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When the positive integer x is divided by the positive integ

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When the positive integer x is divided by the positive integ

by BTGmoderatorDC » Sat Jun 15, 2019 4:21 pm

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When the positive integer x is divided by the positive integer y, the quotient is 2 and the remainder is z. When x is divided by the positive integer a, the quotient is 3 and the remainder is b. Is z > b?

(1) The ratio of y to a is less than 3 to 2.
(2) The ratio of y to a is greater than 2 to 3.

OA A

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Source: — Data Sufficiency |
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by swerve » Sun Jun 16, 2019 3:29 pm

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As per question

\(X=2y+z\)
\(X=3a+b\)

\(2y+z=3a+b\)

I) \(\frac{y}{a} < 1.5\)
\(3a > 2y\) so in order to maintain equality
\(Z > b\) sufficient

II) \(\frac{y}{a} > 0.6\)
\(3a\) can be \(>\) or \(< 2y\)
So can't say about \(z\) or \(b\)

Therefore, __A__ is the correct answer.
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