On Sunday morning, Pugsley and Wednesday are trading pet

Question

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.

(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.

Bunuel · Answer

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.

Answer: B.

goodyear2013 · Answer

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.

manpreetsingh86 · Answer

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

cbh · Answer

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

Tridhipal · Answer

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.

Ayush1692 · Answer

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

SPatel1992 · Answer

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On Sunday morning, Pugsley and Wednesday are trading pet

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