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# If the integer x is rounded to the nearest hundred

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Manager
Joined: 06 Jun 2012
Posts: 131
If the integer x is rounded to the nearest hundred  [#permalink]

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04 Aug 2013, 16:29
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Difficulty:

55% (hard)

Question Stats:

67% (01:56) correct 33% (02:13) wrong based on 281 sessions

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If the integer x is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten. which of the following is a possible value of x?

A. 64
B. 67
C. 99
D. 133
E. 147

What is 99 is rounded to nearest ten? Also what is 133 rounded to nearest ten & hundred?

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Re: If the integer x is rounded to the nearest hundred  [#permalink]

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04 Aug 2013, 16:42
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summer101 wrote:
If the integer x is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten. which of the following is a possible value of x?

A. 64
B. 67
C. 99
D. 133
E. 147

What is 99 is rounded to nearest ten? Also what is 133 rounded to nearest ten & hundred?

We have to check options 1 by 1.

64 rounded to nearest hundred = 100
64 rounded to nearest ten = 60
now difference = 40
the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten.
therefore 40/60)*100 = 66 2/3 ==>this is the answer.

99 rounded to nearest ten = 100
133 rounded to nearest ten = 130
133 rounded to nearest hundred = 100

hope this helps
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Posts: 613
Re: If the integer x is rounded to the nearest hundred  [#permalink]

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04 Aug 2013, 21:48
summer101 wrote:
If the integer x is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten. which of the following is a possible value of x?

A. 64
B. 67
C. 99
D. 133
E. 147

What is 99 is rounded to nearest ten? Also what is 133 rounded to nearest ten & hundred?

Let the integer when rounded to the nearest 10 be $$x^'$$. Also, the integer when x is rounded to the nearest 100 be $$x^{''}$$.
Given that$$\frac{200}{3*100}*x^'+x^' = x^{''}$$ = $$\frac{5}{3}*x^' = x^{''}$$

Thus, $$x^'$$has to be a multiple of 3. The only options, which when rounded to the nearest ten give a multiple of 3 are A(60) and E(150).
It's easy to see that $$\frac{5}{3}*150$$ = 250(not a hundred) and $$\frac{5}{3}*60$$ = 100.

A.

Note: As for your query under the spoiler, 133 rounded to the nearest ten is 130 and to the nearest hundred is 100. 99 rounded to the nearest ten is 100.
For more, you can read this : http://www.basic-mathematics.com/roundi ... mbers.html

Hope this helps.
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Joined: 24 Nov 2013
Posts: 59
Re: If the integer x is rounded to the nearest hundred  [#permalink]

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09 Sep 2015, 06:31
for option a, 64, rounding to 100 gives 100.
rounding to ten, gives 60.
will the % change be (100-60)/60 ?
I was slightly confused with what should go in the denominator. I used 100 initially. then realized it should be 60.

Should the denominator be 60 since the question states "rounded to the nearest hundred, the result represents a 66 2/3% increase over the value obtained when X is rounded to the nearest ten". Please let me know ..thanks
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Re: If the integer x is rounded to the nearest hundred  [#permalink]

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24 Jul 2016, 11:11
summer101 wrote:
If the integer x is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten. which of the following is a possible value of x?

A. 64
B. 67
C. 99
D. 133
E. 147

What is 99 is rounded to nearest ten? Also what is 133 rounded to nearest ten & hundred?

let the number which will added or subtracted when x is rounded to the nearest ten = y

if we look at the question the integer x when rounded to the nearest hundred will only be 100 as all the choices available when rounded to the nearest hundred can only be 100

therefore there will be 2 condition

100= (x+y) + 2/3(x+y)(note 66 2/3 % is 2/3 of number)
300=5(x+y)
60=x+y(not possible as per choices)

or

100= (x-y) + 2/3(x-y)
300=5(x-y)
x-y =60
64 rounded to nearest tenth will result in 60.

Intern
Joined: 31 Aug 2014
Posts: 4
Re: If the integer x is rounded to the nearest hundred  [#permalink]

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01 Oct 2016, 14:53
Actually, you only need to check 2 values, A and B.

For D and E, rounding to the nearest 100 reduces the value compared to rounding to the nearest 10. The nearest 10 is 130 and 150 whereas the nearest 100 is 100. So D and E not possible ever.

For C, the difference is 90 vs 100, it isnt even close to 66.67%. So not possible.

Only have to check 64 and 67. For 67, the difference would be 30/70 = 3/7 (less than 50%)
For 64, it is 100 and 60, so difference % is 40/60 = 2/3. Bam! Under 1 min
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Re: If the integer x is rounded to the nearest hundred  [#permalink]

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13 Oct 2017, 22:50
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Re: If the integer x is rounded to the nearest hundred &nbs [#permalink] 13 Oct 2017, 22:50
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