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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  [#permalink]

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New post Updated on: 15 Jul 2014, 08:03
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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.

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Originally posted by mshrek on 15 Jul 2014, 07:58.
Last edited by Bunuel on 15 Jul 2014, 08:03, edited 1 time in total.
Renamed the topic and edited the question.
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If s is an integer between 0 and 10, is t less than the aver  [#permalink]

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New post 15 Jul 2014, 08:41
1
2
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.
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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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New post 15 Jul 2014, 08:44
1
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.

Answer: B.


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.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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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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New post 15 Jul 2014, 11:36
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.

Answer: B.


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 :shock:
The graphical approach is pretty neat and simple :)
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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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New post 15 Jul 2014, 21:52
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.

Answer: B.


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 :shock:
The graphical approach is pretty neat and simple :)


Here is a post that discusses visual approaches: http://www.veritasprep.com/blog/2013/08 ... mber-line/
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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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New post 18 Jul 2014, 05:02
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.

Answer: A.



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]

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New post 09 Oct 2018, 10:08
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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New post 09 Oct 2018, 10:24
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
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Re: If s is an integer between 0 and 10, is t less than the aver &nbs [#permalink] 09 Oct 2018, 10:24
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