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# Is |x – 3| < 7 ?

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Re: Is |x – 3| < 7 ? [#permalink]
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davidfrank wrote:
Bunuel wrote:
Is |x – 3| < 7 ?

Is $$|x - 3| < 7$$? --> is $$-7<x-3<7$$? --> is $$-4<x<10$$?

(1) x > 0. Not sufficient.
(2) x < 10. Not sufficient.

(1)+(2) $$0<x<10$$, thus x IS from the range (-4, 10). Sufficient.

Answer: C.

Hi Bunuel,

I know this is a fairly easy example but I didn't get it. The value of x as per the question lies between -4 and 10.

1. Statement 1 say x>0, which means x values lies from 0>x> infinity. How should I infer/relate this statement.
2. Statement 2 says the value of x values lies from negative infinity and <10. How should I infer/relate this statement.
Please help me understand this.

The question asks whether $$-4<x<10$$ (it's not given).

(1) says that x>0. If x=1, then the answer to the question is YES but if x=1,000, then the answer to the question is NO. Not sufficient.
(2) says that x<10. If x=1, then the answer to the question is YES but if x=-1,000, then the answer to the question is NO. Not sufficient.

When combined: 0<x<10, thus the answer to the question is YES. Sufficient.

Does this make sense?
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Re: Is |x – 3| < 7 ? [#permalink]
Bunuel wrote:
davidfrank wrote:
Bunuel wrote:
Is |x – 3| < 7 ?

Is $$|x - 3| < 7$$? --> is $$-7<x-3<7$$? --> is $$-4<x<10$$?

(1) x > 0. Not sufficient.
(2) x < 10. Not sufficient.

(1)+(2) $$0<x<10$$, thus x IS from the range (-4, 10). Sufficient.

Answer: C.

Hi Bunuel,

I know this is a fairly easy example but I didn't get it. The value of x as per the question lies between -4 and 10.

1. Statement 1 say x>0, which means x values lies from 0>x> infinity. How should I infer/relate this statement.
2. Statement 2 says the value of x values lies from negative infinity and <10. How should I infer/relate this statement.
Please help me understand this.

The question asks whether $$-4<x<10$$ (it's not given).

(1) says that x>0. If x=1, then the answer to the question is YES but if x=1,000, then the answer to the question is NO. Not sufficient.
(2) says that x<10. If x=1, then the answer to the question is YES but if x=-1,000, then the answer to the question is NO. Not sufficient.

When combined: 0<x<10, thus the answer to the question is YES. Sufficient.

Does this make sense?

Hi Bunuel,

Thanks I got it now. I was able to comprehend the indivdual statements but couldn't understand the meaning of both statements together
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Re: Is |x – 3| < 7 ? [#permalink]
|x – 3| < 7 ?
Case 1 : X-3 <7 -------> X < 10 condition1
Case 2: -(X-3) < 7 -------> X-3 > -7 ------------> X>-4 condition 2

Combining both Condition becomes : Is -4 < X <10 ?

Statement 1 : X< 10 , but x can be -10 too, Not sufficient
Statement 2 : X > 0 , but x can be 11 too , Not sufficient

Combining both St. 0<X<10 , range of this statement is within the range of given condition. Hence sufficient.
Answer C
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Is |x – 3| < 7? [#permalink]
Is |x – 3| < 7 ?

1) x > 0

2) x < 10
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Re: Is |x – 3| < 7 ? [#permalink]
noTh1ng wrote:
Is |x – 3| < 7 ?

1) x > 0

2) x < 10

Refer to the posts above.

Please search for a question before posting.

Topics merged.
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Re: Is |x – 3| < 7 ? [#permalink]
Engr2012 wrote:
noTh1ng wrote:
Is |x – 3| < 7 ?

1) x > 0

2) x < 10

Refer to the posts above.

Please search for a question before posting.

Topics merged.

i did.. could not find it via google / forum search function.
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Re: Is |x – 3| < 7 ? [#permalink]
Expert Reply
jlgdr wrote:
Is |x – 3| < 7 ?

(1) x > 0
(2) x < 10

This is a Yes or No question. Thus, a definitive answer of Yes or No makes the statement sufficient; it is not sufficient if the answer you get is "maybe".

With Stmt 1, we we get "MAYBE" - if x= 2, then the result is less than 7; but, if x = 90, then it does not ==> NOT SUFFICIENT
With Stmt 2, we also get "MAYBE" - if x = 9, the result is less than 7; but if x = -90, then it is greater than 7. ==> NOT SUFFICIENT

Taken together, Stmts 1 and 2 tell us that x is between 0 and 10. Given this, every result would be less than 7, so together they are SUFFICIENT.

Correct answer is C
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Is |x – 3| < 7 ? [#permalink]
noTh1ng wrote:
Is |x – 3| < 7 ?

1) x > 0

2) x < 10

Evaluate from the required condition |x-3|<7 what values/range of values of x will give you a "yes' or "no".

|x-3|<7 ---> -4<x<10

Per statement 1, x>0, now based on our mini analysis above , x<10 for a "yes" answer but x > 0 can also make x = 20 in which case , there will be a "no". Thus this statement is not sufficient.

Per statement 2, x<10, again based on our mini analysis above, if x = = -3, then "yes" but if x =-10, then "no". Thus not sufficient.

Combining, 0<x<10 ---> this goes fine with our analysis that -4<x<10 will always give a "YES". Thus C is the correct answer, both the statements combined are sufficient.
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Re: Is |x – 3| < 7 ? [#permalink]
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Re: Is |x – 3| < 7 ? [#permalink]
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