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# Is x 1/16 greater than 5/8?

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Director
Joined: 10 Feb 2006
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Is x 1/16 greater than 5/8?  [#permalink]

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04 Nov 2007, 07:19
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Difficulty:

85% (hard)

Question Stats:

55% (02:33) correct 45% (02:16) wrong based on 431 sessions

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Is x – 1/16 greater than 5/8?

(1) Four times the value of x is less than three.

(2) One third of two is less than the value of x.

Given : 16x - 1/16 > 5/8 ?
or 16x - 1 > 5 *16/8 = 16x > 10 + 1 = x > 11/16 ? = .6875

(1) -- 4x < 3
x < 3/4 = x <75> 2/3 = x > .67

so .67 <x < .75..

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Re: Is x 1/16 greater than 5/8? (1) Four times the value of x is  [#permalink]

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09 Feb 2012, 01:49
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Is x – 1/16 greater than 5/8?

Find the least common denominator to make fraction comparison easier.

Question: is $$x-\frac{1}{16}>\frac{5}{8}$$? --> is $$\frac{11}{16}=\frac{33}{48}<x$$?

(1) Four times the value of x is less than three --> $$4x<3$$ --> $$x<\frac{3}{4}=\frac{36}{48}$$. Not sufficient.

(2) One third of two is less than the value of x --> $$\frac{2}{3}=\frac{32}{48}<x$$. Not sufficient.

(1)+(2) $$\frac{32}{48}<x<\frac{36}{48}$$. Not sufficient.

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Re: Is x 1/16 greater than 5/8?  [#permalink]

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22 May 2017, 18:45
Is x – 1/16 greater than 5/8?

(1) Four times the value of x is less than three.

(2) One third of two is less than the value of x.

Given : 16x - 1/16 > 5/8 ?
or 16x - 1 > 5 *16/8 = 16x > 10 + 1 = x > 11/16 ? = .6875

(1) -- 4x < 3
x < 3/4 = x <75> 2/3 = x > .67

so .67 <x < .75..

This problem can be tackled algebraically. The trick is make sure you work neatly and stop to reflect before deciding sufficiency.

X-1/16 > 5/8?
Or x>11/16?

Goal: Prove (yes/no) that x is in fact greater than 11/16 (or, conversely, that it is equal to or less than 11/16).

Statement 1: 4x<3 or x<3/4. Use the cross multiplication method to compare fractions (3*16 and 4*11). 48>44, so then 3/4 is greater than 11/16. But we know that x is less than 3/4 so it could be less than 11/16 or more than 11/16 because we do not know the relationship between x and 11/16. So this answer is not sufficient because YES or NO is possible.

Statement 2: For this one, we are told that 2/3<x. We can quickly realize that 2/3<11/16. But once again, we cannot state if x is greater than or less than 11/16 because x > 2/3, so it could be between 2/3 and 11/16 or it could be greater than 11/16. Not sufficient.

Combined: Here we know that 2/3 < x < 3/4, but since 11/16 falls in this range, we cannot state whether 11/16 is greater than x definitively.
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Re: Is x 1/16 greater than 5/8?  [#permalink]

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12 Jan 2018, 13:50
Can someone tell me why it is wrong to say :
(x−1)/16 > 5/8 so 8(x-1) > 5 ( 16) and the question then be : is x > 11 ?
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Joined: 02 Sep 2009
Posts: 52296
Re: Is x 1/16 greater than 5/8?  [#permalink]

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12 Jan 2018, 23:53
Maudinette wrote:
Can someone tell me why it is wrong to say :
(x−1)/16 > 5/8 so 8(x-1) > 5 ( 16) and the question then be : is x > 11 ?

It's x – 1/16 NOT (x – 1)/16. So, It's $$x – \frac{1}{16}$$ NOT $$\frac{x – 1}{16}$$.
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Re: Is x 1/16 greater than 5/8?  [#permalink]

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13 Jan 2018, 02:01
Question stem is asking whether x>0.6875?

(1) tells us that x<0.75 so its not sufficient since it could be 0.62 or 0.72 (or any number within that range)

(2) tells us that x> 0.66 which means x could be 0.67 or 0.77 (any number within that range) so its not sufficient either

(C) together it tells us that 0.66<x<0.75 which means x could either be 0.67 or 0.72 (any number within the range)

Re: Is x 1/16 greater than 5/8? &nbs [#permalink] 13 Jan 2018, 02:01
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