT SUFFICIENT

Statement 2 : ace = 0

i.e. atleast one of a, e and c is zero
but d and e both may be zero or e may be zero hence

NOT SUFFICIENT

Combining the statements  
abc = 30 i.e. a, b and c are non-zero
ace = 0 i.e. atleast one of a, c and e is zero
but since we know from statement 1 that a nd c are non zero therefore
e = 0
now, cde = 0
i.e. e = o but d may be non zero
Also, e = 0 but d as well may be zero hence

NOT SUFFICIENT

Answer: Option E

RaghavKhanna · Answer

If: cde = 0
=> at least one of them is 0.

St. 1:
abc = 30
=> none of them is 0
=> for cde to be 0, 
d =0, or e=0, or both d and e are 0

=> St. 1 is insufficient.

St.2:
ace = 0
=> atleast one of them is 0.

If a = 0, and c, d non zero
=> d = 0

But, if, any one of c , e is 0
=> d may or may not be 0

=> St. 2 is insufficient

Considering st 1 and st 2

From 1
=> a is not 0 
And, c is not 0

=> e is 0 ( since ace = 0)

=> cde = 0
But d may or may not be 0

=> Both together are insufficient.

=> Answer: E

Posted from my mobile device

Lipun · Answer

Given, cde = 0, => (1) any of the 3 can be zero, (2) more than one can be zero.

ST1: abc = 30, => a,b,c != 0
d or e can be zero. Not sufficient.

ST2: ace = 0, => (1) any of the 3 can be zero, (2) more than one can be zero.
if c or e is 0 , then d may or mayn't be 0. Not sufficient.

1+2: a and c are not 0 => e = 0. But still we can't be sure if d is 0 or not. Not sufficient.

Ans: E

yashikaaggarwal · Answer

Given : cde = 0, 
To find: d = 0 ?

(1) abc = 30
We have 3 variables and zero constraint to determine value(insufficient)

(2) ace = 0
Again, We have no constraint to determine 3 variables value(insufficient)

Together : ABC=30
ACE = 0
AC = 30/B ------(1)
AC = 0/E --------(2)
Equating both.
30/B = 0/E
B = 0 = E
(Insufficient)

Answer is E

Posted from my mobile device

Lipun · Answer

Hi  yashikaaggarwal ,

Minor slip there I guess in equation (1). It should be B.
From ST1, we obtain 'c' not equal to 0. ST1 and ST2 together result in only 'e' equal to 0.

Thanks
Lipun

yashikaaggarwal · Answer

Yes. Thank you, Might have missed.

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 • a, b, c, d, and e are integers.
• c*d*e = 0 ………Eq.(i)
• We need to find out whether d = 0 or not.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  abc = 30
 • Since a*b*c ≠ 0
 o So, we can say that none of a, b, and c are equal to zero 
• However, we still don’t know about e.
 o If e = 0, irrespective of d = 0 or d ≠ 0, c*d*e = 0  
So, we cannot tell for sure whether d = 0 or not.
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.

Statement 2:  ace = 0
 • According to this statement a*c*e = 0
 o It means at least one of a, c, and e is 0. 
• Now, if a = 0 and c ≠0 and e ≠0, 
 o Then from Eq.(i) we can say that d = 0 
• However, if c = 0 or e = 0,
 o Then from Eq.(i) d may be or may not be 0.  
We are getting contradictory results here.
Hence, statement 2 is also NOT sufficient and we can eliminate answer Option B.

Step 3: Analyse Statements by combining. 
From statement 1: a≠0 and c≠0
From statement 2: At least one of a, c, and e is 0.
On combining both we get,
 • e = 0
• However, still we cannot decide whether d = 0 or not. 
 o Because d may be 0 or may not be 0, in both the cases c*d*e = 0  
Thus, the correct answer is  Option E.

vipulshahi · Answer

a,b,c,d,e are integers 
c*d*e = 0 
d = 0?

Statement 1: abc= 30
it means whatever be the value of a,b & c but its sure that a,b & c are not equal to "zero"
Not Sufficient

Statement 2: ace = 0 
It tells that "a" or "c" or "e" is equal to "zero" or more than one terms equal to "zero"
Nothing tells about "d"
Not Sufficient

Statement 1 & Statement 2:
From 1) "a" & "c" not equal to "zero"
From 2) e= 0
Still not sure about "d" , it may be "0" or not.
Not Sufficient

Answer :E

sambitspm · Answer

Kindly see the attachment. 
IMO E

HoneyLemon · Answer

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

(1) abc = 30
 
 d or e can be 0 
 Not sufficient

(2) ace = 0
  a ,d, c or e can be zero 
 Not sufficient

Combining 1 and 2 
 
 cde=0
 ace = 0 
abc=30 
still D or E can be zero . 
 Not sufficient

Hence ans is  E

chetan2u · Answer

Now  cde=0 , so  at least one of c, d and e is 0.

We have to answer -  'Whether d=0?'

If we can prove, c and e are not 0, d will be 0.

(1) abc = 30
 So, we can say for sure that none of a, b or c is 0, as otherwise abc would be 0. 
Thus  c
eq{0} , but what about e??
If  e
eq{0} , then d=0. 
If e=0, d may or may not be 0.

(2) ace = 0
Now c or e could be 0 so d may or may not be 0.

Combined.
 c
eq{0} , but e=0.
So d may or may not be 0, as e=0 will make cde=0

E

hk111 · Answer

I ended up selecting "C" as I thought any of these integers cannot be the same. How do you know when to consider this and when not to?

bumpbot · Answer

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If a, b, c, d, and e are integers and cde = 0, is d = 0 ? (1) abc = 3

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