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10 Jun 2008, 22:44
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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if x is a positive integer x = ?
(1) {(x-5)(x+4)}^1/2 >10
(2) {(x-5)(x+4)}^1/2 10
squaring both sides we get
(x-5)(x+4) >100
which means x-5>100 or x+4 >100
which translates to x>105 or x>96
which obviously means x>105
therefore x can be any number greater than 105. so this statement 1 is insufficent
similarly analysing statement 2 we get
{(x-5)(x+4)}^1/2 <11
squaring both sides we get
(x-5)(x+4) <121
which means x-5<121 or x+4 <121
which translates to x<126 or x<117
which obviously means x<126
therefore x can be any number less than 126. so this statement 2 is insufficent
put together both statements we get to know that x can be any value greater than 105 and less than 126
which means there are a number of possible values for x
therefore i deduce that E is the answer
which however, is not the OA
Can you please tell me where i am going wrong or is the OA for this one is wrong
wud appreciate u r help on this one guys
(1) {(x-5)(x+4)}^1/2 >10
(2) {(x-5)(x+4)}^1/2 10
squaring both sides we get
(x-5)(x+4) >100
which means x-5>100 or x+4 >100
which translates to x>105 or x>96
which obviously means x>105
therefore x can be any number greater than 105. so this statement 1 is insufficent
similarly analysing statement 2 we get
{(x-5)(x+4)}^1/2 <11
squaring both sides we get
(x-5)(x+4) <121
which means x-5<121 or x+4 <121
which translates to x<126 or x<117
which obviously means x<126
therefore x can be any number less than 126. so this statement 2 is insufficent
put together both statements we get to know that x can be any value greater than 105 and less than 126
which means there are a number of possible values for x
therefore i deduce that E is the answer
which however, is not the OA
Can you please tell me where i am going wrong or is the OA for this one is wrong
wud appreciate u r help on this one guys
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Hi there,
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10 Jun 2008, 23:01
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1)
if we simplify this , we get
x*(x-1) >120 ....not suff
2) if we simplyfy this ,we get
x*(x-1) < 141 ....again not suff
combining both the only value possible is x*(x-1) = 132 , so x=12 ...ANS C
if we simplify this , we get
x*(x-1) >120 ....not suff
2) if we simplyfy this ,we get
x*(x-1) < 141 ....again not suff
combining both the only value possible is x*(x-1) = 132 , so x=12 ...ANS C
11 Jun 2008, 07:10
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Hi, vdhawan1!
I agree with the solution that the previous author has posted, but still decided to post since it might be helpful for you to know where the flaw in your reasoning was.
This is how you approached the inequality:
This is where the mistake is. In general, a*b>c is not equivalent to a>c or b>c. In fact, the latter does not even follow from the former. Consider a*b>6, for example. a=2, b=4 satisfy this inequality, while neither is greater than 6.
Then, you wrote
Here you applied the same method. While in this case x-5<121 or x+4 <121 indeed follow from the initial inequality, this two inequalities are not equivalent to the initial one, since the range of possible solutions for the system of these two inequalities is larger than that of the initial inequality. Consider x=100. It is one of the solutions of the system {x-5<121 or x+4 <121}, but not of the initial inequality.
In general, I think that it might be useful to review the properties of inequalities of various types, the equivalent ways to transform them etc.
I agree with the solution that the previous author has posted, but still decided to post since it might be helpful for you to know where the flaw in your reasoning was.
This is how you approached the inequality:
Quote:
This is where the mistake is. In general, a*b>c is not equivalent to a>c or b>c. In fact, the latter does not even follow from the former. Consider a*b>6, for example. a=2, b=4 satisfy this inequality, while neither is greater than 6.
Then, you wrote
Quote:
Here you applied the same method. While in this case x-5<121 or x+4 <121 indeed follow from the initial inequality, this two inequalities are not equivalent to the initial one, since the range of possible solutions for the system of these two inequalities is larger than that of the initial inequality. Consider x=100. It is one of the solutions of the system {x-5<121 or x+4 <121}, but not of the initial inequality.
In general, I think that it might be useful to review the properties of inequalities of various types, the equivalent ways to transform them etc.
. Luckily, only one possibility for x, namely x=12, satisfies the equation.
