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Martha and Susan have an equal number of cats. If Martha gives one of

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Martha and Susan have an equal number of cats. If Martha gives one of [#permalink]

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New post 28 Aug 2017, 03:59
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Question Stats:

66% (01:40) correct 34% (00:56) wrong based on 38 sessions

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Martha and Susan have an equal number of cats. If Martha gives one of her cats to Susan, how many cats will Martha have?

(1) The product of the number of cats Martha has and Susan has after Martha gave one cat to Susan is one less than the product of the number of cats Martha and Susan had originally.
(2) The difference in the number of cats each of them has after the change is 2.
[Reveal] Spoiler: OA

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Re: Martha and Susan have an equal number of cats. If Martha gives one of [#permalink]

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New post 28 Aug 2017, 04:05
Bunuel wrote:
Martha and Susan have an equal number of cats. If Martha gives one of her cats to Susan, how many cats will Martha have?

(1) The product of the number of cats Martha has and Susan has after Martha gave one cat to Susan is one less than the product of the number of cats Martha and Susan had originally.
(2) The difference in the number of cats each of them has after the change is 2.


(1) let assume M is the number of cats with Martha before exchange and S is the number of cats with Susan before exchange
if M=S=2;
preexchange = 2*2 =4
postexchange = 3*1 = 3

if M=S=3;
preexchange =3*3 = 9
postexchange = 4*2 = 8
not sufficient

(2)
if M=S=2;
postexchange = 3-1 = 2

if M=S=3;
postexchange = 4-2 = 2
not sufficient

E
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Re: Martha and Susan have an equal number of cats. If Martha gives one of [#permalink]

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New post 28 Aug 2017, 05:46
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Given :
Let no. of cats Martha and susan have initially = x

After change
No of cats Martha has = x-1
No of cats Susan has = x+1

1) By given information we can form equation :
No. of cats Martha has after change * no of cats Susan has after change = product of no. of cats they initially had -1
(x-1)(x+1) = x^2 -1
equation is true. But it does not give any new information. Already given in question stem

1) By given information we can form equation :
No. of cats Susan has after change - No. of cats Martha has after change = 2
(x+1) - (x-1) = 2
equation is true. But it does not give any new information. Already given in question stem

so both insufficient

Answer : E

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Re: Martha and Susan have an equal number of cats. If Martha gives one of [#permalink]

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New post 29 Aug 2017, 04:25
IMO - E

Lets Assume both of them had X cats.

Post exchanges - Martha - ( X-1)

Susan - (x+1) Cats

A) L.H.S = R.H. S we cant solve value for X
2) Value of X We can't find

So E

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Re: Martha and Susan have an equal number of cats. If Martha gives one of [#permalink]

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New post 18 Sep 2017, 00:22
let martha and susan have M andS cats respectively (initially)

1. M*S-1= (M-1)*S Not Sufficient
2. (M-1)-S=2 or S-(M-1) Not Sufficient
hence E

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Re: Martha and Susan have an equal number of cats. If Martha gives one of   [#permalink] 18 Sep 2017, 00:22
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