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13 Jun 2025, 06:42
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B
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Question Stats:
49% (01:45) correct
51%
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wrong
based on 150
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If x is a non-negative integer and |8 - |x + 3|| = 7, then find the number of values of x that satisfy the given absolute value inequality?
A. 0
B. 1
C. 2
D. 3
E. 4
A. 0
B. 1
C. 2
D. 3
E. 4
13 Jun 2025, 06:50
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siddhantvarma
|8 - |x + 3|| = 7
8 - |x + 3| = 7 or 8 - |x + 3| = -7
The first one gives |x + 3| = 1, which implies x = -2 or x = -4. Since given that x is a non-negative integer, we discard both values.
The second one give |x + 3| = 15, which implies x = 12 or x = -18. Again, we discard -18.
So, only one value: x = 12.
Answer: B
Updated on: 09 Jul 2025, 08:24
Originally posted by GMATinsight on 13 Jun 2025, 06:55.
Last edited by GMATinsight on 09 Jul 2025, 08:24, edited 3 times in total.
Last edited by GMATinsight on 09 Jul 2025, 08:24, edited 3 times in total.
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siddhantvarma
We have been given
|8 - |x + 3|| = 7
- Now, the absolute values of Left hand side must be 7
- But the value of |x + 3| is Non-negative due to modulus sign
- Therefore, |x + 3| has to be 1 or 15 for the absolute value of left side part to be 7
- for |x + 3| to be 1, x can be -4 or -2 (rejected due to being negative) and for x+3 to be -15, x can be -18 (Rejected) and for x+3 to be 15, x can be 12 hence Only one non-negative possible value of x
Answer: Option B
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