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If mx ≠ x, is m an integer?

(1) When the reciprocal of m is multiplied by any integer the result is an integer. (2) When the reciprocal of m is added to any integer the result is an integer.

(1) When the reciprocal of m is multiplied by any integer the result is an integer. (2) When the reciprocal of m is added to any integer the result is an integer.

Answer D.

mx is not equal to x, essentially m is not equal to 1.

1. reciprocal of -1 x any integer will give an integer only. Sufficent 2. reciprocal of -1 when added to any integer will give an integer only. Sufficent

(1) When the reciprocal of m is multiplied by any integer the result is an integer. (2) When the reciprocal of m is added to any integer the result is an integer.

i like this qs.

IMO : D

when we simplify the equ we get x (m-1) = 0

so X=0 or M=1

I am able to deduce that m = 1 from both equ, not sure i am missing any cases here

1) The reciprocal of m is an integer and therefore m must be a fraction. m cannot be 0 because 1/m is an integer. 2) The reciprocal of m is an integer and therefore m must be a fraction. m cannot be 0 because 1/m is an integer.

If m is integer then reciprocal multiplied by integer could yield an integer , also if m is a fraction its reciprocal is an integer and yield integer when multiplied by integer ... insuff

From 2

M is not zero and since only an integer when added to integer yield an integer thus m is integer .. suff

If mx ≠ x means m ≠ 1. For Statement 1: M can be -1 or fraction like 1/3 which would satisfy the condition. NOT SUFFICIENT For Statement 2: M can be -1 or fraction like 1/3 which would satisfy the condition. NOT SUFFICIENT Together too -1 and fraction 1/3 would satisfy both the conditions. So we cannot determine whether m is integer or not.

St 1: 1/m into A = B. So, m = always a decimal that gives integer. 1/0.5; 1/0.25; 1/0.125..into any integer that gives NEW integer, then m = decimal. SUFF

St 2: 1/m into A = any integer (A,B,C). However this can only happen is 1/m is reciprocal of 1 (I tried other combinations, it didn't work) so M = 1; and integer. SUFF

St 1: 1/m into A = B. So, m = always a decimal that gives integer. 1/0.5; 1/0.25; 1/0.125..into any integer that gives NEW integer, then m = decimal. SUFF

St 2: 1/m into A = any integer (A,B,C). However this can only happen is 1/m is reciprocal of 1 (I tried other combinations, it didn't work) so M = 1; and integer. SUFF

Ans D.

Ans D.

can you please explain how A works. For eg.

if m is 3/5

and its reciprocal being 5/3....now when this is multiplied by 15 (integer) result is integer 25

for B Any fraction added to an integer wont yield a integer, so m has to be an integer.

Also questions says MX is not equal to X.....so technically M can be any value