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Is k greater than 3?

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Is k greater than 3? [#permalink] New post 08 Oct 2010, 17:55
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Is k greater than 3?

(1) (k - 3)(k - 2)(k - 1) > 0
(2) k > 1
[Reveal] Spoiler: OA
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Re: tricky DS inequalities problem from an old GMAT paper exam [#permalink] New post 08 Oct 2010, 18:32
Expert's post
tonebeeze wrote:
Is k greater than 3?

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

(2) k > 1


Can you help me explain how to simplify statement 1. Is the key to test values between 0 and 1?

Thanks


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.
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Re: tricky DS inequalities problem from an old GMAT paper exam [#permalink] New post 08 Oct 2010, 20:28
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.
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Re: tricky DS inequalities problem from an old GMAT paper exam [#permalink] New post 08 Oct 2010, 22:27
ranjanav22 wrote:
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)
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Re: tricky DS inequalities problem from an old GMAT paper exam [#permalink] New post 15 Oct 2010, 10:33
shrouded1 wrote:
ranjanav22 wrote:
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?
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Re: tricky DS inequalities problem from an old GMAT paper exam [#permalink] New post 15 Oct 2010, 12:01
tonebeeze wrote:
Is k greater than 3?

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

(2) k > 1


Can you help me explain how to simplify statement 1. Is the key to test values between 0 and 1?

Thanks


check out the link inequalities-trick-91482.html
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Re: tricky DS inequalities problem from an old GMAT paper exam   [#permalink] 15 Oct 2010, 12:01
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