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# M04-11

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:22
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45% (medium)

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58% (00:51) correct 42% (00:42) wrong based on 212 sessions

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If $$j \ne 0$$, what is the value of $$j$$ ?

(1) $$|j| = j^{-1}$$

(2) $$j^j = 1$$

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Joined: 02 Sep 2009
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16 Sep 2014, 00:22
Official Solution:

(1) $$|j| = j^{-1}$$. Rewrite as $$|j|*j=1$$. From that we have $$j=1$$ (here $$j$$ cannot be a negative number, since in this case we would have $$|j|*j=\text{positive}*\text{negative}=\text{negative} \ne 1$$). Sufficient.

(2) $$j^j = 1$$. Again only one solution: $$j=1$$. Sufficient.

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19 Sep 2014, 01:57
As per ii) j^j = 1.

So 1 can also be equal to j^0.

Therefore, j^j = j^0. so same base power is equated which brings us to: j=0.

But 0^0 = 0 so that is not our solution.

hence j=1, as any number raised to same power if = 1 then that number is 1.

Am i right in assuming the following rule (highlighted one) based on the above calculations ?

Kindly shed some light on it.
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19 Sep 2014, 02:06
2
earnit wrote:
As per ii) j^j = 1.

So 1 can also be equal to j^0.

Therefore, j^j = j^0. so same base power is equated which brings us to: j=0.

But 0^0 = 0 so that is not our solution.

hence j=1, as any number raised to same power if = 1 then that number is 1.

Am i right in assuming the following rule (highlighted one) based on the above calculations ?

Kindly shed some light on it.

Sorry, but not following you...

Anyway, 0^0, in some sources equals to 1, some mathematicians say it's undefined. But you won't need this for the GMAT because the case of 0^0 is not tested on the GMAT. So on the GMAT the possibility of 0^0 is always ruled out (in our question it's also rules out, notice that we are given that j is not 0).
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19 Sep 2014, 03:07
Bunuel wrote:
earnit wrote:
As per ii) j^j = 1.

So 1 can also be equal to j^0.

Therefore, j^j = j^0. so same base power is equated which brings us to: j=0.

But 0^0 = 0 so that is not our solution.

hence j=1, as any number raised to same power if = 1 then that number is 1.

Am i right in assuming the following rule (highlighted one) based on the above calculations ?

Kindly shed some light on it.

Sorry, but not following you...

Anyway, 0^0, in some sources equals to 1, some mathematicians say it's undefined. But you won't need this for the GMAT because the case of 0^0 is not tested on the GMAT. So on the GMAT the possibility of 0^0 is always ruled out (in our question it's also rules out, notice that we are given that j is not 0).

Thanks for pointing that out. Yes, I was confused because 0^0 = 1 (actually several answers to this solution), some say its 0, some say its undefined.

But, yes the question says "j is not equal to 0".
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13 Apr 2015, 17:02
What if J=-1?
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14 Apr 2015, 04:41
holyrage wrote:
What if J=-1?

J = -1 does not satisfy any of the statements:

(1) |J| = 1 and J^(-1) = (-1)^(-1) = -1.

(2) (-1)^(-1) = -1 not 1.
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18 Feb 2016, 22:12
Hi Bunuel,

Not getting where am I going wrong with statement 1

|j|=j^-1

j=1/j

j^2=1

And j=-(1/j)

j^2=-1

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19 Feb 2016, 01:55
3
NandishSS wrote:
Hi Bunuel,

Not getting where am I going wrong with statement 1

|j|=j^-1

j=1/j

j^2=1

And j=-(1/j)

j^2=-1

j^2=-1 has no real solutions.

j^2=1 has two solutions j=-1 and j=1 but j=-1 does not satisfy |j|=j^(-1), so we are left with j=1 only.

Hope it's clear.
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20 Feb 2016, 03:25
Thanks a lot Bunuel!!!:-)
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25 Feb 2016, 09:59
Bunuel wrote:
If $$j \ne 0$$, what is the value of $$j$$ ?

(1) $$|j| = j^{-1}$$

(2) $$j^j = 1$$

Hi

For stmt 1, what I did was I squared both sides to get rid of the mod sign. So :

j^2=1/j^2

j^4=1
Hence j takes both 1 0r -1. not sufficient.

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25 Feb 2016, 10:21
1
sinhap07 wrote:
Bunuel wrote:
If $$j \ne 0$$, what is the value of $$j$$ ?

(1) $$|j| = j^{-1}$$

(2) $$j^j = 1$$

Hi

For stmt 1, what I did was I squared both sides to get rid of the mod sign. So :

j^2=1/j^2

j^4=1
Hence j takes both 1 0r -1. not sufficient.

When you square any equation, you are invariably increasing the number of solutions to twice the actual number of solution. A linear equation has 1 solution while a quadratic equation has 2 etc.

Statement 1 is linear in j and hence only 1 solution should be possible. When you square, make sure to check back the solutions by plugging them into the main equation and see which one actually satisfies the original linear equation.

After you got 1 and -1 as your solutions, -1 is rejected as it does not satisfy $$|j| = j^{-1}$$. Thus, only j=1 satisfies the given conditions.

Hope this helps.
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17 Sep 2016, 04:59
can u please explain me where i m wrong?
if j=-1
|j|=-1 as if |x|=-x if x<0
then |j|*j=1(-1*-1)
-1 also satisfies this
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08 Jun 2017, 20:37
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. how j^j = 1 results in j=1
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23 Sep 2017, 06:15
Hello Bunuel,

Though I agree with the solution, I am not able to see where I am going wrong when solving for S1.Can you please check my work and suggest where I am going wrong?

S1: $$|J| = J^{-1}$$

Opening the Modulus we have

Case 1:

$$J = J^{-1}$$

$$J^2 = 1$$

$$J = ± 1$$

Case 2 :

$$-J = j^{-1}$$

$$-J^2 = 1$$ (Undefined on GMAT).

Substituting Both J = 1 and J = -1 into the equation we can also see the equation is satisfied.

So, should we not conclude that J = ± 1 ?
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23 Sep 2017, 07:19
1
susheelh wrote:
Hello Bunuel,

Though I agree with the solution, I am not able to see where I am going wrong when solving for S1.Can you please check my work and suggest where I am going wrong?

S1: $$|J| = J^{-1}$$

Opening the Modulus we have

Case 1:

$$J = J^{-1}$$

$$J^2 = 1$$

$$J = ± 1$$

Case 2 :

$$-J = j^{-1}$$

$$-J^2 = 1$$ (Undefined on GMAT).

Substituting Both J = 1 and J = -1 into the equation we can also see the equation is satisfied.

So, should we not conclude that J = ± 1 ?

j = -1 does NOT satisfy |j| = j^(-1):

LHS = |-1| = 1 while RHS = (-1)^(-1) = -1.
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23 Sep 2017, 07:27
How silly of me! <Slapping myself now!>

Thank you so much Bunuel for correcting me!!

Bunuel wrote:
susheelh wrote:
Hello Bunuel,

Though I agree with the solution, I am not able to see where I am going wrong when solving for S1.Can you please check my work and suggest where I am going wrong?

S1: $$|J| = J^{-1}$$

Opening the Modulus we have

Case 1:

$$J = J^{-1}$$

$$J^2 = 1$$

$$J = ± 1$$

Case 2 :

$$-J = j^{-1}$$

$$-J^2 = 1$$ (Undefined on GMAT).

Substituting Both J = 1 and J = -1 into the equation we can also see the equation is satisfied.

So, should we not conclude that J = ± 1 ?

j = -1 does NOT satisfy |j| = j^(-1):

LHS = |-1| = 1 while RHS = (-1)^(-1) = -1.

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21 Oct 2017, 14:40
I understand that when you square both sides of an equation you create another solution that is potentially invalid due to some other parameter (equation, stipulation etc). But how is that happening here? I just multiplied both sides by j, I didn't square anything.

|j| = 1\j
|j| * j = 1

I then considered both cases to remove the modulus and found j = +/- 1.

Now, I am sure the best practice here is just always to check too see that both solutions work, but can someone explain to me here why I ended up with two solutions (one of which does not hold) without squaring both sides of the equation?

Thanks!
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05 Apr 2018, 22:57
Hi Guys

statement 1 : |j| * j = 1

Doesn't this equation have two solutions that is

-j * j = 1 (eq 1) & j * j = 1 (eq 2)

if j=1 then eq 2 satisfies not eq 1
but if j=-1 then eq 2 satisfies but not eq 1

We have two values of "j" here. Then Statement 1 must not be sufficient.

Am i missing something here ?
Any help is appreciated

Thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 49965

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06 Apr 2018, 02:12
Hi Guys

statement 1 : |j| * j = 1

Doesn't this equation have two solutions that is

-j * j = 1 (eq 1) & j * j = 1 (eq 2)

if j=1 then eq 2 satisfies not eq 1
but if j=-1 then eq 2 satisfies but not eq 1

We have two values of "j" here. Then Statement 1 must not be sufficient.

Am i missing something here ?
Any help is appreciated

Thanks.

$$j = -1$$ does NOT satisfy $$|j| = j^{(-1)}$$:

$$LHS = |-1| = 1$$ while $$RHS = (-1)^{(-1)} = -1$$.
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# M04-11

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