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15<|b-11|<16 and b<0
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16 Nov 2020, 07:16
16 Nov 2020, 07:16
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Question Stats:
78% (01:25) correct
21% (01:32) wrong based on 85 sessions
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\(15<|b-11|<16\) and \(b<0\)
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.
Kudos for the right solution and explanation
Source: 320 GRE Math Questions
Quantity A |
Quantity B |
\(|b|\) |
\(4.5\) |
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.
Kudos for the right solution and explanation
Source: 320 GRE Math Questions
Re: 15<|b-11|<16 and b<0
[#permalink]
16 Nov 2020, 22:57
16 Nov 2020, 22:57
2
Carcass wrote:
\(15<|b-11|<16\) and \(b<0\)
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.
Kudos for the right solution and explanation
Source: 320 GRE Math Questions
Quantity A |
Quantity B |
\(|b|\) |
\(4.5\) |
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.
Kudos for the right solution and explanation
Source: 320 GRE Math Questions
15 < |b-11| < 16
-16 < b-11 < -15 and 15 < b-11 < 16.
-5 < b < -4 and 26 < b < 27.
-5 < b < 27.
|b| can be 4.5, in this case both the quantities are equal.
|b| can be 0, in this case quantity B is greater.
Hence option D is the answer.
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15<|b-11|<16 and b<0
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13 Jul 2021, 08:40
13 Jul 2021, 08:40
1
\(b<0\), let's assume b=-k where k>0
\(15<|b-11|<16\)
putting b=-k we get
\(15<|-k-11|<16\) = \(15<|-(k+11)|<16\)
And we know that |-x| = |x|
=> \(15<|k+11|<16\)
=> \(15<k+11<16\) [ As k+11>0 and we know that |x| = x if x>0]
Subtracting 11 from all sides we get
=> \(15-11 < k+11-11 <16-11\)
=> \(4 < k < 5\)
Putting k =-b
=> \(4 < -b < 5\)
Multiplying with -1 on all sides and reversing the inequalities we get
=> \(-4 > b > -5\)
=> \(-5 < b < -4\)
So, b can be any number between -5 and -4
Quantity A = |b|
Since b lies between -5 and -4 => |b| will lie between |-5| and |-4| = 5 and 4
Quantity B = 4.5
Definitely, |b| can be > , = or < 4.5
=> we need to know the exact value of b to answer the problem
So, answer will be D
Hope it helps!
To learn about Absolute value and Inequalities watch the following videos
\(15<|b-11|<16\)
putting b=-k we get
\(15<|-k-11|<16\) = \(15<|-(k+11)|<16\)
And we know that |-x| = |x|
=> \(15<|k+11|<16\)
=> \(15<k+11<16\) [ As k+11>0 and we know that |x| = x if x>0]
Subtracting 11 from all sides we get
=> \(15-11 < k+11-11 <16-11\)
=> \(4 < k < 5\)
Putting k =-b
=> \(4 < -b < 5\)
Multiplying with -1 on all sides and reversing the inequalities we get
=> \(-4 > b > -5\)
=> \(-5 < b < -4\)
So, b can be any number between -5 and -4
Quantity A = |b|
Since b lies between -5 and -4 => |b| will lie between |-5| and |-4| = 5 and 4
Quantity B = 4.5
Definitely, |b| can be > , = or < 4.5
=> we need to know the exact value of b to answer the problem
So, answer will be D
Hope it helps!
To learn about Absolute value and Inequalities watch the following videos
