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

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Manager
Joined: 10 Feb 2011
Posts: 109
If x is a positive number, rounded to the nearest integer,  [#permalink]

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14 Feb 2011, 15:44
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Difficulty:

95% (hard)

Question Stats:

39% (01:22) correct 61% (01:16) wrong based on 168 sessions

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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
Manager
Joined: 20 Dec 2010
Posts: 162
Location: Stockholm, Sweden
Re: If x is a positive number, rounded to the nearest integer,  [#permalink]

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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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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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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
_________________

12/2010 GMATPrep 1 620 (Q34/V41)
01/2011 GMATPrep 2 640 (Q42/V36)
01/2011 GMATPrep 3 700 (Q47/V39)
02/2011 GMATPrep 4 710 (Q48/V39)
02/2011 MGMAT CAT 1 650 (Q46/V32)
02/2011 MGMAT CAT 2 680 (Q46/V36)
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Posts: 1869
Re: If x is a positive number, rounded to the nearest integer,  [#permalink]

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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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Joined: 17 Jan 2011
Posts: 1
Re: If x is a positive number, rounded to the nearest integer,  [#permalink]

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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.
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Joined: 08 Nov 2010
Posts: 349
Re: If x is a positive number, rounded to the nearest integer,  [#permalink]

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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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Posts: 68
Re: If x is a positive number, rounded to the nearest integer,  [#permalink]

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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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23 Sep 2017, 23:43
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