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# What is the value of k - n ? (1) k^2 - n^2 = 0 (2) k = 11

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Joined: 02 Sep 2009
Posts: 62498
What is the value of k - n ? (1) k^2 - n^2 = 0 (2) k = 11  [#permalink]

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18 Feb 2020, 02:43
00:00

Difficulty:

35% (medium)

Question Stats:

77% (01:04) correct 23% (00:46) wrong based on 43 sessions

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What is the value of k - n ?

(1) k^2 - n^2 = 0
(2) k = 11

Project DS Butler Data Sufficiency (DS3)

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Re: What is the value of k - n ? (1) k^2 - n^2 = 0 (2) k = 11  [#permalink]

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18 Feb 2020, 02:54
1
Bunuel wrote:
What is the value of k - n ?

(1) k^2 - n^2 = 0
(2) k = 11

Project DS Butler Data Sufficiency (DS3)

Question: k - n = ?

Statement 1: k^2 - n^2 = 0

i.e. (k+n)*(k-n) = 0
So k-n may be zero but for k+n =0, k-n may have some other value as well hence

NOT SUFFICIENT

Statement 2: k = 11

NOT SUFFICIENT

COmbining the two statements
(k+n)*(k-n) = 0 and k = 11 but n is still unknown

So k-n may be zero but for k+n =0, k-n may have some other value as well hence

NOT SUFFICIENT

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Re: What is the value of k - n ? (1) k^2 - n^2 = 0 (2) k = 11  [#permalink]

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18 Feb 2020, 03:53
1
Bunuel wrote:
What is the value of k - n ?

(1) k^2 - n^2 = 0
(2) k = 11

Solution

Step 1: Analyse Question Stem

• We need to find the value of $$k – n$$.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

Statement 1: $$k^2 - n^2 = 0$$
• $$k^2 – n^2 = 0 ⟹ (k+n)*(k-n) = 0 ⟹$$ $$(k+n) = 0$$ or $$(k-n) =0$$
• So there will be two cases:
o Case 1: $$k - n = 0$$, or
o Case 2: $$k+n = 0 ⟹ n= -k$$ and $$k – n = 2k$$, but we do not know the value of k.
From this statement we are not getting unique value of k – n.
Hence, statement 1 is not sufficient and we can eliminate answer options B, C and E
Statement 2: $$k = 11$$
• We know the value of k but we don’t know n.
So, we cannot find $$k – n$$.
Hence, statement 2 is also not sufficient and we can eliminate answer B.

Step 3: Analyse Statements by combining.

• From statement 1: $$k – n = 0$$ or $$2k$$
• From statement 2: $$k = 11$$
• On combining both statements: $$k – n = 0$$ or $$22$$
Thus, the correct answer is Option E.
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Re: What is the value of k - n ? (1) k^2 - n^2 = 0 (2) k = 11  [#permalink]

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18 Feb 2020, 04:34
1
Bunuel wrote:
What is the value of k - n ?

(1) k^2 - n^2 = 0
(2) k = 11

Project DS Butler Data Sufficiency (DS3)

i) $$k^2 - n^2 = (k+n) (k-n) = 0$$ => either k+n = 0 or k-n =0 -> Insufficient
ii) $$k = 11$$ - Insufficient

Combining i) and ii)
$$11^2 = n^2$$=> n = +-11 => k-n = 0 or 22 - Insufficient

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Re: What is the value of k - n ? (1) k^2 - n^2 = 0 (2) k = 11  [#permalink]

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18 Feb 2020, 07:38
Bunuel wrote:
What is the value of k - n ?

(1) k^2 - n^2 = 0
(2) k = 11

Project DS Butler Data Sufficiency (DS3)

#1 k^2 - n^2 = 0
(k+n)(k-n) = 0
many possible values insufficient
#2
k=11 ; n not know
insufficient
from 1&2
we can say
121= n^2
n = +/-11
and k-n = 0 or 22
insufficient
IMO E
Re: What is the value of k - n ? (1) k^2 - n^2 = 0 (2) k = 11   [#permalink] 18 Feb 2020, 07:38
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