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# If s is an integer between 0 and 10, is t less than the aver

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Re: If s is an integer between 0 and 10, is t less than the aver [#permalink]
Bunuel wrote:
Bunuel wrote:
If s is an integer between 0 and 10, is t less than the average (arithmetic mean) of s and 10?

----0--s---(average)---10--- The average of s and 10 is halfway between s and 10.
The question asks whether t is in green area.

(1) t is closer to 10 on the number line than it is to s --> t is not in the green area. So, the answer to the question is NO. Sufficient.

(2) t is 5 times as large as s. If s=1 and t=5, then the answer is YES but if s=2 and t=10, then the answer is NO. Not sufficient.

Similar questions to practice:
if-x-is-a-positive-number-less-than-10-is-z-greater-than-th-167734.html
if-x-is-a-positive-number-less-than-10-is-z-less-than-the-131322.html
if-a-is-a-positive-number-less-than-10-is-c-greater-than-105650.html
if-y-is-a-negative-number-greater-than-8-is-x-greater-than-95138.html

Hope it helps.

Thanks for the suggestion. I tried to solve algebraically and somehow ended up rejecting option A
The graphical approach is pretty neat and simple
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If s is an integer between 0 and 10, is t less than the aver [#permalink]
mshrek wrote:
Bunuel wrote:
Bunuel wrote:
If s is an integer between 0 and 10, is t less than the average (arithmetic mean) of s and 10?

----0--s---(average)---10--- The average of s and 10 is halfway between s and 10.
The question asks whether t is in green area.

(1) t is closer to 10 on the number line than it is to s --> t is not in the green area. So, the answer to the question is NO. Sufficient.

(2) t is 5 times as large as s. If s=1 and t=5, then the answer is YES but if s=2 and t=10, then the answer is NO. Not sufficient.

Similar questions to practice:
https://gmatclub.com/forum/if-x-is-a-pos ... 67734.html
https://gmatclub.com/forum/if-x-is-a-pos ... 31322.html
https://gmatclub.com/forum/if-a-is-a-pos ... 05650.html
https://gmatclub.com/forum/if-y-is-a-neg ... 95138.html

Hope it helps.

Thanks for the suggestion. I tried to solve algebraically and somehow ended up rejecting option A
The graphical approach is pretty neat and simple

Check out the blog posts on the link given in my signature below.

Originally posted by KarishmaB on 15 Jul 2014, 22:52.
Last edited by KarishmaB on 17 Oct 2022, 00:54, edited 1 time in total.
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Re: If s is an integer between 0 and 10, is t less than the aver [#permalink]
Bunuel wrote:
If s is an integer between 0 and 10, is t less than the average (arithmetic mean) of s and 10?

----0--s---(average)---10--- The average of s and 10 is halfway between s and 10.
The question asks whether t is in green area.

(1) t is closer to 10 on the number line than it is to s --> t is not in the green area. So, the answer to the question is NO. Sufficient.

(2) t is 5 times as large as s. If s=1 and t=5, then the answer is YES but if s=2 and t=10, then the answer is NO. Not sufficient.

I think, everyone should check out how you've solved sufficiency for Statement 1. Clear demonstration of the 'Gmat eye'.
Brilliant Bunnel. Thank you!
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Re: If s is an integer between 0 and 10, is t less than the aver [#permalink]
mshrek wrote:
If s is an integer between 0 and 10, is t less than the average (arithmetic mean) of s and 10?

(1) t is closer to 10 on the number line than it is to s.

(2) t is 5 times as large as s.

$$1 \leqslant s \leqslant 9\,\,\,\,\operatorname{int} \,\,\,\left( * \right)$$

$$t\,\,\mathop < \limits^? \,\,\frac{{s + 10}}{2}$$

$$\left( 1 \right)\,\, \Rightarrow \,\,\,\,\left\{ \begin{gathered}\\ \,\,t \geqslant 10\,\,\,\,\mathop \Rightarrow \limits^{{\text{FOCUS}}!} \,\,\,t \geqslant \frac{{10 + 10}}{2}\,\,\,\mathop > \limits^{\left( * \right)} \,\,\,\frac{{s + 10}}{2}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\,\,\, \hfill \\\\ \,\,{\text{OR}} \hfill \\\\ \,s < \,\,\frac{{s + 10}}{2} < t\,\, < \,\,\,10\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\ \\ \end{gathered} \right.$$

$$\left( 2 \right)\,\,\,\left\{ \begin{gathered}\\ \,{\text{Take}}\,\,s = 1\,\,\,\, \Rightarrow \,\,\,\,t = 5\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\\\ \,{\text{Take}}\,\,s = 2\,\,\,\, \Rightarrow \,\,\,\,t = 10\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\ \\ \end{gathered} \right.$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: If s is an integer between 0 and 10, is t less than the aver [#permalink]
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Is t < (s+10)/2 ?

(1)
The right side is the midpoint of s and 10
If t is closer to 10 than it is to s, then t is greater than the midpoint
Sufficient

(2)
t = 5s
Is 5s < (s+10)/2 ?
Is 10s < s + 10 ?
Is 9s < 10 ?
Is s < 10/9 ?
This is yes when s = 0,1, and no when s=2,3,4,5,6,7,8,9,10
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Re: If s is an integer between 0 and 10, is t less than the aver [#permalink]
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Re: If s is an integer between 0 and 10, is t less than the aver [#permalink]
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