The digit m is greater than 1, what is m?

from stem m is integer such that 1<m<=9

from 1

m could be 5 or 6 ... insuff

from 2

m has 2 factors , only primes does thus m could be 2,3,5,7... insuff

from both

m = 5

C

FROM STATEMENT - I ( INSUFFICIENT )

\(m\) & \(m^2\) can have same digits only when m (greater than 1) = 5 & 6

So, there are multiple possible values..

FROM STATEMENT - II ( INSUFFICIENT )

This statement alone is insufficient to find the value of m

FROM STATEMENT I & II ( SUFFICIENT )

The value of m must be 5 as 6 has three factors 1, 2 & 3

Hence, BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked , correct answer must be (C)

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Why not m=11? 11^2=121 and 11 have same units digit. Also, 11 has only 2 factors.

It's given that m is a digit, so 0, 1, 2, 3, 4, 5, 6, 7, ,8, 9.
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The digit m is greater than 1, what is m?

(1) The units digit of m is the same as the units digit of m^2
(2) m has 2 factors

St I
The units digit of m is the same as the units digit of m^2
Numbers with 5 or 6 as unit digit follow the above statement. ----------Insufficient

St II
m has 2 factors => m is prime number and m >1 so m can be 2,3,5... ------------Insufficient

Combining St I and II, we have Only 5 that satisfies both the conditions where 5 is prime and 5>1 and units digit of 5 and \(5^2\) is same i.e. 5

Hence Option C is correct

PS : # The correct option will be C only if m is a single digit number (Note : The digit m is greater than 1)

# But if m is not a single digit number then the Option will be E as m can also be 11, where 11 > 1 and
units digit of 11 and \(11^2\)=121 is same i.e. 1 and 11 is prime

Hit Kudos if you liked it

Option 1. It can be 5 or 6.
As 5^2=25 and 6^2=36. Not sufficient
Option 2. It is prime number. Not sufficient.
Together sufficient. Ans is 5.
Option c

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Merging topics. Please refer to the discussion above.
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