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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] Around the World in 80 Questions (Day 8): What is the value of   26 Jul 2023, 08:00
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E

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Question Stats:

50% (01:31) correct 50% (01:12) wrong based on 251 sessions
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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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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] Around the World in 80 Questions (Day 8): What is the value of   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


 


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

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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] Around the World in 80 Questions (Day 8): What is the value of   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


 


This question was provided by GMAT Club
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] Around the World in 80 Questions (Day 8): What is the value of   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

Win over $20,000 in prizes: Courses, Tests & more

 



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

Win over $20,000 in prizes: Courses, Tests & more

 



(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] Around the World in 80 Questions (Day 8): What is the value of   26 Jul 2023, 09:36
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Statement a gives value of m as 3,1,-1 so not sufficient

Statement b gives value of m as 1 and -1 so not sufficient

Combining both

M value comes out to be 1 and -1

So both together also do not give solution hence E

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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] Around the World in 80 Questions (Day 8): What is the value of   26 Jul 2023, 09:50
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Bunuel wrote:
What is the value of nonzero integer m ?

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



Statement 1:
There are three possible values of m from this statement:
m = 1, -1 or 3
Hence, not sufficient

Statement 2:
There are two possible values of m from this statement
m = 1 or -1
Hence, not sufficient

Combining both the statements:
m = 1 or -1
Still not sufficient

Hence answer option E
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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink] Around the World in 80 Questions (Day 8): What is the value of   26 Jul 2023, 10:03
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What is the value of nonzero integer m ?
m cannot be zero
Statement (1) m^m = m^3
(m^m)/(m^3) =1
hence m^m-3 =1
m can be -1/ 3 /1
Statement 1 not sufficient

(2) |m^3| = 1
m can be -1/ 1
Statement 2 not sufficient

Combining 1 & 2
m can be -1/ 1
Hence combination of Statement 1 & 2 is not sufficient

Option E
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Re: Around the World in 80 Questions (Day 8): What is the value of [#permalink]
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