Using 1 M could be 50,100,150 etc
choose lowest i.e. 50 root 50 is 5*root(2) i.e less than 25
choose 2500 then root 2500 is 25 so eaual
choose 75000 the n root 7500 is greater than 25

insuff


Same logic for 2. u can prove it could be les equal ot more than 25

togather find LCM of 50 and 52

2*26*25 = M

The root will be greater than 25 beacuse root of 25 is 5 and root of 26 is greater than 5


Answer C

This question can be solved with a little bit of number picking and analysis.
I believe everybody can easily come to the conclusion that each statement on its own is not sufficient.
Lets combine both statements

In Data sufficiency questions, we need to look at the question stem to try to rephrase the question to something that is easier to understand.
Its like, Ok, i understand what you are asking .. But what are you REALLY asking ?
Let me deviate a bit. Here is a conversation between between a guy and a gal on a first time date.

Gal : Where do you work and how long have you been working ? (Real Question : Give me a good estimate of how much you make ?)
Guy : How many boy friends have you had ? ( Real Question : Do you remain committed in relationships ? )

Sorry for puns, but i hope that i have been able to drive home the point that, when trying to solve GMAT questions, we need to peel back the layers and
ask, -OK guyz, what do you REALLY want to know ?

Lets rephrase the question a lil bit
IS SQRT (M) > 25

This can be rephrased to IS M > 625 ? ( Squaring both sides)

A) M is divisible by 50
What does this really mean ?
We need to identify the prime factors and their respective powers
M is divisible by 50, implies M is divisible by all prime factors of 50.
50 can be factorized as 5 x 5 x 2
This implies that M contains in its factors ATLEAST 2 FIVES and 1 TWO

A) M is divisible by 52
Following the same line of thinking that we followed above
52 = 13 x 2 x 2
This implies that M contains in its factors ATLEAST 1 THIRTEEN and 2 TWOs

Lets combine these statements. When combining these statements, lets ONLY focus on the highest powers of the prime factors.

50 = 5 x 5 x 2
52 = 13 x 2 x 2

We can establish these factors conclusively
a) M has as its factor AT LEAST 1 instance of 13
b) M has as its factors AT LEAST 2 instances of 5
c) M has as its factors AT LEAST 2 instances of 2
Hence M = K * 13 x 5 x 5 x 2 x 2 ( Where K is some integer .)
Hence M = K * 1300

Hence M is a multiple of 1300 and any multiple of 1300 is always greater than 625.
Hence We can conclusively establish that regardless of the value of K, M > 625

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C.

Stat 1: M could be 50 or a much bigger number whose sqrt is greater than 25. Insuff.

Stat 2: M could be 52 or a much bigger number whose sqrt is greater than 25. Insuff.

Stat 1 & 2: The least value that M can take is 1300 (LCM of 50, 52). Therefore, sqrt (M) has to be greater than 25 the answer is a definite yes. Suff.

Ans : C

1) M can be 50, 100, 150....
2) M can be 52, 104, 156 ...

Using both..

LCM of 52, 50 = 1300

Question :
Is sqrt(m) > 25
=> m > 625..

As LCM is 1300 , we get the one answer .

so Condition is sufficient when both the statements taken together.

I make similar mistakes to raghavsp

I miss things in the first part of the question (I think it is officially called the stem) after I get to working at the problem. Recently I have started rewriting the sentences in inequalities.

So we take a look at the first part of the question.



Because it is written "....m is a positive integer..."
I write out "m>0" on my whiteboard

Then we continue on.



Based on (1) m is the set
M {0,50,100,150.....n50}

It is key to remember that divisible means when m is divided by 50 there is no remainder. So M could equal 0. Except in this situation the stem tells us M>0.



As others have said (2) alone is not enough.

I took some time to calculate the smallest common denominator of \frac{m}{50} and \frac{m}{52}. I came up with 1300.

Does anyone know a quick way to do this? I had to do trial and error until I found 1300 (25x52)

Hi YalePhd,

Thanks for the explanation. but i am not clear..

square root of a positive integer can be +ve or -ve. for eg. sq.rt of 4 = +2, -2.
so sqrt of m can be +ve or -ve..

am i missing something.

thanx in advance.

I don't understand how M could be equal to 100 or 150 based on the information we are given in the first clue. The prime factorization only gives us 2*5*5 which at most equals 50.

The second clue gives us the prime factorization of 2*2*13. Using both clues we have a prime factorization of 2*2*5*5*13 which equals 1300.

So I do understand why the answer is C but your response to clue 1 though me off completely. Please xplain if you don't mind. Thanks, H

I guess I'm confused as to why we know the sqrt(M) is positive. M is positive as stated in the stem but how does that mean that the sqrt(M) is positive. If M were 4 wouldn't the sqrt(M) be -2 or 2? The stem only specifies that M be positive, not the sqrt(M). What am I not seeing?

Clearly its C
we know sqrt M >25 means M >625
1. Insufficient because it can any multiple of 50
2. Insufficient because it again any multiple of 52
Now combining both M= 2X 25X 2 X 13 which greater than 50*26 = 1300 assuming 2 is common in 50 & 52
Sufficient
Bingo C

Came down to choosing between C and E.

Considering both together, the possible values for "m" by plugging in values (multiples of both 50 and 52) come down to 5200, 10400, etc, The square-root of each is greater than 25. Hence I chose C.
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