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If |p 8| = 3p, then p = 4 2 1 2 4
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04 Sep 2024, 01:34
04 Sep 2024, 01:34
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Question Stats:
84% (01:07) correct
15% (00:39) wrong based on 13 sessions
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If \(|p – 8| = 3p\), then p =
A. –4
B. –2
C. 1
D. 2
E. 4
A. –4
B. –2
C. 1
D. 2
E. 4
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Joined: 02 Jan 2020
Status:GRE Quant Tutor
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Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
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If |p 8| = 3p, then p = 4 2 1 2 4
[#permalink]
17 Oct 2024, 08:08
17 Oct 2024, 08:08
1
|p – 8| = 3p
Let's solve it using two methods
Method 1: Algebra
( To MASTER Absolute Value Problems, watch this video )
Method 2: Substitution
| p - 8 | = 3p
Let's pick values in the range of each option choice and see if it satisfies the above equation
A. –4
| -4 - 8| = 3 * (-4)
=> | -12| = -12
=> 12 = -12 which is NOT TRUE
B. –2
| -2 - 8| = 3 * (-2)
=> | -10| = -6
=> 10 = -6 which is NOT TRUE
C. 1
| 1 - 8| = 3 * (1)
=> | -7| = 3
=> 7 = 3 which is NOT TRUE
D. 2
| 2 - 8| = 3 * (2)
=> | -6| = 6
=> 6 = 6 which is TRUE
E. 4
| 4 - 8| = 3 * (4)
=> | -4| = 12
=> 4 = 12 which is NOT TRUE
So, Answer will be D
Hope it helps!
To learn how to solve absolute value problems, watch the following video
Let's solve it using two methods
Method 1: Algebra
( To MASTER Absolute Value Problems, watch this video )
| As we have |p - 8| in the equation so we will have two cases | |
| -Case 1: p - 8 ≥ 0 => p ≥ 8 => | p - 8 | = p - 8 => p - 8 = 3p => 2p = -8 => p = -4 But condition was p ≥ 8 => NO SOLUTION | -Case 2: p - 8 ≤ 0 => p ≤ 8 => | p - 8 | = -(p - 8) = 8 - p => 8 - p = 3p => 4p = 8 => p = 2 But condition was p ≤ 8 and 2 ≤ 8 => p = 2 is a SOLUTION |
Method 2: Substitution
| p - 8 | = 3p
Let's pick values in the range of each option choice and see if it satisfies the above equation
A. –4
| -4 - 8| = 3 * (-4)
=> | -12| = -12
=> 12 = -12 which is NOT TRUE
B. –2
| -2 - 8| = 3 * (-2)
=> | -10| = -6
=> 10 = -6 which is NOT TRUE
C. 1
| 1 - 8| = 3 * (1)
=> | -7| = 3
=> 7 = 3 which is NOT TRUE
D. 2
| 2 - 8| = 3 * (2)
=> | -6| = 6
=> 6 = 6 which is TRUE
E. 4
| 4 - 8| = 3 * (4)
=> | -4| = 12
=> 4 = 12 which is NOT TRUE
So, Answer will be D
Hope it helps!
To learn how to solve absolute value problems, watch the following video
gmatclubot
If |p 8| = 3p, then p = 4 2 1 2 4 [#permalink]
17 Oct 2024, 08:08
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