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# |2y -5|<1

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|2y -5|<1 [#permalink]  21 Dec 2017, 16:54
Expert's post
00:00

Question Stats:

68% (01:02) correct 31% (00:51) wrong based on 41 sessions
$$|2y -5|<1$$

 Quantity A Quantity B y 1

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.

kudo for the right solution and explanation
[Reveal] Spoiler: OA

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Re: |2y -5|<1 [#permalink]  21 Dec 2017, 23:39
1
KUDOS
2y - 5 < 1
So 2y < 6
Y < 2
So Y could be 1 so C but can be also less so Answer D
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Re: |2y -5|<1 [#permalink]  22 Dec 2017, 08:54
1
KUDOS
Carcass wrote:
$$|2y -5|<1$$

 Quantity A Quantity B y 1

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.

kudo for the right solution and explanation

Here we have to consider negative and positive value of |2y -5|.

Considering (2y - 5) to be negative

or -(2y - 5) < 1

or 2y - 5 > -1 (equality changes as the sign changes)

or 2y > 4 (adding 5 on both side)

or y > 2

Now consider positive

|2y -5|<1

or 2y - 5 < 1

or 2y < 6 (adding 5 on both side)

or y <3

Therefore the value of y is = 2 < y < 3

Hence statement A.
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Re: |2y -5|<1 [#permalink]  09 Jan 2018, 12:45
2
KUDOS
Expert's post
Carcass wrote:
$$|2y -5|<1$$

 Quantity A Quantity B y 1

When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then –k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive

Given: |2y - 5| < 1
So, by Rule #1, we get: -1 < 2y - 5 < 1
Add 5 to all sides to get: 4 < 2y < 6
Divide all sides by 2 to get: 2 < y < 3

Since y is between 2 and 3, y MUST be greater than 1

Cheers,
Brent
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Intern
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Re: |2y -5|<1 [#permalink]  03 Feb 2018, 03:54
Could you suggest the tougher inequalities and absolute problems for practice?
I take the GRE in 2 weeks and I keep getting problems in absolute/inequalities wrong.
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Joined: 18 Apr 2015
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Re: |2y -5|<1 [#permalink]  04 Feb 2018, 14:49
Expert's post
Just click on the tag above the question "absolute value" and you do have all the questions present on the board

Here https://greprepclub.com/forum/search.ph ... tag_id=234

Also. here on the correct usage of the tags https://greprepclub.com/forum/using-tag ... tml#p15585

Regards
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Re: |2y -5|<1 [#permalink]  07 Feb 2018, 02:35
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Re: |2y -5|<1 [#permalink]  17 Feb 2018, 01:12
pranab01 wrote:
Carcass wrote:
$$|2y -5|<1$$

 Quantity A Quantity B y 1

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.

kudo for the right solution and explanation

Here we have to consider negative and positive value of |2y -5|.

Considering (2y - 5) to be negative

or -(2y - 5) < 1

or 2y - 5 > -1 (equality changes as the sign changes)

or 2y > 4 (adding 5 on both side)

or y > 2

Now consider positive

|2y -5|<1

or 2y - 5 < 1

or 2y < 6 (adding 5 on both side)

or y <3

Therefore the value of y is = 2 < y < 3

Hence statement A.

I used same method, and yes that's correct answer. Choice A
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Re: |2y -5|<1 [#permalink]  17 Feb 2018, 16:07
GreenlightTestPrep wrote:
Carcass wrote:
$$|2y -5|<1$$

 Quantity A Quantity B y 1

When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then –k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive

Given: |2y - 5| < 1
So, by Rule #1, we get: -1 < 2y - 5 < 1
Add 5 to all sides to get: 4 < 2y < 6
Divide all sides by 2 to get: 2 < y < 3

Since y is between 2 and 3, y MUST be greater than 1

Cheers,
Brent

thanks for the insight
Re: |2y -5|<1   [#permalink] 17 Feb 2018, 16:07
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# |2y -5|<1

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