If mx = m, then what is the value of m?
(1) m has only one multiple.
(2) x has only one distinct factor.
The OA is A.
Why is not sufficient the statement (2)? Experts, may you help me to solve this DS question? Thanks in advanced.
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If mx = m, then what is the value of m?
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Jay@ManhattanReview
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Given: mx = mVJesus12 wrote:If mx = m, then what is the value of m?
(1) m has only one multiple.
(2) x has only one distinct factor.
The OA is A.
Why is not sufficient the statement (2)? Experts, may you help me to solve this DS question? Thanks in advanced.
We have to find out the value of m.
Let's take each statement one by one.
(1) m has only one multiple.
0 is the only number that has only one multiple, thus m = 0. Sufficient. Sufficient. Note multiples of 1 are 1, 2, 3, ...
(2) x has only one distinct factor.
1 is the only number that has only one distinct factor, thus x = 1, but we cannot get the unique value m. m can take any value; for example 0*1 = 0; 10*1 = 10, etc. Insufficient.
The correct answer: A
Hope this helps!
-Jay
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Vincen
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Hello Vjesus12.
I'd solve it as follows:
(1) m has only one multiple.
This implies that, given any integers x and y, we get that $$m\cdot x=m\cdot y\ \ \ \ \forall\ x,y\ \in R.$$ Now, the only number that satisfy this condition is m=0.
Hence, this statement is Sufficient.
(2) x has only one factor.
This implies that the prime factorization of x is only one number, and the unique number that satisfy this condition is x=1.
Therefore, we have that mx=m implies that m=m. But this doesn't tell us what is the value of m. INSUFFICIENT.
Because of this, the answer is the option A.
I'd solve it as follows:
(1) m has only one multiple.
This implies that, given any integers x and y, we get that $$m\cdot x=m\cdot y\ \ \ \ \forall\ x,y\ \in R.$$ Now, the only number that satisfy this condition is m=0.
Hence, this statement is Sufficient.
(2) x has only one factor.
This implies that the prime factorization of x is only one number, and the unique number that satisfy this condition is x=1.
Therefore, we have that mx=m implies that m=m. But this doesn't tell us what is the value of m. INSUFFICIENT.
Because of this, the answer is the option A.
