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T is no more than 20 percent greater than the integer x and T is no sm

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Math Expert
Joined: 02 Sep 2009
Posts: 58320
T is no more than 20 percent greater than the integer x and T is no sm  [#permalink]

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06 Feb 2019, 02:37
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Difficulty:

45% (medium)

Question Stats:

57% (02:12) correct 43% (02:09) wrong based on 23 sessions

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T is no more than 20 percent greater than the integer x and T is no smaller than a number 20 percent less than the integer x. If T=60, which of the following indicates the smallest possible interval for x?

A 40 <= x <= 80
B 48 <= x <= 75
C 48 <= x <= 72
D 50 <= x <= 78
E 50 <= x <= 75

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Concentration: Accounting, Finance
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Re: T is no more than 20 percent greater than the integer x and T is no sm  [#permalink]

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06 Feb 2019, 04:13
Bunuel wrote:
T is no more than 20 percent greater than the integer x and T is no smaller than a number 20 percent less than the integer x. If T=60, which of the following indicates the smallest possible interval for x?

A 40 <= x <= 80
B 48 <= x <= 75
C 48 <= x <= 72
D 50 <= x <= 78
E 50 <= x <= 75

Amazing question.

I first look at the answer choices . This question is all about range .

T=60.

1. T is 20% greater that x. In this case we have to take the lowest value of x. If we don't take the lowest value T will be larger then x.

x*120% = 60

120x / 100 = 60

x= 60*100 / 120

x = 50.

2. T is 20% lower than x. In this case we must consider the greatest value of x.

x*80% = 60

80x / 100 = 60

x = 60*100 /80

x = 75.

Now we can create a range for x.

50geq\xleq\75

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Re: T is no more than 20 percent greater than the integer x and T is no sm  [#permalink]

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06 Feb 2019, 05:01
Bunuel wrote:
T is no more than 20 percent greater than the integer x and T is no smaller than a number 20 percent less than the integer x. If T=60, which of the following indicates the smallest possible interval for x?

A 40 <= x <= 80
B 48 <= x <= 75
C 48 <= x <= 72
D 50 <= x <= 78
E 50 <= x <= 75

T= % more or less * x
T= 60
60 = 1.2x
x= 50
and
60 = 0.8x
x= 75
so
range
50 <= x <= 75
IMO E
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Re: T is no more than 20 percent greater than the integer x and T is no sm   [#permalink] 06 Feb 2019, 05:01
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