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If 5 < x < 10 and y = x + 5, what is the greatest possible

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If 5 < x < 10 and y = x + 5, what is the greatest possible [#permalink] New post 12 Jun 2012, 21:05
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If 5 < x < 10 and y = x + 5, what is the greatest possible integer value of x + y ?

A. 18
B. 20
C. 23
D. 24
E. 25
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Jun 2012, 02:04, edited 1 time in total.
Edited the question, added the answer choices and OA
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Re: Inequalities Question - Request help [#permalink] New post 12 Jun 2012, 22:14
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shivanigs wrote:
Hi,

Request your help to understand the concept behind the following question :

If 5 < x < 10 and y = x + 5,what is the greatest possible integer value of x + y?

Hi,

To find the greastest possible integer value of x + y, it is not necessary that both x & y should be integers,
x, y should be chosen in such a way that their sum is an integral value.

so, to find, max value of (x + y)
x + y = 2x + 5
maximum value of x such that 2x is integer would be 9.5 (given, 5 < x < 10)
x + y (maximum) = 19 + 5 =24

Let me know if you need any more assistance on this topic.

Regards,
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Re: Inequalities Question - Request help [#permalink] New post 13 Jun 2012, 02:03
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shivanigs wrote:
Hi,

Request your help to understand the concept behind the following question :

If 5 < x < 10 and y = x + 5,what is the greatest possible integer value of x + y?


Please read and follow: 11-rules-for-posting-133935.html Pay attention to the points #3, 7 and 8.

Original question is below:

If 5 < x < 10 and y = x + 5, what is the greatest possible integer value of x + y ?

A. 18
B. 20
C. 23
D. 24
E. 25

Since y=x+5 then x+y=x+(x+5)=2x+5. So, we need to find the greatest possible integer value of 2x+5.

Multiply 5 < x < 10 by 2: 10<2x<20. Now add 5 to each part of the inequality: 15<2x+5<25. As you can see the greatest possible integer value of 2x+5 is 24.

Answer: D.

Hope it's clear.
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Re: Inequalities Question - Request help [#permalink] New post 13 Jun 2012, 03:52
Bunuel wrote:
shivanigs wrote:
Hi,

Request your help to understand the concept behind the following question :

If 5 < x < 10 and y = x + 5,what is the greatest possible integer value of x + y?


Please read and follow: 11-rules-for-posting-133935.html Pay attention to the points #3, 7 and 8.

Original question is below:

If 5 < x < 10 and y = x + 5, what is the greatest possible integer value of x + y ?

A. 18
B. 20
C. 23
D. 24
E. 25

Since y=x+5 then x+y=x+(x+5)=2x+5. So, we need to find the greatest possible integer value of 2x+5.

Multiply 5 < x < 10 by 2: 10<2x<20. Now add 5 to each part of the inequality: 15<2x+5<25. As you can see the greatest possible integer value of 2x+5 is 24.

Answer: D.

Hope it's clear.


Dear Bunuel,
1.)can't understand what is the need to take 2x+5? wont it be easy to calculate with x less than 10.?
2.) when x is not integer but x+y to be integer - we can take x=9.5 and y = 14.5 - giving 24 - is this right?
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Re: Inequalities Question - Request help [#permalink] New post 13 Jun 2012, 03:59
Expert's post
kashishh wrote:
Bunuel wrote:
shivanigs wrote:
Hi,

Request your help to understand the concept behind the following question :

If 5 < x < 10 and y = x + 5,what is the greatest possible integer value of x + y?


Please read and follow: 11-rules-for-posting-133935.html Pay attention to the points #3, 7 and 8.

Original question is below:

If 5 < x < 10 and y = x + 5, what is the greatest possible integer value of x + y ?

A. 18
B. 20
C. 23
D. 24
E. 25

Since y=x+5 then x+y=x+(x+5)=2x+5. So, we need to find the greatest possible integer value of 2x+5.

Multiply 5 < x < 10 by 2: 10<2x<20. Now add 5 to each part of the inequality: 15<2x+5<25. As you can see the greatest possible integer value of 2x+5 is 24.

Answer: D.

Hope it's clear.


Dear Bunuel,
1.)can't understand what is the need to take 2x+5? wont it be easy to calculate with x less than 10.?
2.) when x is not integer but x+y to be integer - we can take x=9.5 and y = 14.5 - giving 24 - is this right?


What do you mean by "need"? One can solve a question with different approaches and you can choose the approach you personally find easier.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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 5 < x < 10 and y = x + 5, what is the greatest possible [#permalink] New post 13 Jun 2012, 04:09
Dear Bunuel,

Apologies for the wrongful post..did not know the rules.Have gone thru the same,will not happen again.Thanks for your help!

Regards
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Re: If 5 < x < 10 and y = x + 5, what is the greatest possible [#permalink] New post 13 Jun 2012, 08:29
Dear Bunuel,
sorry for the word 'need'. i just only wanted to know whether the way i did is right.
thanx for the reply.
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Re: If 5 < x < 10 and y = x + 5, what is the greatest possible [#permalink] New post 13 Jun 2012, 08:43
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Re: If 5 < x < 10 and y = x + 5, what is the greatest possible [#permalink] New post 23 Sep 2013, 22:26
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Re: If 5 < x < 10 and y = x + 5, what is the greatest possible [#permalink] New post 14 Oct 2013, 09:36
The question asks what is the greatest integer value of 2X+5, where 5<X<10, the greatest value of 2X which is integer will be achieved if X=9.5

Hence the greatest integer value of X+Y = 2x9.5+5=24, answer - D
Re: If 5 < x < 10 and y = x + 5, what is the greatest possible   [#permalink] 14 Oct 2013, 09:36
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