If m and n are the positive integers such that m is prime and

If m and n are the positive integers such that m is prime and n is composite. Then
A. m-n cannot be an even number...This cannot be as m= 23 and n =15 (3*5) and hence m- n is even
B. m-n cannot be odd number...this cannot be as m= 23 and n = 6 (2*3) and hence m-n = 17 is odd
C. mn cannot be even...this cannot be as m = 23 and n = 6(2*3) and hence mn= 23*6= 138 is even
D. (m+n)/m cannot be even....this cannot be as m = 23 and n = 69 (3*23) and (m+n)=92 and m+n/m= 92/23= 4 which is even
E. None of the above statements is true

E is the answer

A. m-n cannot be an even number: m=11 and n=9 m-n=2 even
B. m-n cannot be odd number: m=11 and n=8 m-n=3 odd
C. mn cannot be even: m=11 and n=4 mn=44 even
D. (m+n)/m cannot be even: m=2 n=14 (m+n)/m=8 even
E. None of the above statements is true RIGHT

If m and n are the positive integers such that m is prime and n is composite. Then
Let's assume, case I: m=2 and n=6 or case II: m=2 and n=4, or case III: m=2 and n=15, or case IV: m=3 and n=15, then go to the options directly.

A. m-n cannot be an even number, by considering all four cases, m-n can be even or odd. So out
B. m-n cannot be odd number, by considering all four cases, m-n can be even or odd. So out
C. mn cannot be even, by considering all four cases, mn can be even or odd. So out
D. (m+n)/m cannot be even, by considering all four cases, m+n/m can be even or odd. So out
E. None of the above statements is true. So E is correct as all above options are incorrect.

Ans. E

m is prime then m can be of form 2 , 3, 5, 7
n can be any number of the form having 2 or more factors
A. m-n cannot be an even number ex 6-2 =4 , 9-3 = 6 possible (false)
B. m-n cannot be odd number: 8-3 = 5 odd possible (false)
C. mn cannot be even = 2*5 = 10 possible (false)
D. (m+n)/m cannot be even = 1+m/n example 1+21/3 = 1+7 = 8 even possible (false)
Thus E is correct
E. None of the above statements is true

If m and n are the positive integers such that m is prime and n is composite. Then

A. m-n cannot be an even number
if m = 11 and n = 9
then m-n = 2 can be an even number (incorrect)

B. m-n cannot be odd number
if m = 11 and n = 4
then m-n = 7 can be odd number (incorrect)

C. mn cannot be even
if m = 11 and n = 4
then mn = 44 can be even (incorrect)

D. (m+n)/m cannot be even
if m = 2 and n = 10
then (m+n)/m = 6 can be even (incorrect)

E. None of the above statements is true (correct)

IMO E

A. m-n cannot be an even number

if m happens to be 2 then (m-n) will be even.

B. m-n cannot be odd number.

if m happens to be 3 then (m-n) will be odd.

C. mn cannot be even

mn is even since n is a composite no.

D. (m+n)/m cannot be even.

Value of(m+n)/m depends on value of M.

E. None of the above statements is true.

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Solution:

Question 8: If m and n are the positive integers such that m is prime and n is composite. Then

A. m-n cannot be an even number
B. m-n cannot be odd number
C. mn cannot be even
D. (m+n)/m cannot be even
E. None of the above statements is true

According to this question, m and n are positive integers. Therefore, m and n cannot be equal to 0. Moreover, m is prime and n is composite or n also has factors other than 1 and number 'n' itself. We need to select the option in which the statement is true.

Considering the options:

Option A: m-n cannot be an even number. Let m = 13 and n = 9. Then, \(m - n = 13 - 9 = 4\), which is an even number. Thus, option A is eliminated.
Option B: m-n cannot be odd number. Let, m = 7 and n = 6. Then, \(m - n = 7 - 6 = 1\), which is an odd number. Thus, option B is eliminated.
Option C: mn cannot be even . This statement is also false. If m = 7 and n = 6 then, \(mn = 7*6 = 42\), which is even number. Thus, option C is eliminated.
Option D: \(\frac{(m+n)}{m}\) cannot be even. This statement is not true. If \(m = 2\) as 2 is the lowest prime number and \(n = 14\). Then, \(\frac{(m + n)}{m} = \frac{(2 + 14)}{2} = \frac{16}{2} = 8\), which is even number. Thus, option D is also eliminated.

Therefore, the correct answer is Option E that states 'None of the above statements is true'.

This question can easily be solved by substituting different values for m and n.

Solution:

Lets do it by options:
A.m-n cannot be an even number, not possible: m =5,n=1, m-n is even
B. m-n cannot be odd number, m-17,n=4 , m-n is odd
C. mn cannot be even = m=17, n=4 =>17*4 = 68, even
D. (m+n)/m cannot be even true, it will always be a fraction.

Answer D

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