A can of nuts has almonds and cashews in a ratio of $x:y.$ If there are $z$ almonds in the can, which of the followi

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Wed Aug 26, 2020 3:18 am

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A can of nuts has almonds and cashews in a ratio of $x:y.$ If there are $z$ almonds in the can, which of the following represents the number of cashews?

A. $y(x + z)$
B. $y(z - y)$
C. $\dfrac{xy}{z}$
D. $\dfrac{yz}{x}$
E. $x$

Answer: D

Source: Princeton Review

Source: Beat The GMAT — Problem Solving | Wed Aug 26, 2020 3:18 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: A can of nuts has almonds and cashews in a ratio of $x:y.$ If there are $z$ almonds in the can, which of the fol

by deloitte247 » Sat Aug 29, 2020 9:21 pm

Ratio of almonds to cashew => x:y => x/y
If total almonds = z
Let total nuts = a
$$\frac{Almonds}{Cashew}=\frac{x\cdot a}{y\cdot a}$$
Almonds = xa
i.e z = xa
and a = z/x
Cashew = ya, where a = z/x
$$Therefore,\ cashew\ =\ y\ \cdot\ \frac{z}{x}=\frac{yz}{x}$$

Answer = option D

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