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# What is the value of │x + 7│?

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What is the value of │x + 7│?  [#permalink]

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13 May 2010, 10:36
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What is the value of │x + 7│?

(1) |x + 3│= 14
(2) (x + 2)^2 = 169
Intern
Joined: 29 Mar 2010
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Schools: SBS, JBS(ding w/o interview), HEC
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Re: What is the value of │x + 7│?  [#permalink]

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13 May 2010, 10:42
ajitsah wrote:
What is the value of │x + 7│?
(1) │x + 3│= 14
(2) (x+2)$$2$$ = 169

OA: D

Am I missing something here. My ans was C.
Stat 1 gives two results; x= 11,-17
Stat 2 gives two results; x= 11,-15

Combining these two, we get that x=11 satisfies the statements and answers the question.
I have read this reasoning somewhere. Pls suggest whether the logic is correct or not, or what should be the strategy behind these type of questions when one variable satisfies both statements and in turn becomes sufficient to answer the question.
Thanks
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Re: What is the value of │x + 7│?  [#permalink]

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13 May 2010, 10:44
ajitsah wrote:
What is the value of │x + 7│?
(1) │x + 3│= 14
(2) (x+2)$$2$$ = 169

One unknown, two equations.

Start with either one and you realize there are two possible values.

For (1): 11 and -17
For (2): 11 and -15

Thus each alone are not sufficient (knock off A, B and D).

Put the together and you see 11 is the only outcome in both that is the same.

The answer is C - together sufficient.

Yeah something is wrong with the OA (typo maybe)
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Re: What is the value of │x + 7│?  [#permalink]

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13 May 2010, 10:47
yeah I just had that exact same reaction...

Statement One X = 11 or -17 plugging it back into the equation X+7= 18 or,10 So NS

Statement Two X=11 or -15 plugging it back into the equation X+7 = 18 or 8

X=11 and X+7 is the only solution that is a constant and thus the answer C

There is no way this can be D unless you forgot to include a clause about X>0
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Re: What is the value of │x + 7│?  [#permalink]

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14 May 2010, 00:40
can you please quote the source ..the answer should not be D it should be C

1) x = 11 or x = -17
so |x + 7 | = 18 or x= 10

so 1 is not sufficient ...and if 1 is not sufficient how can the answer be D ??
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Re: What is the value of │x + 7│?  [#permalink]

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18 Aug 2010, 12:43

A. gives us two values of x i.e. x = 11 or x = -11. However when you substitute these values back into equation given in A, x = 11 is the only valid value. Hence we can find mod ( x + 7 ) = 18

Hence A sufficient.

B. also gives us two values of x, i.e. 11 and -11. Resubstitute both values and validate the equation given in B. It holds true only for x = 11. Hence we are able to find mod (x + 7).

Hence B is sufficient as well.

Hence D is correct answer. Thank You.

Thanks,
Akhil M.Parekh
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Re: What is the value of │x + 7│?  [#permalink]

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18 Aug 2010, 19:14
amp0201 wrote:

A. gives us two values of x i.e. x = 11 or x = -11. However when you substitute these values back into equation given in A, x = 11 is the only valid value. Hence we can find mod ( x + 7 ) = 18

Hence A sufficient.

B. also gives us two values of x, i.e. 11 and -11. Resubstitute both values and validate the equation given in B. It holds true only for x = 11. Hence we are able to find mod (x + 7).

Hence B is sufficient as well.

Hence D is correct answer. Thank You.

Thanks,
Akhil M.Parekh

B gives 2 values as 11 and -15

$$(x+2)^2= 13 ^2$$

$$(x+2)=+-13$$

x=11 , -15

Hence 2 different values

Can you explain how did you get values as 11 and -11 in statement B?
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Re: What is the value of │x + 7│?  [#permalink]

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18 Aug 2010, 21:15
amp0201 wrote:

A. gives us two values of x i.e. x = 11 or x = -11. However when you substitute these values back into equation given in A, x = 11 is the only valid value. Hence we can find mod ( x + 7 ) = 18

Hence A sufficient.

B. also gives us two values of x, i.e. 11 and -11. Resubstitute both values and validate the equation given in B. It holds true only for x = 11. Hence we are able to find mod (x + 7).

Hence B is sufficient as well.

Hence D is correct answer. Thank You.

Thanks,
Akhil M.Parekh

I think its C.

1) This raises two values, X=11 and -17. Therefore, insufficient.
2) This again raises to two values, X=11 and -15. Therefore, insufficient.

Considering 1 and 2, the common value X=11 is considered. Therefore, sufficient.
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Re: What is the value of │x + 7│?  [#permalink]

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18 Aug 2010, 22:11
Sorry my bad. Yes I calculated it wrong.

For B - it is 11 and -15. Hence insufficient.

Together A and B -> x = 11. Hence C is correct answer.

Thanks for pointing out the mistake.

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Re: What is the value of │x + 7│?  [#permalink]

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03 Sep 2010, 10:40

Statement (1) gives two values, x = 11, and x = -17. Both of these values adequately satisfy the equation |x+3|=14. Plug them into |x+7| to get |11+7|=18 and |-17+7|=10. Two different values, thus we can't determine a single solution for x.

Statement (2) also gives two values, x = 11 and x = -15. Both of these values satisfy the equation (x+2)^2=169. Plug them into |x+7| to get |11+7|=18 and |-15+7|=8. Two different values again, thus we can't determine a single solution for x.

Combine (1) and (2) to get x = 11, which results in a single value for |x+7|.
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Re: What is the value of │x + 7│?  [#permalink]

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09 Sep 2010, 11:47
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What is the value of |x + 7|?

(1) $$|x+3|=14$$ --> $$x=11$$ or $$x=-17$$, so $$|x+7|=18$$ or $$|x+7|=10$$. Not sufficient.

(2) $$(x+2)^2=169$$ --> $$x=11$$ or $$x=-15$$, so $$|x+7|=18$$ or $$|x+7|=8$$. Not sufficient.

(1)+(2) $$|x+7|=18$$. Sufficient.

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Re: What is the value of │x + 7│?  [#permalink]

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07 Apr 2018, 01:01
Bunuel wrote:
What is the value of |x + 7|?

(1) $$|x+3|=14$$ --> $$x=11$$ or $$x=-17$$, so $$|x+7|=18$$ or $$|x+7|=10$$. Not sufficient.

(2) $$(x+2)^2=169$$ --> $$x=11$$ or $$x=-15$$, so $$|x+7|=18$$ or $$|x+7|=8$$. Not sufficient.

(1)+(2) $$|x+7|=18$$. Sufficient.

The working is fairly simple here. My only doubt is we getting lX+7l=18 in each of the statement 1 and 2. So, the answer is C
But we also getting lX+7l = 10 (from statement 1 ) and lX+7l=8 (statement 2). So why we ignoring this values of lX+7l. And both of these are different values of lX+7l
Thanks
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Re: What is the value of │x + 7│?  [#permalink]

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07 Apr 2018, 01:34
cruiseav wrote:
Bunuel wrote:
What is the value of |x + 7|?

(1) $$|x+3|=14$$ --> $$x=11$$ or $$x=-17$$, so $$|x+7|=18$$ or $$|x+7|=10$$. Not sufficient.

(2) $$(x+2)^2=169$$ --> $$x=11$$ or $$x=-15$$, so $$|x+7|=18$$ or $$|x+7|=8$$. Not sufficient.

(1)+(2) $$|x+7|=18$$. Sufficient.

The working is fairly simple here. My only doubt is we getting lX+7l=18 in each of the statement 1 and 2. So, the answer is C
But we also getting lX+7l = 10 (from statement 1 ) and lX+7l=8 (statement 2). So why we ignoring this values of lX+7l. And both of these are different values of lX+7l
Thanks

In DS when you have say a = 1 or a = 2 in (1) and a = 1 or a = 3 in (2), then when considering (1)+(2) you are taking the common value, so a = 1.

The same in the given question, both (1) and (2) give two possible values of |x+7|. When considering (1)+(2) |x+7| could only be one of those value, the one which is common for (1) and (2).
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Re: What is the value of │x + 7│? &nbs [#permalink] 07 Apr 2018, 01:34
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