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If ab=c, b=?

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If ab=c, b=? [#permalink]

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New post 19 Dec 2016, 01:10
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

45% (00:59) correct 55% (01:04) wrong based on 161 sessions

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If ab=c, b=?

1) c≠0
2) |a-c|≤0

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Re: If ab=c, b=? [#permalink]

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New post 19 Dec 2016, 01:22
b=c/a ?? We need to find the value.

1) c not equals 0... Clearly Insufficient

2) |a-c|<= 0. So
I)a-c<= 0 I.e a<=c if a=c;b=1, and if a<c we don't have any value
2) -(a-c) <= 0 I.e c<= a. Same as above
So clearly insufficient.

Combining the 2 we don't get any concrete answer so answer is (E)

Correct me if wrong

Omkar Kamat
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Re: If ab=c, b=? [#permalink]

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New post 20 Dec 2016, 08:13
what's wrong with option E please explain
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Re: If ab=c, b=? [#permalink]

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New post 20 Dec 2016, 09:49
Omkar.kamat wrote:
b=c/a ?? We need to find the value.

1) c not equals 0... Clearly Insufficient

2) |a-c|<= 0. So
I)a-c<= 0 I.e a<=c if a=c;b=1, and if a<c we don't have any value
2) -(a-c) <= 0 I.e c<= a. Same as above
So clearly insufficient.

Combining the 2 we don't get any concrete answer so answer is (E)

Correct me if wrong

Omkar Kamat
When The Going Gets Tough, The Tough Gets Going !!



2nd stmnt can't be less than zero but it can be equal to zero. therefore a=c.

ab-c=0; a=c; c(b-1)=0. from stmnt 1 C not equal to zero . b=1. solution is C
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Re: If ab=c, b=? [#permalink]

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New post 20 Dec 2016, 11:08
Initially i was thinking around c but still took E :-/, anyway thank you robu

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Re: If ab=c, b=? [#permalink]

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New post 21 Dec 2016, 01:42
==> In the original condition, there are 3 variables (a, b, c) and 1 equation (ab=c). In order to match the number of variables to the number of equations, there must be 2 equations, and therefore C is most likely to be the answer.
By solving con 1) and con 2), from con 2), you get a=c, and if you substitute this into ab=x, you get ab=a. In order to divide a from both sides, it needs to be a≠0. From con 1), it is c=a≠0, and if you divide both sides by a, you get b=1, hence it is unique and sufficient.

Therefore, the answer is C.
Answer: C
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Re: If ab=c, b=? [#permalink]

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New post 24 Dec 2016, 01:57
Omkar.kamat wrote:
b=c/a ?? We need to find the value.

1) c not equals 0... Clearly Insufficient

2) |a-c|<= 0. So
I)a-c<= 0 I.e a<=c if a=c;b=1, and if a<c we don't have any value
2) -(a-c) <= 0 I.e c<= a. Same as above
So clearly insufficient.

Combining the 2 we don't get any concrete answer so answer is (E)

Correct me if wrong

Omkar Kamat
When The Going Gets Tough, The Tough Gets Going !!




|a-c| can never be <0 it can only equate to a-c=0 => a=c
from statement 1 A not equals C therefore b=c/a =1
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Re: If ab=c, b=? [#permalink]

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New post 24 Dec 2016, 02:17
robu wrote:
Omkar.kamat wrote:
b=c/a ?? We need to find the value.

1) c not equals 0... Clearly Insufficient

2) |a-c|<= 0. So
I)a-c<= 0 I.e a<=c if a=c;b=1, and if a<c we don't have any value
2) -(a-c) <= 0 I.e c<= a. Same as above
So clearly insufficient.

Combining the 2 we don't get any concrete answer so answer is (E)

Correct me if wrong

Omkar Kamat
When The Going Gets Tough, The Tough Gets Going !!



2nd stmnt can't be less than zero but it can be equal to zero. therefore a=c.

ab-c=0; a=c; c(b-1)=0. from stmnt 1 C not equal to zero . b=1. solution is C

Thanks Robu ,

I completely missed out that modulus of something cannot be < 0

Omkar Kamat
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If ab=c, b=? [#permalink]

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New post 10 Jan 2017, 23:17
nks2611 wrote:
what's wrong with option E please explain


Hi nks2611,

In the original condition, there are 3 variables(a,b,c) and 1 equation(ab=c).
Hence, C is likely to be an answer.

Happy Studying!
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Re: If ab=c, b=? [#permalink]

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New post 04 May 2017, 16:05
how can |a-c|<=0?
|a-c| is already >0.
only option left is if |a-c| = 0
a-c=0 -> a=c
-a+c=0
c=a
same thing
if ab=c and a=c, then b=1.

my vision was poor, and i thought 1st statement says c=0...
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Re: If ab=c, b=? [#permalink]

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New post 04 May 2017, 22:40
1
mvictor wrote:
how can |a-c|<=0?
|a-c| is already >0.
only option left is if |a-c| = 0
a-c=0 -> a=c
-a+c=0
c=a
same thing
if ab=c and a=c, then b=1.

my vision was poor, and i thought 1st statement says c=0...


Since \(|a-c| \ge 0\), \(|a-c| \le 0\) means \(a - c = 0\) or \(a = c\).
When we consider both conditions together, \(ab = c\) is equivalent to \(ab - c = 0\) or \(ab - c = cb - c = c ( b - 1 ) = 0\).
Since \(c \ne 0\), we have \(b = 1\).

Therefore the answer is C.
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Re: If ab=c, b=? [#permalink]

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New post 05 May 2017, 06:25
MathRevolution wrote:
mvictor wrote:
how can |a-c|<=0?
|a-c| is already >0.
only option left is if |a-c| = 0
a-c=0 -> a=c
-a+c=0
c=a
same thing
if ab=c and a=c, then b=1.

my vision was poor, and i thought 1st statement says c=0...


Since \(|a-c| \ge 0\), \(|a-c| \le 0\) means \(a - c = 0\) or \(a = c\).
When we consider both conditions together, \(ab = c\) is equivalent to \(ab - c = 0\) or \(ab - c = cb - c = c ( b - 1 ) = 0\).
Since \(c \ne 0\), we have \(b = 1\).

Therefore the answer is C.


thanks! this actually makes sense! I didn't think of that!
Re: If ab=c, b=?   [#permalink] 05 May 2017, 06:25
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