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When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7]*[4]

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When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7]*[4]  [#permalink]

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New post 06 May 2012, 07:28
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When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7]*[4] = ?

A. [22]
B. [44]
C. [45]
D. [88]
E. [90]
Most Helpful Expert Reply
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Joined: 02 Sep 2009
Posts: 53020
Re: When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7]*[4]  [#permalink]

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New post 06 May 2012, 09:13
5
5
Galiya wrote:
When X is even, [x]=a/2+1, when X is odd [x]=2a+1 then [7]*[4]=?

A. [22]
B. [44]
C. [45]
D. [88]
E. [90]

your thoughts?
i went with C and was happy till didn't see the official answer


[7]*[4]=(2*7+1)(4/2+1)=45.

Now, notice that the answer choices are also in boxes, so we have that [x]=45, which means that for even x it should be 45=x/2+1 --> x=88=even and for odd x it should be 45=x*2+1 --> x=22=even, so not a valid solution.

Answer: D. ([88]=88/2+1=45).

Similar question to practice: for-all-positive-integers-m-3m-when-m-is-odd-and-123618.html

Hope it helps.
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Re: When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7]*[4]  [#permalink]

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New post 06 May 2012, 09:18
thanks, Bunuel! i was hoping for such an easy explanation
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Re: When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7]*[4]  [#permalink]

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New post 26 Jun 2012, 02:42
Bunuel
was reviewing my posts and got a question (im pretty sure, after the explanation ill think- OMG it was so obvious, but anyway):
looking at the question above, why do we substitute [x], e.g. [7] or [4], instead of a and b?
x and a (or b) are not the same numbers.
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Re: When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7]*[4]  [#permalink]

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New post 26 Jun 2012, 02:47
1
Galiya wrote:
Bunuel
was reviewing my posts and got a question (im pretty sure, after the explanation ill think- OMG it was so obvious, but anyway):
looking at the question above, why do we substitute [x], e.g. [7] or [4], instead of a and b?
x and a (or b) are not the same numbers.


It should be: "When X is even, [x]=x/2+1, when X is odd [x]=2x+1 then [7]*[4]=?"
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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

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Re: When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7]*[4]  [#permalink]

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New post 26 Jun 2012, 03:00
+1 thank you for this and a lot of previous answers&explanations
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Re: When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7]*[4]  [#permalink]

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New post 03 Nov 2014, 07:47
Bunuel wrote:
Galiya wrote:
When X is even, [x]=a/2+1, when X is odd [x]=2a+1 then [7]*[4]=?

A. [22]
B. [44]
C. [45]
D. [88]
E. [90]

your thoughts?
i went with C and was happy till didn't see the official answer


[7]*[4]=(2*7+1)(4/2+1)=45.

Now, notice that the answer choices are also in boxes, so we have that [x]=45, which means that for even x it should be 45=x/2+1 --> x=88=even and for odd x it should be 45=x*2+1 --> x=22=even, so not a valid solution.

Answer: D. ([88]=88/2+1=45).

Similar question to practice: for-all-positive-integers-m-3m-when-m-is-odd-and-123618.html

Hope it helps.



Hi Bunuel,

Why do we not consider 22 as an answer? Is it because 22 as an answer was even when equated to an odd equation, i.e 2a+1? Does the solution also
have to be odd when equated to an odd equation (2a+1)?
I hope my question makes sense ... not sure if I was able to explain myself clearly? =P Please let me know!

Thanks as always!!
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53020
Re: When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7]*[4]  [#permalink]

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New post 03 Nov 2014, 07:58
1
Rca wrote:
Bunuel wrote:
Galiya wrote:
When X is even, [x]=a/2+1, when X is odd [x]=2a+1 then [7]*[4]=?

A. [22]
B. [44]
C. [45]
D. [88]
E. [90]

your thoughts?
i went with C and was happy till didn't see the official answer


[7]*[4]=(2*7+1)(4/2+1)=45.

Now, notice that the answer choices are also in boxes, so we have that [x]=45, which means that for even x it should be 45=x/2+1 --> x=88=even and for odd x it should be 45=x*2+1 --> x=22=even, so not a valid solution.

Answer: D. ([88]=88/2+1=45).

Similar question to practice: for-all-positive-integers-m-3m-when-m-is-odd-and-123618.html

Hope it helps.



Hi Bunuel,

Why do we not consider 22 as an answer? Is it because 22 as an answer was even when equated to an odd equation, i.e 2a+1? Does the solution also
have to be odd when equated to an odd equation (2a+1)?
I hope my question makes sense ... not sure if I was able to explain myself clearly? =P Please let me know!

Thanks as always!!


We got that [7]*[4] = 45.

Now, [22], since 22 is even, is 22/2 + 1 = 12, not 45.

Does this make sense?
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7]*[4]  [#permalink]

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Re: When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7]*[4]   [#permalink] 15 Oct 2018, 06:18
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