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# What is the value of w?

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Senior Manager
Joined: 22 Dec 2009
Posts: 253
What is the value of w?  [#permalink]

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Updated on: 04 Jan 2014, 06:16
2
7
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:45) correct 41% (01:33) wrong based on 309 sessions

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What is the value of w?

(1) $$w^2=18$$

(2) $$\frac{w^3}{\sqrt{18}}$$ is an integer

Source: PR 1012

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Originally posted by jeeteshsingh on 10 Mar 2010, 03:43.
Last edited by Bunuel on 04 Jan 2014, 06:16, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: What is the value of w?  [#permalink]

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10 Mar 2010, 04:32
2
2
1) $$w^2=18$$ ---> $$w=\pm\sqrt{18}$$. Insufficient.

2) $$\frac{w^3}{\sqrt{18}}$$ is an integer. if $$w^3 = n*\sqrt{18}$$, where n is an integer, we will get infinite number of possible answers. Insufficient.

1)&2) $$\frac{w^3}{\sqrt{18}}=\frac{18*\pm\sqrt{18}}{\sqrt{18}}=\pm18$$. Two integers satisfies both conditions. Insufficient
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Re: What is the value of w?  [#permalink]

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27 Apr 2014, 07:06
This is how I solved.

First statement clearly W could be equal to either 3 sqrt (2) or -3 sqrt (2), therefore insufficient.
Second statement, w^3 / sqrt (18) is an integer this doesn't really tell us much.

Both statements together, if we factorize w^3 as w*w^2 and replace statement 1 in this equation we will have 18w = sqrt (18) * k, where 'k' is an integer.

Therefore after simplifying we are left with w = k / sqrt (18), where 'k' is an integer. Since 'k' could be any number there is NOT a definite value for 'w' and thus answer is E.

Hope this helps
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J
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Re: What is the value of w?  [#permalink]

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30 Apr 2014, 05:40
I also did it this way. First statement w^2 = 18. Now we don't know the sign of w, so abs (w) = sqrt (18). Insufficient. Statement 2 only tells us that w^3 = sqrt (18)(k) where 'k' is an integer. Both together we can replace w^2 in the second staetment and we get that w = sqrt (18) (k) where 'k' could be any integer.

Hence insufficient too.

Hope this helps
Cheers
J
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Re: What is the value of w?  [#permalink]

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22 Jan 2018, 06:58
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Re: What is the value of w?   [#permalink] 22 Jan 2018, 06:58
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