What is the value of integer x ?
(1) 4 < (x-1)*(x-1) < 16
(2) 4 < (x+1)*(x-1) < 16
OA C
Can some experts determine whether the statements are sufficient?
What is the value of integer x ?
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Hi ardz24,
We're told that X is an INTEGER. We're asked for the value of X. A bit of 'brute force' math can help you to work through this question relatively quickly.
1) 4 < (x-1)(x-1) < 16
Since X has to be an INTEGER, you can start at X=0 and 'work up' to find a solution. X cannot be 0, 1, 2 or 3 (since none of those results would fit the given range. However, X = 4 does fit - but no other positive integer value will fit that range. The prompt did not state that X had to be positive though, so we also have to consider NEGATIVE solutions. 'Working down' from 0, you'll find that X = -2 is also a solution (but no other negative integer solution exists).
Fact 1 is INSUFFICIENT
2) 4 < (x+1)(x-1) < 16
The same approach that we used in Fact 1 can be used here. You'll find that X = 3 and X = 4 are solutions and X = -3 and X = -4 are also solutions.
Fact 2 is INSUFFICIENT
Combined, there is only one answer that 'fits' BOTH Facts: X = 4
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
We're told that X is an INTEGER. We're asked for the value of X. A bit of 'brute force' math can help you to work through this question relatively quickly.
1) 4 < (x-1)(x-1) < 16
Since X has to be an INTEGER, you can start at X=0 and 'work up' to find a solution. X cannot be 0, 1, 2 or 3 (since none of those results would fit the given range. However, X = 4 does fit - but no other positive integer value will fit that range. The prompt did not state that X had to be positive though, so we also have to consider NEGATIVE solutions. 'Working down' from 0, you'll find that X = -2 is also a solution (but no other negative integer solution exists).
Fact 1 is INSUFFICIENT
2) 4 < (x+1)(x-1) < 16
The same approach that we used in Fact 1 can be used here. You'll find that X = 3 and X = 4 are solutions and X = -3 and X = -4 are also solutions.
Fact 2 is INSUFFICIENT
Combined, there is only one answer that 'fits' BOTH Facts: X = 4
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
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Statement 1:ardz24 wrote:What is the value of integer x ?
(1) 4 < (x-1)*(x-1) < 16
(2) 4 < (x+1)*(x-1) < 16
4 < (x-1)² < 16.
Implication:
x-1=±3, with the result that (x-1)²=9.
If x-1 = 3, than x=4.
If x-1 = -3, than x=-2.
Since x can be different values, INSUFFICIENT.
Statement 2:
4 < x² - 1 < 16
5 < x² < 17.
Implication:
x²=9 or x²=16.
Options for x:
±3, ±4.
Since x can be different values, INSUFFICIENT.
Statements combined:
Of the options for x in Statement 1, only x=4 is among the options for x in Statement 2.
Thus, x=4.
SUFFICIENT.
The correct answer is C.
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Solution:BTGmoderatorAT wrote: ↑Sun Sep 10, 2017 6:43 amWhat is the value of integer x ?
(1) 4 < (x-1)*(x-1) < 16
(2) 4 < (x+1)*(x-1) < 16
OA C
Can some experts determine whether the statements are sufficient?
Statement One Alone:
4 < (x-1)*(x-1) < 16
Rewriting the inequality, we have:
4 < (x - 1)^2 < 16
Square rooting all 3 sides, we have:
2 < |x - 1| < 4
Since x is an integer, we see that |x - 1| = 3. That is, either x - 1 = 3 or x - 1 = -3. The former equation yields x = 4 while the latter yields x = -2. Statement one alone is not sufficient.
Statement Two Alone:
4 < (x+1)*(x-1) < 16
Rewriting the the inequality, we have:
4 < x^2 - 1 < 16
5 < x^2 < 17
Square rooting all 3 sides, we have:
√5 < |x| < √17
Since x is an integer, we see that |x| = 3 or |x| = 4. The former equation yields x = 3 or -3 while the latter yields x = 4 or -4. Statement two alone is not sufficient.
Statements One and Two Together:
Since the values of x in statement one could be 4 or -2 and the values of x in statement two could be 3, -3, 4 or -4, we see that x could only be 4 when we consider both statements together. The two statements together are sufficient.
Answer: C
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