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Joined: 16 May 2014
Posts: 590
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GRE 1: Q165 V161
GRE Math Challenge #5- Solve |x + 5| = 3 and |2y - 1|/3
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18 Aug 2014, 10:04
18 Aug 2014, 10:04
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If \(|x + 5| = 3\) and \(\frac{|2y - 1|}{3} = 5\), then \(|x + y|\) could equal each of the following EXCEPT
A) 0
B) 6
C) 8
D) 9
E) 15
A) 0
B) 6
C) 8
D) 9
E) 15
Re: GRE Math Challenge #5- Solve |x + 5| = 3 and |2y - 1|/3
[#permalink]
11 Apr 2020, 20:06
11 Apr 2020, 20:06
1
soumya1989 wrote:
If \(|x + 5| = 3\) and \(|2y - 1|/3 = 5\), then |x + y| could equal each of the following EXCEPT
a) 0
b) 6
c) 8
d) 9
e) 15
a) 0
b) 6
c) 8
d) 9
e) 15
Here,
\(|x + 5| = 3\)
CASE 1
or x + 5 = -3
or x = -8
CASE 2
x + 5 = 3
or x = -2
Now,
\(\frac{{|2y - 1|}}{3} = 5\)
or |2y - 1| = 15
CASE 1
or 2y - 1 = 15
or y = 8
CASE 2
2y - 1 = -15
or y = -7
Now we can find the values of |x + y| , except Option C , rest all values are possible
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Re: GRE Math Challenge #5- Solve |x + 5| = 3 and |2y - 1|/3
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16 Jul 2021, 10:56
16 Jul 2021, 10:56
1
Theory: |x+a| = b, then x = b-a, x= -b-a
\(|x + 5| = 3\) => x = 3-5, x= -3-5 (watch this video to learn how to solve absolute value problems)
=> x = -2, -8
\(\frac{|2y - 1|}{3} = 5\)
=> |2y - 1| = 3*5 = 15
=> 2y-1 = 15, 2y-1 = -15
=> 2y = 16, 2y = -14
=> y = 8, -7
|x+y| = | -2 + 8 | = | 6 | = 6
or, |x+y| = | -2 -7 | = | -9 | = 9
or, |x+y| = | -8 + 8 | = | 0 | = 0
or, |x+y| = | -8 - 7 | = | -15 | = 15
So, answer will be C
Hope it helps!
Watch the following video to know how to solve absolute value problems
\(|x + 5| = 3\) => x = 3-5, x= -3-5 (watch this video to learn how to solve absolute value problems)
=> x = -2, -8
\(\frac{|2y - 1|}{3} = 5\)
=> |2y - 1| = 3*5 = 15
=> 2y-1 = 15, 2y-1 = -15
=> 2y = 16, 2y = -14
=> y = 8, -7
|x+y| = | -2 + 8 | = | 6 | = 6
or, |x+y| = | -2 -7 | = | -9 | = 9
or, |x+y| = | -8 + 8 | = | 0 | = 0
or, |x+y| = | -8 - 7 | = | -15 | = 15
So, answer will be C
Hope it helps!
Watch the following video to know how to solve absolute value problems
soumya1989 wrote:
If \(|x + 5| = 3\) and \(\frac{|2y - 1|}{3} = 5\), then \(|x + y|\) could equal each of the following EXCEPT
A) 0
B) 6
C) 8
D) 9
E) 15
A) 0
B) 6
C) 8
D) 9
E) 15
