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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.
_________________

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
_________________

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. Please help. Thanks.

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

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17 Oct 2014, 23:21

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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?

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

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28 Jun 2016, 08:58

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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