Around the World in 80 Questions (Day 5): What is the value of the

Question

What is the value of the three-digit positive integer m ?

(1) m has 4 positive factors.

(2) The sum of any 2 digits of m adds up to the same number k.

Muskaan09 · Accepted Answer

The answer will be C.
1. Clearly not sufficient.
2. This gives us that all the three digits are same. It could be 111, 222,333,444,555,666,777,888,999. Not sufficient.

Both will be sufficient as only 111 has 4 factors 1,3,37 and 111.

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nivivacious · Answer

1. m has 4 positive numbers:
A three-digit positive integer m has 4 positive factors. Therefore m is a square of a prime number. The three-digit squares of prime numbers are 121, 169, 289, 361, 529, 841.
But not conclusive as an option to know which one. Hence insufficient

2. Not sufficient on its own

Combining 1+2 : We see that only 121 fits the bill
Hence C

Archit3110 · Answer

target what is the value of 3 digit +ve integer m
#1

m has 4 positive factors.
least value 1*101 ; 2*51 ; 3*37 ; 5*31 ; so on 
insufficient
#2
The sum of any 2 digits of m adds up to the same number k.
possible values 111,222,333,444,555... so on 
insufficient
from 1 &2
111 is only possible number 3*37 ; +ve factors are 4
   option C is correct

NiranjanaV · Answer

3-digit +ve integer = a b c (a, b, c = digits)

1) m has 4 +ve factors => 1, m , prime no. x, prime no. y 
m = xy ---> NOT SUFFICIENT

2) a+b = b+c = c+a => all digits of m are equal (111, 222, 333, .... 999) ---> NOT SUFFICIENT

Combine:
If m = 111 => factors: 1, 111, 3, 37 (four factors)
If m = 222, 333, or any other multiple of 111, # of factors would be greater than 111
 => SUFFICIENT

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