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What is the value of |x-7| + |x+8|?
\(A. x^2 < 25\)
\(B. x^2 > 36\)
\(A. x^2 < 25\)
\(B. x^2 > 36\)
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WiziusCareers1
Joined: 27 Apr 2009
Last visit: 07 Dec 2024
Posts: 116
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Location: India
Schools: HBS '14 (A)
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10 Jul 2019, 22:15
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Considering statement (1) alone:
x^2 < 25
=> -5 < x < 5
Let x = -4
=> |x - 7| + |x + 8| = |-4 - 7| + |-4 + 8| = 11 + 4 = 15
Let x = 0
=> |x - 7| + |x + 8| = |0 - 7| + |0 + 8| = 7 + 8 = 15
Let x = 4
=> |x - 7| + |x + 8| = |4 - 7| + |4 + 8| = 3 + 12 = 15
Hence, SUFFICIENT
Considering statement (2) alone:
x^2 > 36
=> x > 6 and x < -6
Let x = 7
=> |x - 7| + |x + 8| = |7 - 7| + |7 + 8| = 0 + 15 = 15
Let x = 10
=> |x - 7| + |x + 8| = |10 - 7| + |10 + 8| = 3 + 18 = 21
Hence, INSUFFICIENT
The answer is (A).
x^2 < 25
=> -5 < x < 5
Let x = -4
=> |x - 7| + |x + 8| = |-4 - 7| + |-4 + 8| = 11 + 4 = 15
Let x = 0
=> |x - 7| + |x + 8| = |0 - 7| + |0 + 8| = 7 + 8 = 15
Let x = 4
=> |x - 7| + |x + 8| = |4 - 7| + |4 + 8| = 3 + 12 = 15
Hence, SUFFICIENT
Considering statement (2) alone:
x^2 > 36
=> x > 6 and x < -6
Let x = 7
=> |x - 7| + |x + 8| = |7 - 7| + |7 + 8| = 0 + 15 = 15
Let x = 10
=> |x - 7| + |x + 8| = |10 - 7| + |10 + 8| = 3 + 18 = 21
Hence, INSUFFICIENT
The answer is (A).
firas92
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Products:
10 Jul 2019, 22:34
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All values within the range -8 ≤ x ≤ 7 will give the same unique solution
1) |x|<5 or -5<x<5
Thus x always lies within the range -8 ≤ x ≤ 7
Sufficient
2) |x|>6
This means x<-6 or x>6
So, x may or may not be within the range -8 ≤ x ≤ 7
Insufficient
Answer is (A)
1) |x|<5 or -5<x<5
Thus x always lies within the range -8 ≤ x ≤ 7
Sufficient
2) |x|>6
This means x<-6 or x>6
So, x may or may not be within the range -8 ≤ x ≤ 7
Insufficient
Answer is (A)
