Combining Inequalities

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Combining Inequalities

by BKNY718 » Wed Aug 24, 2011 7:02 pm
Hello, can someone explain the following:

If -2<a<11 and 3<b<12, then which of the following is NOT true?

1<a+b<23
-14<a-b<8
-7<b-a<14
1<b+a<23
-24<ab<132

Thanks

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by winniethepooh » Wed Aug 24, 2011 8:59 pm
BKNY718 wrote:Hello, can someone explain the following:

If -2<a<11 and 3<b<12, then which of the following is NOT true?

1<a+b<23
-14<a-b<8
-7<b-a<14
1<b+a<23
-24<ab<132

Thanks
The answer is C.
For Addition of a and b.
Take maximum value for maximum range = 11 + 12 = less than 23
And minimum vakue = -1 + 3 = greater than 1
So , A and D are true.

For multiplication the Maximum value can be obtained by multiplying the maximum values greater than 0= 12*11 = less than 132
Mimimum value can be obtained by multiplying th maximum number in the range with the least number on the negative side = 12*(-2) = greatert than -24
So, E is true.

For subtraction there will be 2 results:

For a-b = Maximum value can be maximum of a minus mimimum of b = 11-3 = less than 8
and minimum value can be minimum can be minimum of a minus maximum of b = -2-12 = greater than -14
So, B is true.

For b-a = maximum value can be maximum of b minus minimum of a = 12-(-2) = less than 14
and mimimum value can be minimum of b minus maximum of a = 3-11 = greater than -8
So, C is not true.

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by navami » Thu Aug 25, 2011 3:47 am
ANS : -7<b-a<14

becaz the correct value should be -8<b-a<14

to solve these think about the lowest and highest possible value for (b-a).
for lowest value b = 3 and a = 11 => b-a = -8
This time no looking back!!!
Navami

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by BKNY718 » Thu Aug 25, 2011 3:12 pm
winniethepooh wrote:
BKNY718 wrote:Hello, can someone explain the following:

If -2<a<11 and 3<b<12, then which of the following is NOT true?

1<a+b<23
-14<a-b<8
-7<b-a<14
1<b+a<23
-24<ab<132

Thanks
The answer is C.
For Addition of a and b.
Take maximum value for maximum range = 11 + 12 = less than 23
And minimum vakue = -1 + 3 = greater than 1
So , A and D are true.

For multiplication the Maximum value can be obtained by multiplying the maximum values greater than 0= 12*11 = less than 132
Mimimum value can be obtained by multiplying th maximum number in the range with the least number on the negative side = 12*(-2) = greatert than -24
So, E is true.

For subtraction there will be 2 results:

For a-b = Maximum value can be maximum of a minus mimimum of b = 11-3 = less than 8
and minimum value can be minimum can be minimum of a minus maximum of b = -2-12 = greater than -14
So, B is true.

For b-a = maximum value can be maximum of b minus minimum of a = 12-(-2) = less than 14
and mimimum value can be minimum of b minus maximum of a = 3-11 = greater than -8
So, C is not true.
So these seem to be rules for +,-,and * when dealing with inequality values?

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by winniethepooh » Thu Aug 25, 2011 3:18 pm
Yep.
But before applying practice them, so that you can be faster in solving during the test!

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by [email protected] » Thu Aug 25, 2011 4:32 pm
BKNY718 wrote:Hello, can someone explain the following:

If -2<a<11 and 3<b<12, then which of the following is NOT true?

1<a+b<23
-14<a-b<8
-7<b-a<14
1<b+a<23
-24<ab<132

Thanks
Am not sure, is this a DS Question!

i thought it as from PS, so that way i say Option:1 is false! as 3<= a+b <=21

Let me know what's the answer please.

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by crackinggmat » Thu Aug 25, 2011 7:47 pm
BKNY718 wrote:Hello, can someone explain the following:

If -2<a<11 and 3<b<12, then which of the following is NOT true?

1<a+b<23
-14<a-b<8
-7<b-a<14
1<b+a<23
-24<ab<132

Thanks
good question ...C is the correct answer

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by BKNY718 » Sat Aug 27, 2011 3:27 pm
Thanks so much!
winniethepooh wrote:Yep.
But before applying practice them, so that you can be faster in solving during the test!