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Around the World in 80 Questions (Day 8): What is the value of

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Bunuel
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Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 08:00
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What is the value of nonzero integer m ?

(1) m^m = m^3
(2) |m^3| = 1


 


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E
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Harshita21988
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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 08:08
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Both statements together are not sufficient to answer the question as according to first statement we can have 1, 3 , -1 etc as possible values then according to second statement we get 1 and -1 as possible values even with both together we can't arrive at a specific value

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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 08:11
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given that m is nonzero integer
what is value of m

#1
m^m = m^3
m can be +1 or -1
insufficient

#2
|m^3| = 1
m can be +1 or -1
insufficient
from 1 &2
m= +1 or -1
insufficient
OPTION E

Bunuel wrote:
What is the value of nonzero integer m ?

(1) m^m = m^3
(2) |m^3| = 1


 


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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 08:11
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The Answer is E
As per Statement 1 m can have a value of 1 or -1. Since both satisfy the statement, we cannot get a unique answer
As per Statement 2- the absolute value of m is 1. Hence m can be 1 or -1. This also does not give us a unique answer
Combining both, we cannot deduce a unique answer for m. Hence E
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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 08:22
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Bunuel wrote:
What is the value of nonzero integer m ?

(1) m^m = m^3
(2) |m^3| = 1


 


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for the Around the World in 80 Questions

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(1) m^m = m^3

a) m = -1

(-1)^(-1) = (-1)^3

b) m = 1

(1)^(1) = (1)^3

m can +1 or m can be -1

Not sufficient.

(2) |m^3| = 1

Taking square on both sides

m^6 = 1

m can +1 or m can be -1

Not sufficient.

Combined

Both values are applicable. Hence the statements combined isn't sufficient as well.

IMO E
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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 08:26
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Bunuel wrote:
What is the value of nonzero integer m ?

(1) m^m = m^3
(2) |m^3| = 1


 


This question was provided by GMAT Club
for the Around the World in 80 Questions

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Statement 1 alone:
m^m = m^3; m can be 3, 1, or -1 so LH = RH so we have 3 different non-zero intergers
so statement 1 alone is not sufficient to answer the question.

Statement 2 alone:
m can be 1 or -1, we have 2 different values of m so
statement 2 alone is not sufficient to answer the question.

Combine (1+2)
still, we can have the two different values of m (1 and -1)
so combining 1+2 is also not sufficient.

So the correct answer is a statement E
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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 08:28
My Answer: C, both statements together are sufficient.

Statement (1): Two possible values of m: 1,3. Both will satisfy the statement hence, insufficient.
Statement (2): m^3=1,-1 So two possible values of m: 1,-1. Both will satisfy the statement hence, insufficient.

Combining both the statements, m=1 so, sufficient.
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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 08:29
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Bunuel wrote:
What is the value of nonzero integer m ?

(1) m^m = m^3
(2) |m^3| = 1


 


This question was provided by GMAT Club
for the Around the World in 80 Questions

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(1) m^m = m^3
Possible solutions are m=3,-1, 1
so, 1 is not sufficient.

(2) |m^3| = 1
Possible solutions are m = 1, -1
So, 2 is not sufficient.

Together, possible solutions are m = 1,-1
So, not sufficient.

E is the right choice.
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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 08:30
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What is the value of nonzero integer m ?

(1) m^m = m^3
(2) |m^3| = 1

Statement 1 :

where m = 3
3^3 = 3^3

where m = 1
1^1 = 1^3

where m = -1
(-1)^(-1) = (-1)^3

Clearly Not Sufficient

Statement 2 :

where m = 1
|1^3| = 1

where m = -1
|(-1)^3| = 1

Clearly Not Sufficient

Combining 1&2

Since m can either be 1 or -1, Not Sufficient

Hence, Option E
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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 08:38
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What is the value of nonzero integer m ?

We know that m is not 0.

(1) m^m = m^3

Case 1: m=1, 1^1=1^3, Case 2: m=-1, -1^1=-1^3, Case 3 m=3, 3^3=3^3 So three cases can prove the statement so it's insufficient.

(2) |m^3| = 1

Case 1: m=1, |1^3|=1, Case 2: m=-1, |-1^3|=1 so two cases can prove the statement so insufficient.

Combining Statement 1 and 2 is still in sufficient because m can either be 1 or -1. Therefore, the answer is (E)
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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 08:44
Bunuel wrote:
What is the value of nonzero integer m ?

(1) m^m = m^3
(2) |m^3| = 1


 


This question was provided by GMAT Club
for the Around the World in 80 Questions

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(1) m^m = m^3
From this m can be 1 or 3 hence insufficient

(2) |m^3| = 1
From this m can be -1 or 1 hence insufficient

A+B we learn that m =1. Hence C is sufficient
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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 08:46
statement 1
m^m=m^3
m=3
sufficient
statement 2
|m^3|=1^3
m=1,-1
sufficient
answer is d
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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 08:46
Asked: What is the value of nonzero integer m ?

(1) m^m = m^3
m = 3
SUFFICIENT

(2) |m^3| = 1
m^3 = 1; m = 1
m^3 = -1; m = -1
m = 1 or -1
NOT SUFFICIENT

IMO A
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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 08:53
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Case 1:

For m = 1
m^m = 1^1 = 1
m^3 = 1^3 = 1

For m = -1
m^m = -1^-1 = 1/-1 = -1
m^3 = -1^3 = -1

Case 2:

For m = 1
|m^3| = 1^3 = 1

For m = -1
|m^3| = |-1^3| = 1

So, both cases gives same result and is inconclusive.

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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 08:55
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Bunuel wrote:
What is the value of nonzero integer m ?

(1) m^m = m^3
(2) |m^3| = 1

 


This question was provided by GMAT Club
for the Around the World in 80 Questions

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(1) m^m = m^3
We can try substituting multiple values like 1,2,3,.... .
\(1^1 = 1^3\\
{-1}^{-1} = {-1}^3\\
3^3=3^3\)
After substituting few values we can see that m can have values 1 , -1 , 3.
Since we have multiple values of m, this choice is insufficient.

(2) |m^3| = 1
m^3 = 1 or m^3 = -1
m=1 or m= -1
Since we have multiple values of m, this choice is insufficient.

(1) + (2)
From 1 and 2, we get two values of m : 1 and -1 .
Thus insufficient.

Answer : E
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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 08:57
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m is a non-zero integer
Q: m?

1) m^m = m^3
m could be 1, -1, or 3 ---> NOT SUFFICIENT

2) |m^3| = 1
=> m^3 = 1 or m^3 = -1 => m = 1 or -1 ---> NOT SUFFICIENT

Combine: m = 1 or -1 --> NOT SUFFICIENT

Answer = [E]
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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 08:58
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Quote:
What is the value of nonzero integer m ?

(1) m^m = m^3
(2) |m^3| = 1


(1) This will hold true for m = 1, -1, 3---------> NOT SUFFICIENT.

(2) case1: m^3 = 1 implies that m = 1
case2: m^3 = -1 implies that m = -1------------> NOT SUFFICIENT.

(1)+(2): two possible values of m = 1 0r -1.------------> NOT SUFFICIENT.

OA: E
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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 09:04
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What is the value of nonzero integer m ?

(1) m^m = m^3
let m=1; 1=1
let m= -1 -1=-1
hence A and D are out
(2) |m^3| = 1
let m=1 then lm^3l =1
let m=-1 then lm^3l =1
hence B is also out
and using 1 and 2 we could not find the value of m. Therefore, it is E
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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 09:16
Statement 1: m^m = m^3

\(m^m - m^3 = 0 => m^3(m^{m-3} - 1) = 0 => \) Either \( m^3 = 0 => m = 0 \) Not Possible or \( (m^{m-3} - 1) => m = 1 & m = 3\) Both possible

So Statement 1 is not sufficient

Statement 2: |m^3| = 1

This statement tells us that the absolute value of m cubed equals 1. This equation holds true for m = 1 and m = -1. So, from this statement alone, we cannot determine the unique value of m.

So Statement 2 is not sufficient

Now, let's consider both statements together.

From statement 1, we know that m = 1 or 3. From statement 2, we know that m = 1 or -1. The only value that satisfies both conditions is m = 1.

Both the statements are sufficient.

Correct answer is C
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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] New post   26 Jul 2023, 09:19
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S1) trying with graphs
see the intersection of f(x)=x^x and g(x)=x^3

x=1 or -1 (NS)
or m=1 or -1

S2) x^3=1 or -1

m=1 or -1 (NS)

S1+S2) we get m=1 or -1
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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink]
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