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If m/m < m which of the following must be true about m?
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28 Mar 2020, 18:19
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GMATBusters’ Quant Quiz Question 4 If \(\frac{m}{m}<m\) which of the following must be true about \(m\)? (A) \(m>1\) (B) \(m>2\) (C) \(m<1\) (D) \(m=1\) (E) \(m^2>1\)
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Re: If m/m < m which of the following must be true about m?
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28 Mar 2020, 18:41
If \(\frac{m}{m}<m\) which of the following must be true about mm?
(A) m>1
(B) m>−2
(C) m<1
(D) m=1
(E) \(m^2>1\)
\(\frac{m}{m}<m\)
\(\frac{m}{m}m<0\) \(\frac{(mm^2)}{m}<0\)
Case i) m<0; mm^2>0 \(m > m^2\) Squaring both sides \(m^2 > m^4\) \(m^4  m^2 < 0 \) \(m^2(m+1)(m1) < 0\) 1<m<1 when m < 0 => 1<m<0  i)
Case ii) m>0; mm^2<0 \(m < m^2\) Squaring both sides \(m^2 < m^4\) \(m^4  m^2 > 0 \) \(m^2(m+1)(m1) > 0\) m > 1 or m < 1 when m > 0 => m > 1  ii)
Only option satisfying both the conditions of i) and ii) is option B
i.e. m > 2
Answer  B



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Re: If m/m < m which of the following must be true about m?
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28 Mar 2020, 20:49
If m/m<m, which of the following must be true about m?
If m = 0, 0/0 <0, not possible If m = 0.5, then 0.5/0.5<0.5, 1<0.5, not possible If m = Positive = 1, then 1/1<1, 1<1, so m can not be 1. If m = Positive = 2, then 2/2<2, 1<2, so m can be 2 or greater than 2. If m= negative = 1, then 1/1<1, 1<1, not possible If m = 0.5, then 0.5/0.5<0.5, 1<0.5. So m can be between 0 to 1. If m= negative = 2, then 2/2<2, 1<2, again not possible Last one m=3, then 3/3<3, 1<3, not possible.
So, m can be between 1 and 0 or > 1, as per option only B, which states that m can be anything above 2, fits the condition.
Ans. B.



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Re: If m/m < m which of the following must be true about m?
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28 Mar 2020, 21:07
If m/m<m, which of the following must be true about m? m/m  m <0 (mm^2)/m <0 If m>m^2; m<0; m = m; m>m^2; m^2+m<0 ; m(m+1)<0; 1<m<0; m<1 But if m<m^2; m>0; m = m; m<m^2; m^2m>0 ; m(m1)>0; m>1; m = (1,0)U(1,infinity) 1<m<0 or m>1 are solutions (A) m>1 1<m<0 or m>1 Since 1<m<0 is possible COULD BE TRUE but MUST NOT BE TRUE (B) m>−2 1<m<0 or m>1 m MUST BE >2 MUST BE TRUE (C) m<1 1<m<0 or m>1 If 1<m<0; m<1 But if m>1; m>1 COULD BE TRUE but MUST NOT BE TRUE (D) m=1 1<m<0 or m>1 m = 1 is NOT Possible MUST NOT BE TRUE (E) m^2>1 m>1 1<m<0 or m>1 If 1<m<0; m^2<1 But if m>1; m^2>1 COULD BE TRUE but MUST NOT BE TRUE IMO B
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Re: If m/m < m which of the following must be true about m?
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28 Mar 2020, 22:06
Ans A If m/m<m then m would be greater than 1 let m=2, then 2/2=1<m
or m would be between 0 and 1 let m=1/2, then , 1/2/1/2=1<m
A only addresses 1st option



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Re: If m/m < m which of the following must be true about m?
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28 Mar 2020, 22:42
If mm<mmm<m which of the following must be true about mm?
(A) m>1m>1
(B) m>−2m>−2
(C) m<1m<1
(D) m=1m=1
(E) m2>1
Let's test some numbers, m, and plug them into f(m) = abs(m)/m. The key domains to test will be negative numbers, and fractions, and combinations.
m=2, f(m) = 2/2=1, f(m)>m m=1/2, f(m) = 1, f(m)< m m=1/2, f(m) = 1, f(m) > m m = 2, f(m) = 1, f(m) < m
therefore, we need an answer that accounts for m being negative fractions or greater than 1. m > 2, which is (b)



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Re: If m/m < m which of the following must be true about m?
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29 Mar 2020, 04:37
as only x>2 will have all the values of the equation



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Re: If m/m < m which of the following must be true about m?
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29 Mar 2020, 04:52
We can see with a value \(\frac{1}{2}\),we satisfy the given equation This value suffices (C) m<1 Answer: C



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Re: If m/m < m which of the following must be true about m?
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29 Mar 2020, 05:10
m/m is defined so m≠0
If m is positive, m=m and so m/m<m means m>1
If m is negative, m=m and so m/m<m means m>1
We see that in both cases, m>2
Answer is (B)
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Re: If m/m < m which of the following must be true about m?
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29 Mar 2020, 05:17
For must be true questions, the quickest approach is the prove the answer choices wrong.
B) m>2 does not hold for value m= 1 C) m<1 does not hold for value m= 1/2 D) m=1 does not hold for value m= 1 E) m^2 >1 does not hold for value m= 2
Correct Answer: A



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Re: If m/m < m which of the following must be true about m?
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29 Mar 2020, 05:48
Option (B) Let's break the inequality m/m<m into two cases Case 1: m>0 In such a case, m=m Therefore the LHS of the equation reduces to m/m=m/m=1 Putting the LHS back, this leads to 1<m Case 2: m<0 In such a case, m=m Therefore the LHS of the equation reduces to m/m= 1 Putting this back, this leads to 1<m. Implying that solution in this case is 1<m<0 (because this case if for m<0)
Combining the two cases, we get the solution space to be (1,0)U(1,inf). The only option that satisfies this is option (B) m>2
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Re: If m/m < m which of the following must be true about m?
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29 Mar 2020, 05:54
m/m<m
If m>0, m = m => 1<m If m<0, m= m => 1<m => 1<m<0
Only option B is true for both above equation. Hence B is the answer



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Re: If m/m < m which of the following must be true about m?
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29 Mar 2020, 14:26
m < m^2 When m > 1, like m = 2, this is true. Again when, m < 1, this holds true. Only for values of m between  1 to 1 this doesn't work. So, m^2 > 1. E is the answer.




Re: If m/m < m which of the following must be true about m?
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29 Mar 2020, 14:26




