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# If |y /2- 1/6| < 2/3, then y could be all of the following except?

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Joined: 12 Aug 2015
Posts: 2551
Schools: Boston U '20 (M)
GRE 1: Q169 V154
If |y /2- 1/6| < 2/3, then y could be all of the following except?  [#permalink]

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Updated on: 14 Jun 2017, 22:10
1
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Difficulty:

45% (medium)

Question Stats:

68% (01:59) correct 32% (01:54) wrong based on 334 sessions

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If $$|\frac{y}{2}- \frac{1}{6}| < \frac{2}{3}$$, then y could be all of the following EXCEPT

A. $$-\frac{4}{3}$$

B. $$-\frac{5}{6}$$

C. 0

D. $$\frac{5}{6}$$

E. $$\frac{4}{3}$$

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Originally posted by stonecold on 14 Jun 2017, 19:05.
Last edited by Bunuel on 14 Jun 2017, 22:10, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If |y /2- 1/6| < 2/3, then y could be all of the following except?  [#permalink]

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14 Jun 2017, 19:37
3
stonecold wrote:

$$|\frac{y}{2} - \frac{1}{6}| < \frac{2}{3}$$

Case 1: $$\frac{y}{2} - \frac{1}{6} <\frac{2}{3}$$
$$\frac{y}{2} < \frac{2}{3} + \frac{1}{6}$$
$$\frac{y}{2} < \frac{4+ 1}{6}$$
$$\frac{y}{2} < \frac{5}{6}$$
$$y<\frac{5}{3}$$

Case 2: $$- (\frac{y}{2} - \frac{1}{6}) < \frac{2}{3}$$
$$-\frac{y}{2} + \frac{1}{6} < \frac{2}{3}$$
$$-\frac{y}{2} < \frac{2}{3} - \frac{1}{6}$$
$$-\frac{y}{2} < \frac{4 - 1}{6}$$
$$-\frac{y}{2} < \frac{3}{6}$$
$$-\frac{y}{2} < \frac{1}{2}$$
$$-y < 1$$
$$y > -1$$

Value of $$y ==> -1 < y < \frac{5}{3}$$

Values which come between this range are $$-\frac{5}{6}, 0, \frac{5}{6}, \frac{4}{3}.$$

Therefore y cannot be $$-\frac{4}{3}$$. Answer A...
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Re: If |y /2- 1/6| < 2/3, then y could be all of the following except?  [#permalink]

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14 Jun 2017, 22:11
1
stonecold wrote:
If $$|\frac{y}{2}- \frac{1}{6}| < \frac{2}{3}$$, then y could be all of the following EXCEPT

A. $$-\frac{4}{3}$$

B. $$-\frac{5}{6}$$

C. 0

D. $$\frac{5}{6}$$

E. $$\frac{4}{3}$$

Similar question: https://gmatclub.com/forum/if-y-1-2-11- ... 36878.html
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Posts: 2809
Re: If |y /2- 1/6| < 2/3, then y could be all of the following except?  [#permalink]

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06 Jul 2017, 17:35
stonecold wrote:
If $$|\frac{y}{2}- \frac{1}{6}| < \frac{2}{3}$$, then y could be all of the following EXCEPT

A. $$-\frac{4}{3}$$

B. $$-\frac{5}{6}$$

C. 0

D. $$\frac{5}{6}$$

E. $$\frac{4}{3}$$

For this absolute value problem, we have two cases to consider: when (y/2 - ⅙) is positive and when (y/2 - ⅙) is negative. Let’s start with the positive case:

Case 1: (y/2 - ⅙) is positive

y/2 - 1/6 < 2/3

Multiplying by 6, we have:

3y - 1 < 4

3y < 5

y < 5/3

Case 2: (y/2 - ⅙) is negative

-(y/2 - ⅙) < 2/3

-y/2 + 1/6 < ⅔

Multiplying by 6, we have:

-3y + 1 < 4

-3y < 3

y > -1

Thus, -1 < y < 5/3. Thus, y cannot be -4/3.

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Re: If |y /2- 1/6| < 2/3, then y could be all of the following except?  [#permalink]

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19 Mar 2019, 09:21
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Re: If |y /2- 1/6| < 2/3, then y could be all of the following except?   [#permalink] 19 Mar 2019, 09:21
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