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# If z = |x+y|, is z > 8?

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Director
Joined: 12 Feb 2015
Posts: 915
If z = |x+y|, is z > 8?  [#permalink]

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10 Feb 2019, 09:33
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Difficulty:

15% (low)

Question Stats:

84% (01:01) correct 16% (01:33) wrong based on 70 sessions

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If z = |x+y|, is z > 8?

(1) x > 4

(2) |y| > 4

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Manish

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Re: If z = |x+y|, is z > 8?  [#permalink]

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10 Feb 2019, 09:48
CAMANISHPARMAR wrote:
If z = |x+y|, is z > 8?

(1) x > 4

(2) |y| > 4

To find $$|x+y|>8$$

from 1. we dont know anything about Y so insufficient
from 2.y>4,y<-4 ,insufficient

Combining both also it is insufficient.
Option E
Director
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Re: If z = |x+y|, is z > 8?  [#permalink]

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10 Feb 2019, 09:49
1
CAMANISHPARMAR wrote:
If z = |x+y|, is z > 8?

(1) x > 4

(2) |y| > 4

IMO E

KeyWord = x and y can be +ive or -ive integers/numbers

if z = |x+y|

(1) x > 4, here y can take any value

2) |y| > 4, will imply that
y > 4 or -4 > y

Lets combine now
x = 5.1 and y = 5.1, z > 8 Yes
x = 4.2 and y = -6, z> 8 No
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If z = |x+y|, is z > 8?  [#permalink]

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Updated on: 13 Feb 2019, 22:33

Solution

Given:
• z = |x + y|

To find:
• Whether the value of z greater than 8 or not

Analysing Statement 1
As per the information given in statement 1, x > 4.
• However, from this statement we cannot infer any relevant information regarding y.

Hence, statement 1 is not sufficient to answer the question.

Analysing Statement 2
As per the information given in statement 2, |y| > 4
• From this statement, we can say that y > 4 or y < -4.
• However, from this statement we cannot infer any relevant information regarding x.

Hence, statement 2 is not sufficient to answer the question.

Combining Both Statements
Combining both statements, we get
• x > 4
• y > 4 or y < -4

Now there can be different cases possible. For example,
• If x = 5 and y = 5, then x + y = 5 + 5 = 10, and |x + y| = |10| = 10, which is greater than 8.
• Alternatively, if x = 5 and y = -5, then x + y = 5 + (-5) = 0, and |x + y| = |0| = 0, which is less than 8.

Therefore, even after combining the statements, we cannot determine a unique answer.

Hence, the correct answer is option E.

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Originally posted by EgmatQuantExpert on 12 Feb 2019, 02:29.
Last edited by EgmatQuantExpert on 13 Feb 2019, 22:33, edited 1 time in total.
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Re: If z = |x+y|, is z > 8?  [#permalink]

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12 Feb 2019, 02:35
CAMANISHPARMAR wrote:
If z = |x+y|, is z > 8?

(1) x > 4

(2) |y| > 4

Option E

z = |x+y|

Option A, x>4
If y=2, x=5
then z = |5+2| = 7<8
Hence not true

Option B, |y>4|
if y=5, x=2
then z=|2+5|=7<8
Hence not true

Therefore, none of the two are true
Re: If z = |x+y|, is z > 8?   [#permalink] 12 Feb 2019, 02:35
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