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# Each student of the school Z is a member of either club X or club Y

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Each student of the school Z is a member of either club X or club Y  [#permalink]

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20 Sep 2018, 22:20
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Difficulty:

95% (hard)

Question Stats:

31% (02:49) correct 69% (02:21) wrong based on 48 sessions

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Each student of the school Z is a member of either club X or club Y, but not both. If each club has some international students, is the ratio of the number of domestic students to the number of international students greater for club X than for school Z?

(1) The ratio of the number of domestic students to the number of international students is less for Class Y than school Z.

(2) More than half of the domestic students of school Z are members of club X and more than half of the international students of school Z are members of club Y.

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Re: Each student of the school Z is a member of either club X or club Y  [#permalink]

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21 Sep 2018, 10:00
1
Each student of the school Z is a member of either club X or club Y, but not both. If each club has some international students, is the ratio of the number of domestic students to the number of international students greater for club X than for school Z?

Is $$\frac{D_x}{I_x}>\frac{D_z}{I_z}.............\frac{I_z}{I_x}>\frac{D_z}{D_x}..........\frac{I_y+I_x}{I_x}>\frac{D_x+D_y}{D_x}...........\frac{I_y}{I_x}>\frac{D_y}{D_x}..............\frac{D_x}{I_x}>\frac{D_y}{I_y}.$$

(1) The ratio of the number of domestic students to the number of international students is less for Class Y than school Z.
$$\frac{D_y}{I_y}<\frac{D_z}{I_z}$$..
$$\frac{D_y}{I_y}<\frac{D_z}{I_z}.............\frac{I_z}{I_y}<\frac{D_z}{D_y}..........\frac{I_y+I_x}{I_y}<\frac{D_x+D_y}{D_y}...........\frac{I_x}{I_y}<\frac{D_x}{D_y}..............\frac{D_x}{I_x}>\frac{D_y}{I_y}.$$
suff

(2) More than half of the domestic students of school Z are members of club X and more than half of the international students of school Z are members of club Y.
$$D_x>D_y$$ and $$I_y>I_x$$
since all terms are positive, dividing bigger quantity $$D_x$$ by a smaller number $$I_x$$ will be greater than dividing smaller $$D_y$$ by bigger $$I_y$$
so $$\frac{D_x}{I_x}>\frac{D_y}{I_y}$$
suff

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Re: Each student of the school Z is a member of either club X or club Y  [#permalink]

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24 Sep 2018, 06:54
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Re: Each student of the school Z is a member of either club X or club Y   [#permalink] 24 Sep 2018, 06:54
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