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# Is there a difference between (D) and (E) in the ques below?

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Manager
Joined: 12 Sep 2006
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Is there a difference between (D) and (E) in the ques below? [#permalink]  15 Feb 2007, 06:23
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Is there a difference between (D) and (E) in the ques below? Does the order of the sign matter?

Q. If the sum of two integers is 6, then it must be true that
(A) both integers are even
(B) both integers are odd
(C) both integers are positive
(D) if one integer is negative, the other is positive
(E) if one integer is positive, the other is negative

sum of two int = 6
(1,5), (3,3) Negates A
(2,4) Negates B
(-1,7), (-2,8), (-3,9),... Negates C

And options D E look similar to me.

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Director
Joined: 05 Feb 2006
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It is D....

Look at it this way...

If one interger is negative, lets say, -10 the other one MUST be positive +16 to have a value of 6. There is no other way to get a positive value of 6.

Now in E, if one interger is positive, the other figure NEED NOT BE necessarily negative.... 2+4=6, the other option for this one is 10-4=6... Two possible scenarios, thus E is out....
Senior Manager
Joined: 24 Oct 2006
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IMO, D is the ans.

If one is -ve, then the other has to be +ve to give a +ve result. eg: -1,7 or 8,-2. The order does not matter.
But, if one is +ve, the other need not be -ve.eg:5,1

Manager
Joined: 12 Sep 2006
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wow! pretty good explanations SimaQ and Sumithra. Didnt think that way. Yes that does ans to my this ques. Thanks
But I am still looking for a solution for my below mentioned ques

Q. [x] is the greatest integer less than or equal to the real number x. How many natural numbers n satisfy the equation [n ^(1/2) ] = 17?
#17
#34
#35
#36
#38
Intern
Joined: 04 Apr 2006
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n can have values btw 17*17 = 289 and 18*18-1 = 323

323-289 = 34

Remark:
It's not difficult do subtract these two numbers, but on all basic mathematical calculations, when you calculate unit digit of a solution, check the given answers.

If there is only one answer with that unit digit, don't bother to calculate thens or hundreds

So when you calculate 13-9 = 4 its obvious that 34 is the solution
Manager
Joined: 12 Sep 2006
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Thanks for your reply jvujuc but I didnt get the question at the first place. What are we trying to calculate? how did you get 18*18-1? Please explain. Thanks
jvujuc wrote:
n can have values btw 17*17 = 289 and 18*18-1 = 323

323-289 = 34

Remark:
It's not difficult do subtract these two numbers, but on all basic mathematical calculations, when you calculate unit digit of a solution, check the given answers.

If there is only one answer with that unit digit, don't bother to calculate thens or hundreds

So when you calculate 13-9 = 4 its obvious that 34 is the solution
Intern
Joined: 04 Apr 2006
Posts: 35
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Kudos [?]: 4 [0], given: 0

You have [n ^(1/2) ] = 17 or [√n] = 17

17Â² = 289, 18Â² = 324

√289 = 17.0
√290=17.something
√291= 17.something
.
.
.
√323=17.9
√324=18

All real numbers 17.something and 17.0, by the definition of [x]
Quote:
[x] is the greatest integer less than or equal to the real number x
are equal to 17

You have 323-289 such numbers
Manager
Joined: 12 Sep 2006
Posts: 83
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Kudos [?]: 5 [0], given: 0

I think i follow what you're saying jvujuc. Geeeeezzzz...
We are looking for real numbers for the function.
Thanks a lot for the explantion.

jvujuc wrote:
You have [n ^(1/2) ] = 17 or [√n] = 17

17Â² = 289, 18Â² = 324

√289 = 17.0
√290=17.something
√291= 17.something
.
.
.
√323=17.9
√324=18

All real numbers 17.something and 17.0, by the definition of [x]
Quote:
[x] is the greatest integer less than or equal to the real number x
are equal to 17

You have 323-289 such numbers
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