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Kyle and Reed together have p baseball cards, where p is a

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macjas
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Kyle and Reed together have p baseball cards, where p is a [#permalink] New post   02 Jun 2012, 23:48
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73% (01:38) correct 27% (01:55) wrong based on 249 sessions
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Kyle and Reed together have p baseball cards, where p is a positive integer. Reed has q less baseball cards then Kyle, where q is a positive integer less than p. Which of the following represents the number of baseball cards Kyle has?

A. (p-q)/2
B. (p+2)/q
C. p/q
D. (p+q)/2
E. 2q - p
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D
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Bunuel
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Re: Kyle and Reed together have p baseball cards, where p is a [#permalink] New post   03 Jun 2012, 03:43
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macjas wrote:
Kyle and Reed together have p baseball cards, where p is a positive integer. Reed has q less baseball cards then Kyle, where q is a positive integer less than p. Which of the following represents the number of baseball cards Kyle has?

A. (p-q)/2
B. (p+2)/q
C. p/q
D. (p+q)/2
E. 2q - p


Say Kyle has K cards and Reed has R cards.

Given:
K+R=P
K-R=Q

Sum these two equations: (K+R)+(K-R)=P+Q --> 2K=P+Q --> K=(P+Q)/2.

Answer: D.
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Re: Kyle and Reed together have p baseball cards, where p is a [#permalink] New post   10 Jun 2012, 00:35
What is wrong with this algebraically:

K+R = P
R+Q = K

R+Q+R = P
2R = P-Q
R = (P-Q)/2

I know this is the wrong answer, but isn't this algebraically sound? So where is the discrepancy?
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Re: Kyle and Reed together have p baseball cards, where p is a [#permalink] New post   10 Jun 2012, 00:50
macjas wrote:
What is wrong with this algebraically:

K+R = P
R+Q = K

R+Q+R = P
2R = P-Q
R = (P-Q)/2

I know this is the wrong answer, but isn't this algebraically sound? So where is the discrepancy?


Algebraically that looks correct, but in that case you solved for how many cards Reed has. The question asks for how many cards Kyle has.

So really if you took your answer of R=(P-Q)/2 and substituted it back into K=R+Q, then K would equal (P+Q)/2.
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Re: Kyle and Reed together have p baseball cards, where p is a [#permalink] New post   10 Jun 2012, 01:08
:lol: Gotta read the questions more carefully!! :oops:
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Re: Kyle and Reed together have p baseball cards, where p is a [#permalink] New post   10 Jun 2012, 01:13
macjas wrote:
What is wrong with this algebraically:

K+R = P
R+Q = K

R+Q+R = P
2R = P-Q
R = (P-Q)/2

I know this is the wrong answer, but isn't this algebraically sound? So where is the discrepancy?



No Discrepancy.
You solved for R.

Solve for K, you will get the answer.
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Re: Kyle and Reed together have p baseball cards, where p is a [#permalink] New post   10 Jun 2012, 01:36
Too many tequilas the night before can do this to you.. :drunk
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Re: Kyle and Reed together have p baseball cards, where p is a [#permalink] New post   17 Jun 2012, 12:45
Answer: D

The trick is that once you solve the unknown, look back at the problem and make sure you answer the question asked.

k+r = p
r = k -q
k+k-q=p

k=(p+q)/2
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Re: Kyle and Reed together have p baseball cards, where p is a [#permalink] New post   27 Feb 2013, 01:13
Let cards with Kyle = x
So, cards with Reed = (p-x).............. as both in total have p cards.
From the other information
x-q = p -x ....
So x = (p+q) / 2
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Re: Kyle and Reed together have p baseball cards, where p is a [#permalink] New post   22 Dec 2014, 10:21
This one doesnt deserve any explanation ;)
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Re: Kyle and Reed together have p baseball cards, where p is a [#permalink] New post   23 Dec 2014, 10:44
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Hi All,

This question is perfect for TESTing VALUES

We're told Kyle and Reed have a total of P cards and that Reed has Q fewer cards than Kyle:

Kyle = 5
Reed = 2
Total = P = 7
Q = 3

We're asked for the number of cards KYLE has. Based on these VALUES, the answer is 5. Now lets TEST our values for P and Q....

Answer A: (7-3)/2 = 2 NOT a match
Answer B: (7+2)/3 = 3 NOT a match
Answer C: 7/3 NOT a match
Answer D: (7+3)/2 = 5 This IS a MATCH
Answer E: 6 - 7 = -1 NOT a match

Final Answer:
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D


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Re: Kyle and Reed together have p baseball cards, where p is a [#permalink] New post   03 Dec 2019, 07:37
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I think the Best way to solve this problem is to assume some values for variables p and q

let p = 7 and q = 3

that means Kyle has 5 and Reed has 2

now substitute the values in the options D is the answer.
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Re: Kyle and Reed together have p baseball cards, where p is a [#permalink] New post   03 Dec 2019, 07:47
RajKomanapalli wrote:
I think the Best way to solve this problem is to assume some values for variables p and q

let p = 7 and q = 3

that means Kyle has 5 and Reed has 2

now substitute the values in the options D is the answer.

Great Approach, Kudos added.
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Re: Kyle and Reed together have p baseball cards, where p is a [#permalink]
03 Dec 2019, 07:47
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