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24 Oct 2016, 14:56
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Difficulty:
95%
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Question Stats:
39% (02:39) correct
61%
(02:51)
wrong
based on 855
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If x is any integer from -6 to 2 inclusive, how many values of x satisfy the following inequality: 2 - |x3 + 10x2 - 24x| < 2 ?
A) 5
B) 6
C) 7
D) 8
E) 9
A) 5
B) 6
C) 7
D) 8
E) 9
Updated on: 04 Oct 2020, 13:50
Originally posted by BrentGMATPrepNow on 25 Oct 2016, 08:37.
Last edited by BrentGMATPrepNow on 04 Oct 2020, 13:50, edited 1 time in total.
Last edited by BrentGMATPrepNow on 04 Oct 2020, 13:50, edited 1 time in total.
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GMATPrepNow
If x is any integer from -6 to 2 inclusive, how many values of x satisfy the following inequality: 2 - |x³ + 10x² - 24x| < 2 ?
A) 5
B) 6
C) 7
D) 8
E) 9
A) 5
B) 6
C) 7
D) 8
E) 9
My solution:
First note that there are 9 integers from -6 to 2 inclusive.
Given: 2 - |x³ + 10x² - 24x| < 2
Add |x³ + 10x² - 24x| to both sides: 2 < 2 + |x³ + 10x² - 24x|
Subtract 2 from both sides to get: 0 < |x³ + 10x² - 24x|
Now let's apply some number sense.
We know that the absolute value of something will always be greater than or equal to zero. So the ONLY values that DON'T satisfy the inequality 0 < |x³ + 10x² - 24x| will be those values where |x³ + 10x² - 24x| = 0
In other words, x³ + 10x² - 24x = 0
Factor to get: x(x² + 10x - 24) = 0
Factor more: x(x + 12)(x - 2) = 0
Solve to get: x = 0, or x = -12 or x = 2
So, x = 0, or x = -12 or x = 2 are the ONLY values of x that DON'T satisfy the inequality 0 < |x³ + 10x² - 24x|
Since x = -12 is not within the given range of values (-6 to 2 inclusive), we need only consider the 2 values (x = 0 and x = 2)
So, the number of integer values that DO satisfy the inequality = 9 - 2 = 7
Answer: C
24 Oct 2016, 15:16
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GMATPrepNow
If x is any integer from -6 to 2 inclusive, how many values of x satisfy the following inequality: 2 - |x³ + 10x² - 24x| < 2 ?
A) 5
B) 6
C) 7
D) 8
E) 9
*Kudos for all correct solutions
A) 5
B) 6
C) 7
D) 8
E) 9
*Kudos for all correct solutions
Total 9 integers are there in the given range.
2 - |x³ + 10x² - 24x| < 2
Find the number of values for which the equation inside modulus is zero. Then subtract that number from total
x³ + 10x² - 24x=0
x(x^2+10x-24)=0
x(x+12)(x-2)=0
So the inequality doesn't hold good when x= 0,-12 or 2
0 and 2 are there in given range.
Answer = 9-2=7
C
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