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If the integer x is rounded to the nearest hundred, the result represe

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If the integer x is rounded to the nearest hundred, the result represe  [#permalink]

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New post 04 Nov 2019, 04:12
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Difficulty:

  55% (hard)

Question Stats:

57% (02:04) correct 43% (02:13) wrong based on 68 sessions

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If the integer x is rounded to the nearest hundred, the result represents a \(66 \frac{2}{3}\)% 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


Are You Up For the Challenge: 700 Level Questions
Spoiler: OA

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If the integer x is rounded to the nearest hundred, the result represe  [#permalink]

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New post Updated on: 04 Nov 2019, 10:37
1
Assume x='abc'= 100a+b+c

x when rounded to nearest hundred > x when rounded to nearest ten

x when rounded to nearest hundred= 100(a+1)

There are 2 possible cases

1. c<5

100(a+1)=5/3(100a+10b)
4a+b=6

when a=0, b=6.......(1)
60,61,62,63,64

when a=1, b=2........(2)
120, 121,122,123,124

2. c≥5
100(a+1)=5/3[100a+10(b+1)]

4a+b=5

if a=0, b=5.......(2)
55,56,57,58,59

if a=1, b=1.......(4)
115,116,117,118,119


We can solve it using options too

Bunuel wrote:
If the integer x is rounded to the nearest hundred, the result represents a \(66 \frac{2}{3}\)% 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


Are You Up For the Challenge: 700 Level Questions

Originally posted by nick1816 on 04 Nov 2019, 05:28.
Last edited by nick1816 on 04 Nov 2019, 10:37, edited 1 time in total.
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Re: If the integer x is rounded to the nearest hundred, the result represe  [#permalink]

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New post 04 Nov 2019, 10:26
1
Bunuel wrote:
If the integer x is rounded to the nearest hundred, the result represents a \(66 \frac{2}{3}\)% 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


Are You Up For the Challenge: 700 Level Questions


Solving via options:

A. 64
Rounded off to nearest hundreds = 100
Rounded off to nearest tens = 60
% increase = \(40/60*100 = 200/3 = 66 \frac{2}{3}\) —> YES

IMO Option A

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Re: If the integer x is rounded to the nearest hundred, the result represe   [#permalink] 04 Nov 2019, 10:26
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