Is k greater than 3?

Is \(k>3\)?

(1) \((k-3)(k-2)(k-1)>0\)

The product of 3 numbers is positive if all three are positive (+++) OR two of them are negative and the third one is positive (+--).

Note that: out of 3 numbers \(k-3\) is the least one and \(k-1\) is the biggest one.

\((+)(+)(+)\) is when even the least one is positive so when \(k-3>0\) --> \(k>3\);
\((+)(-)(-)\) is when the biggest one is positive (\(k-1>0\) --> \(k>1\)) and the next one (hence the leas one too) negative (\(k-2<0\) --> \(k<2\)), so when \(1<k<2\);

So \((k-3)(k-2)(k-1)>0\) means that: \(k>3\) or \(1<k<2\) --> \(k\) may or may not be more than 3. Not sufficient.

(2) \(k>1\). Clearly insufficient.

(1)+(2) Intersection of the ranges from (1) and (2) is the range we had in (1) \(k>3\) or \(1<k<2\), so \(k\) may or may not be more than 3. Not sufficient.

Answer: E.
_________________

If (k-3)(k-2)(k-1)>0, doesnt that mean, K>3 or K>2 or K>1?
Why is it K>3 or 1>k>2?
Please explain. Thank you.

When you have inequalities like this one A*B*C>0
Either all three terms are greater than 0 (k>3)
Or exactly one term is greater than 0, and other two are less than 0 (1<k<2)
_________________

Is there a reason for choosing K>3 ? Can it be K<3,K<2 and K>1?

check out the link inequalities-trick-91482.html
_________________

St. 1 gives us that k>2 since the equation is +ve only when all 3 are +ve i.e. k>3 or when 2 -ve and 1+ve fig is there i.e. K>2 -- Not sufficient

St. 2 tells us k>1 -- Not sufficient

Merging St. 1 and St. 2 tells us that k>2 -- Not sufficient.

Therefore, answer is E

If the numbers are (k-3), (k-2), and (k-1), then these are consecutive numbers. Accordingly, (--+) won't exist as it needs to have 0 as well and we know the product is greater than zero.

Can any one of you explain why is my understanding incorrect?

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________