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# On Sunday morning, Pugsley and Wednesday are trading pet

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Senior Manager
Joined: 21 Oct 2013
Posts: 409

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06 Jun 2014, 12:32
9
00:00

Difficulty:

75% (hard)

Question Stats:

63% (03:01) correct 37% (03:16) wrong based on 136 sessions

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On Sunday morning, Pugsley and Wednesday are trading pet spiders. If Pugsley were to give Wednesday four of his spiders, Wednesday would then have five times as many spiders as Pugsley does. But, if Wednesday were to give Pugsley four of her spiders, Pugsley would now have four fewer spiders than Wednesday had before they traded. How many pet spiders does Pugsley have before the trading game commences?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

Hi, Though it looks easy, it has a trick at last step. Can anyone help me with this question, please.
Math Expert
Joined: 02 Sep 2009
Posts: 64250

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06 Jun 2014, 12:57
2
goodyear2013 wrote:
On Sunday morning, Pugsley and Wednesday are trading pet spiders. If Pugsley were to give Wednesday four of his spiders, Wednesday would then have five times as many spiders as Pugsley does. But, if Wednesday were to give Pugsley four of her spiders, Pugsley would now have four fewer spiders than Wednesday had before they traded. How many pet spiders does Pugsley have before the trading game commences?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

Hi, Though it looks easy, it has a trick at last step. Can anyone help me with this question, please.

If Pugsley were to give Wednesday four of his spiders, Wednesday would then have five times as many spiders as Pugsley does:
(w + 4) = 5(p - 4)

If Wednesday were to give Pugsley four of her spiders, Pugsley would now have four fewer spiders than Wednesday had before they traded:
p + 4 = w - 4

Solving gives p = 8 and w = 16.

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Manager
Joined: 13 Jun 2013
Posts: 248

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07 Jun 2014, 03:00
1
goodyear2013 wrote:
Hi Bunuel,

Thank you for the explanation.

Could you explain what "Pugsley would now have four fewer spiders than Wednesday had before they traded" is doing in this question, please.

After the second trade we have the following scenario (as mentioned in the pic).

now question states Pugsley would now have four fewer spiders than Wednesday had before they traded

see after trade pugsley have p+4 which is 4 fewer than wednesday had before which was w.

so, we can represent the above relationship mathematically as w-(p+4)=4
Attachments

pugsley.PNG [ 2.53 KiB | Viewed 2802 times ]

Senior Manager
Joined: 21 Oct 2013
Posts: 409

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07 Jun 2014, 01:50
Hi Bunuel,

Thank you for the explanation.

Could you explain what "Pugsley would now have four fewer spiders than Wednesday had before they traded" is doing in this question, please.
Manager
Joined: 24 Jun 2017
Posts: 113

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23 Sep 2017, 15:21
let x be pugsley and y be wednesday
5(x-4)=y+4
5x-y=24
y=5x-24
Second exchange
y=5x-24-4=x+4
5x-28=x+4
4x=32
x=8

but honestly I was confused a bit by wording for the second exchange (not a native-speaker)
took me 5 mins to put it down and fix the logic for equations
Manager
Joined: 01 May 2016
Posts: 71
Location: United States
GPA: 3.8

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24 Feb 2018, 08:40
Bunuel wrote:
goodyear2013 wrote:
On Sunday morning, Pugsley and Wednesday are trading pet spiders. If Pugsley were to give Wednesday four of his spiders, Wednesday would then have five times as many spiders as Pugsley does. But, if Wednesday were to give Pugsley four of her spiders, Pugsley would now have four fewer spiders than Wednesday had before they traded. How many pet spiders does Pugsley have before the trading game commences?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

Hi, Though it looks easy, it has a trick at last step. Can anyone help me with this question, please.

If Pugsley were to give Wednesday four of his spiders, Wednesday would then have five times as many spiders as Pugsley does:
(w + 4) = 5(p - 4)

If Wednesday were to give Pugsley four of her spiders, Pugsley would now have four fewer spiders than Wednesday had before they traded:
p + 4 = w - 4

Solving gives p = 8 and w = 16.

Hi Bunuel,

The equation which you wrote "If Wednesday were to give Pugsley four of her spiders, Pugsley would now have four fewer spiders than Wednesday had before they traded: p + 4 = w - 4".....could you please explain?.....I thought its.. (P+4)=(W-4)-4. Because Wednesday gives away 4 of hers to Pugsley...Please clarify.
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Intern
Joined: 18 Jun 2017
Posts: 22

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24 Feb 2018, 09:33
The answer to the question is 9.

Solution:

Let Pugsley has 'x' spiders and Wednesday has 'y' spiders.

Let us denote Pugsley as P and Wednesday as W

After P gives W 4 spiders,

Number of spiders with each of them,
P= x-4
W= y+4

According to the question,

W=5P
So, y+4 = 5*(x-4)

5x-y=24 ---- (Equation 1)

Now, W gives 4 spiders to P,

P= x+4
W=y-4

According to the question W has still 4 more spiders than P, So we need to add 4 to P to equalize

P+4=W
(x+4) +4 = y-4
y=x+12 ---------(Equation 2)

Solving (1) and (2)

x= 9 , y=21

Verification
P= 9 ; W = 21

9-4= 5
21+4= 25 and 25 = 5*5.

Also, 9+4= 13
21-4= 17 and 17= 13+4

Thanks
Manager
Joined: 23 Jul 2015
Posts: 84
Schools: Marshall '22 (S)

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28 Aug 2019, 08:37
Bunuel wrote:
goodyear2013 wrote:
On Sunday morning, Pugsley and Wednesday are trading pet spiders. If Pugsley were to give Wednesday four of his spiders, Wednesday would then have five times as many spiders as Pugsley does. But, if Wednesday were to give Pugsley four of her spiders, Pugsley would now have four fewer spiders than Wednesday had before they traded. How many pet spiders does Pugsley have before the trading game commences?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

Hi, Though it looks easy, it has a trick at last step. Can anyone help me with this question, please.

If Pugsley were to give Wednesday four of his spiders, Wednesday would then have five times as many spiders as Pugsley does:
(w + 4) = 5(p - 4)

I don't know what I am doing wrong, but I am getting the answer 9.

Equation 1= 5(P-4)=W+4
Upon solving: 5P-W=24

Equation 2
W-4- (P+4)=4
Upon solving W-P=12

If Wednesday were to give Pugsley four of her spiders, Pugsley would now have four fewer spiders than Wednesday had before they traded:
p + 4 = w - 4

Solving gives p = 8 and w = 16.

Re: On Sunday morning, Pugsley and Wednesday are trading pet   [#permalink] 28 Aug 2019, 08:37