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If x is a positive number, rounded to the nearest integer,

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If x is a positive number, rounded to the nearest integer,  [#permalink]

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New post 14 Feb 2011, 15:44
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If x is a positive number, rounded to the nearest integer, is x^2 equal to 25?

(1) x rounded to the nearest integer is 5.
(2) x^3 rounded to the nearest integer is 125
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Re: If x is a positive number, rounded to the nearest integer,  [#permalink]

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New post 16 Feb 2011, 07:37
2
1)
\(4.5<=x<5.5\) - if we square every object

\(~20<=x^2<~30\) - approximately

Not sufficient, x^2 could be 20 or 30 or anything between.

2)
\(124.5<=x^3<125.5\)

Lets check a few numbers
4^2 = 16
4.5^2 = ~20
5^2 = 25

4^3 = 64
4.5^3 = ~94 or so
5^3 = 125

So if x^3 rounded to the nearest integer is 125 then x would need to be very close to 5, like 4.99 or so

2 - sufficient.
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Re: If x is a positive number, rounded to the nearest integer,  [#permalink]

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New post 16 Feb 2011, 09:38
banksy wrote:
If x is a positive number, rounded to the nearest integer, is x^2 equal to 25?
(1) x rounded to the nearest integer is 5.
(2) x^3 rounded to the nearest integer is 125


I am having trouble understanding these statements;

x is positive number which is rounded to nearest integer; means x can be 1,2,3,4,5,6,7,...

is x^2=25. or is x=5?

(1) x rounded to nearest integer is 5; well, if x is already a rounded integer; what does this statement tell us? if it tells us that some real number from 4.5 to 5.4 was rounded to 5 and is treated as x and has value 5. then x=5 and x^2=25. Sufficient.

(2) x^3 rounded to nearest integer is 125. Well if x was already a rounded integer as per the question stem, how come it's cube need a rounding.

I am lost.

Someone please break this down for me.
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Re: If x is a positive number, rounded to the nearest integer,  [#permalink]

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New post 16 Feb 2011, 09:55
fluke wrote:
banksy wrote:
If x is a positive number, rounded to the nearest integer, is x^2 equal to 25?
(1) x rounded to the nearest integer is 5.
(2) x^3 rounded to the nearest integer is 125


I am having trouble understanding these statements;

x is positive number which is rounded to nearest integer; means x can be 1,2,3,4,5,6,7,...

is x^2=25. or is x=5?

(1) x rounded to nearest integer is 5; well, if x is already a rounded integer; what does this statement tell us? if it tells us that some real number from 4.5 to 5.4 was rounded to 5 and is treated as x and has value 5. then x=5 and x^2=25. Sufficient.


The question says that x rounded is 5 and asks whether x^2 (where x is not rounded!) is equal to 25 rounded
4.5^2 = ~20.25 which rounds to 20.

fluke wrote:
banksy wrote:
(2) x^3 rounded to nearest integer is 125. Well if x was already a rounded integer as per the question stem, how come it's cube need a rounding.

I am lost.

Someone please break this down for me.


The question does not state whether X is an integer or not, x could any number in the range given.

x in cube rounded to the nearest integer is 125.

x could be 5.001 or 4.995

4.995^3 = 124.625 = rounded to 125
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Re: If x is a positive number, rounded to the nearest integer,  [#permalink]

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New post 16 Feb 2011, 10:01
Mackieman wrote:
fluke wrote:
banksy wrote:
(2) x^3 rounded to nearest integer is 125. Well if x was already a rounded integer as per the question stem, how come it's cube need a rounding.

I am lost.

Someone please break this down for me.


The question does not state whether X is an integer or not, x could any number in the range given.

x in cube rounded to the nearest integer is 125.

x could be 5.001 or 4.995

4.995^3 = 124.625 = rounded to 125


So; what this statement in the question actually convey:

"If x is a positive number, rounded to the nearest integer,"

Shouldn't it ask; "if x is a +ve number, is x^2 equal to 25?" Why this extra information- "rounded to the nearest integer"
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Re: If x is a positive number, rounded to the nearest integer,  [#permalink]

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New post 16 Feb 2011, 17:12
Mackieman wrote:
1)
\(4.5<=x<5.5\) - if we square every object

\(~20<=x^2<~30\) - approximately

Not sufficient, x^2 could be 20 or 30 or anything between.

2)
\(124.5<=x^3<125.5\)

Lets check a few numbers
4^2 = 16
4.5^2 = ~20
5^2 = 25

4^3 = 64
4.5^3 = ~94 or so
5^3 = 125

So if x^3 rounded to the nearest integer is 125 then x would need to be very close to 5, like 4.99 or so

2 - sufficient.



Thanks for the explanation. Need some help though. The question states if x^2 = 25 ? It does not state that if x^2 rounded to the nearest integer = 25. So if X = 4.99 then if x^2 = 24.9 which is not the same as 25. However if X = 5 then x^2 = 25. Hence I think both the statements are not sufficient to provide answer.
Please help. Thanks.
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Re: If x is a positive number, rounded to the nearest integer,  [#permalink]

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New post 17 Feb 2011, 12:52
my only problem is that its not proving its equal to... just somewhere near...
is that enough?!?!

after all, the question is asking if its equals to...
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Re: If x is a positive number, rounded to the nearest integer,  [#permalink]

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New post 17 Oct 2014, 23:38
banksy wrote:
If x is a positive number, rounded to the nearest integer, is x^2 equal to 25?
(1) x rounded to the nearest integer is 5.
(2) x^3 rounded to the nearest integer is 125



From statement 2 we infer that x^3 must be in the range 124.5 to 125.5 , anything between this range when rounded will be 125.

so we need to know if the cube root of the numbers in the range 124.5 to 125.5 , are such that after taking the cube root , if the numbers obtained are squared , and the squared term rounded , is the rounded squared term = 25

For example Let x^3 = 124.5
cube root of 124.5 =4.99
(4.99)^2= 24.9
24.9 rounded to the nearest integer is 25

So B is sufficient.

But my question was how to find the cube root of 124.5 ?
)( Above I have used a calculator for this )
any ideas?
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Re: If x is a positive number, rounded to the nearest integer,  [#permalink]

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Re: If x is a positive number, rounded to the nearest integer, &nbs [#permalink] 23 Sep 2017, 23:43
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