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# How many dolls does Josephine currently have? (1) If Josephine gets 2

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
How many dolls does Josephine currently have? (1) If Josephine gets 2  [#permalink]

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20 Mar 2018, 06:51
00:00

Difficulty:

25% (medium)

Question Stats:

85% (00:57) correct 15% (01:00) wrong based on 22 sessions

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How many dolls does Josephine currently have?

(1) If Josephine gets 2 more dolls for her birthday, she will have a least 14 dolls.
(2) If Josephine donates 3 of her dolls to a toy drive, she will have less than 10 dolls

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Re: How many dolls does Josephine currently have? (1) If Josephine gets 2  [#permalink]

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20 Mar 2018, 07:13
Bunuel wrote:
How many dolls does Josephine currently have?

(1) If Josephine gets 2 more dolls for her birthday, she will have a least 14 dolls.
(2) If Josephine donates 3 of her dolls to a toy drive, she will have less than 10 dolls

We'll translate the statements into equations to see if they can be solved.
This is a Precise approach.

(1) our equation is j + 2 >= 14 which simplifies to j > 11
This has infinite solutions; insufficient.

(2) j - 3 < 10 which simplifies to j < 13
This also has many solutions. Insufficient.

Combined.
j > 11 and j < 13 have only one (integer) solution: j = 12.
Sufficient.

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Re: How many dolls does Josephine currently have? (1) If Josephine gets 2  [#permalink]

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20 Mar 2018, 08:38
Bunuel wrote:
How many dolls does Josephine currently have?

(1) If Josephine gets 2 more dolls for her birthday, she will have a least 14 dolls.
(2) If Josephine donates 3 of her dolls to a toy drive, she will have less than 10 dolls

If X is the number of Dolls Josephine has,

St1 implies that, X+2>=14
or X>=12
Alone insufficient.

St2 : X - 3 < 10
or X<13
Again alone insufficient.

Combining 1 and 2, X=12

Re: How many dolls does Josephine currently have? (1) If Josephine gets 2   [#permalink] 20 Mar 2018, 08:38
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