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

Question

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.

Bunuel · Answer

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.

Answer: A.

Bunuel · Answer

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.

mshrek · Answer

Thanks for the suggestion. I tried to solve algebraically and somehow ended up rejecting option A :shock:

The graphical approach is pretty neat and simple

KarishmaB · Answer

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

Kconfused · Answer

I think, everyone should check out how you've solved sufficiency for Statement 1. Clear demonstration of the 'Gmat eye'.
Brilliant Bunnel. Thank you!

fskilnik · Answer

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

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

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

\left( 2 ight)\,\,\,\left\{ \begin{gathered}
 \,{	ext{Take}}\,\,s = 1\,\,\,\, \Rightarrow \,\,\,\,t = 5\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{	ext{YES}}} ightangle \,\, \hfill \
 \,{	ext{Take}}\,\,s = 2\,\,\,\, \Rightarrow \,\,\,\,t = 10\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{	ext{NO}}} ightangle \hfill \ 
\end{gathered} ight.

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

Regards, 
Fabio.

gmatzpractice · Answer

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
Insufficient

bumpbot · Answer

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

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

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