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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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New post 20 Sep 2018, 22:20
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34% (03:11) correct 66% (02:30) wrong based on 41 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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New post 21 Sep 2018, 10:00
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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?

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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New post 24 Sep 2018, 06:54
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The answer is D
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Re: Each student of the school Z is a member of either club X or club Y &nbs [#permalink] 24 Sep 2018, 06:54
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