jabhatta@umail.iu.edu wrote:
VeritasKarishma wrote:
kashishh wrote:
If m is a positive odd integer between 2 and 30, then m is divisible by how many different positive prime numbers?
(1) m is not divisible by 3.
(2) m is not divisible by 5.
OA is A
My doubt is when we analyse stat. 1, aren’t we left with
7,11,13,17,19,23,25,29
out of which isn’t 25 has a different answer to the question than the other numbers?
don’t we need stat. 2 to answer it?
The question asks for "... how many
different prime numbers?"
If you are thinking that 25 is divisible by 5 and 5, it still counts as one.
(1) m is not divisible by 3
m is not divisible by 2 anyway since we are talking about odd numbers. Next prime number is 5. The next one is 7 but 5*7 = 35 which is greater than 30. So even if we take the two smallest possible primes, no odd number in the given range can have both as factors. So m must have only one prime number as a factor.
(2) m is not divisible by 5
m could be divisible by 3 and 7 (since 3*7 = 21 which lies in our range). So m could be divisible by one prime or by two different primes. So this statement is not sufficient.
Answer (A)
Hi
VeritasKarishmaI am struggling to see what the question is asking
We are being asked per my understanding -- m is divisible by how many
different prime numbers ?
Isn't thus the answer to S1 /S2 plausibly -- 1 prime is divisible only / 2 primes are divisible only / 3 primes are divisible only /4 prime numbers are divisible only only .......n prime numbers are divisible only
If i solve for S1 -- i see 9 different prime numbers possibly [5 / 7 / 11 / 13 / 17 / 19 / 23 / 25 (5x5 is still one prime number only, i.e. 5) / 29 ]
I marked S1 as sufficient because i got 9 different prime numbers
Is my answer to S1 (=9) incorrect ?
--------------------------------
On the other hand my answer to S2 is 9 as well
S2 set : 3 / 7 / 9 / 11 / 13 / 17 / 19 / 23 / 25(5*5) / 29
prime numbers = 3 / 7 / 11 / 13 / 17 / 19 / 23 / 5 / 29
Please let me know, where is the break in my logic
I don't think you have understood the question. Let me break it down:
Given: "m is a positive odd integer between 2 and 30."
Conclusion: m can be 3/5/7/9/11/13... 29
Question: m is divisible by how many different positive prime numbers?
Answer; Depends on the value of m.
If m is 3, answer is that m is divisible by 1 prime number.
If m is 5, answer is that m is divisible by 1 prime number.
...
If m is 15, answer is that m is divisible by 2 prime numbers.
...
Let's look at the stmnts that will give us more info about m.
(1) m is not divisible by 3.
- m could be 5 in which case it has 1 prime factor.
- m could have 2 prime factors the smallest acceptable ones being 5 and 7. But that would mean m = 5*7 = 35 but m must be less than 30. So m cannot have 2 prime factors and then obviously, not more than 2 either.
Hence m must have only 1 different positive prime factor.
Sufficient
(2) m is not divisible by 5.
- m could be 3 in which case it has 1 prime factor.
- m could be 21 in which it has 2 prime factors (3 and 7)
Not sufficient.
Answer (A)
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