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If 2s > 8 and 3t < 9

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If 2s > 8 and 3t < 9 [#permalink]

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If 2s > 8 and 3t < 9, which of the following could be the value of s-t?

I. -1
II. 0
III. 1

A. None
B. I only
C. II only
D. III only
E. II and III
[Reveal] Spoiler: OA

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Last edited by tulsa on 25 Mar 2013, 13:30, edited 2 times in total.
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Re: If 2s > 8 and 3t < 9 [#permalink]

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New post 27 Mar 2013, 07:18
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If 2s > 8 and 3t < 9, which of the following could be the value of s-t?

I. -1
II. 0
III. 1

A. None
B. I only
C. II only
D. III only
E. II and III

Solution :
----------
2s > 8 => s > 4
3t < 9 => t < 3

The given values can be represented on the number line as follows :

--t-----------3---------------4--------s-----------
|----+ve---|---------1-----|-+ve-+|

So,s-t will be greater than 1.
Correct option is A.
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Re: If 2s > 8 and 3t < 9 [#permalink]

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New post 25 Mar 2013, 12:18
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tulsa wrote:
If 2s > 8 and 3t < 9, which of the following could be the value of s-t?

I. -1
II. 0
III. 1

A. None
B. I only
C. II only
D. III only
E. II and III



s>4

t<3 (multiply by -1) --> -t>-3

Add both of them

Thus s-t >4-3

or s-t>1. As none of the options given are greater than 1, the answer is none.

A.
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Re: If 2s > 8 and 3t < 9 [#permalink]

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New post 04 Jul 2015, 02:46
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Sapient wrote:
Hi,


The Problem description is not precise, could you provide clear problem solving strategy.

Thanks.



If 2s > 8 and 3t < 9, which of the following could be the value of s-t?

I. -1
II. 0
III. 1

A. None
B. I only
C. II only
D. III only
E. II and III

we have two equations..
2s > 8 .. s>4, so' s' can be 4.1,5,5.05 etc
and 3t < 9 .. t<3 so 't'can be 2.9999, 2,-1 etc..

if we take the lowest possible difference between s and t, we will take lowest value of s, which is just above 4 and highest value of t, which is just lower to 3..
s-t >4.0000000001 -2.999999999 .... so s-t>1
therefore all values of -1,0,1 are not possible
ans none A
hope it helped
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Re: If 2s > 8 and 3t < 9 [#permalink]

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Re: If 2s > 8 and 3t < 9 [#permalink]

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New post 04 Jul 2015, 02:00
Hi,


The Problem description is not precise, could you provide clear problem solving strategy.

Thanks.
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Re: If 2s > 8 and 3t < 9 [#permalink]

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New post 04 Oct 2015, 15:14
I understand how we get s>4 and t<3, but I'm having a hard time wrapping my head around why t cannot be negative. Can someone please explain?
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If 2s > 8 and 3t < 9 [#permalink]

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New post 04 Oct 2015, 15:22
ada453 wrote:
I understand how we get s>4 and t<3, but I'm having a hard time wrapping my head around why t cannot be negative. Can someone please explain?


We don't need to check when t<0 but for the sake of your question, even if t <0 ---> -t>0 and you know that s>0, giving you s-t > 1 for all values of s and t as s>1

Any positive quantity added to a quantity >1 will give you the sum as >1

Consider s= 7, t= -5 or -0.3

Both these cases make it s-t >1.

Hope this helps.
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Re: If 2s > 8 and 3t < 9 [#permalink]

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New post 05 Oct 2015, 11:50
Thank you. I neglected to utilize the fact that s must be positive when testing cases. Appreciate the help
Re: If 2s > 8 and 3t < 9   [#permalink] 05 Oct 2015, 11:50
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