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# Is k greater than 3?

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Is k greater than 3? [#permalink]

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08 Oct 2010, 18:55
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62% (00:53) correct 38% (00:59) wrong based on 109 sessions

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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]

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08 Oct 2010, 19:32
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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.

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Re: tricky DS inequalities problem from an old GMAT paper exam [#permalink]

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08 Oct 2010, 21:28
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?

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Re: tricky DS inequalities problem from an old GMAT paper exam [#permalink]

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08 Oct 2010, 23:27
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?

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]

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15 Oct 2010, 11:33
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?

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]

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15 Oct 2010, 13:01
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

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Re: Is k greater than 3? [#permalink]

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30 Jan 2016, 08:26
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Re: Is k greater than 3? [#permalink]

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21 Sep 2017, 00:15
Hello from the GMAT Club BumpBot!

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Re: Is k greater than 3?   [#permalink] 21 Sep 2017, 00:15
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