# If A divided by B is equal to C and C is larger than D …

If A divided by B is equal to C and C is larger than D, and all these number are positive whole numbers other than one, it follows that

1. A is always larger than D
2. B is always smaller than C
3. B is always smaller than D
4. C is always larger than B
5. D is always larger than B

I got this from reasoning skill section. How would I choose it ?

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$$\frac{A}{B} = C$$ $$\frac{A}{B} \geq D$$ $$A \geq BD$$

As $B$ is a natural number greater than 1:

1. A is always larger than D.
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$A=CB$, $C>D$ and $A,B, C, D >1$

1. We have $C=\cfrac AB >D$ thus $A>BD>D$, so $A>D$ since $B>1$
2. $B<C$ is not necessarily true for example $2\times 2 =4$ and $2=2$.
3. From 1. $A>BD$, so take for example $5>2\times 2$, $2=2$ so $B<D$ is not necessarily true.
4. $C>B \iff B<C$ Same argument as 1.
5. $D>B \iff B<D$ Same argument as 1.

Choice 1. is the only choice that is always true.

$a>b-$ means $a$ is greater or larger than $b$.

$a<b-$ means $a$ is less or smaller than $b$.

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I quite understand with you details explanation. Thanks you – Megamind Nov 25 '12 at 17:07