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# Test 16

Author Message
Manager
Joined: 19 Aug 2010
Posts: 76

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30 Jan 2011, 13:40
If a, b ,c and d are non-zero numbers such that $$a/b=c/d$$ and $$a/d=b/c$$ , which of the following must be true?

• lal=lcl
• lbl=ldl
• lal=ldl
• lbl=lal
• lbl=lcl

This is a question from Test 16. OA is D although I receive every time lcl=ldl
Could someone help me?
Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 39695

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30 Jan 2011, 14:21
medanova wrote:
If a, b ,c and d are non-zero numbers such that $$a/b=c/d$$ and $$a/d=b/c$$ , which of the following must be true?

• lal=lcl
• lbl=ldl
• lal=ldl
• lbl=lal
• lbl=lcl

This is a question from Test 16. OA is D although I receive every time lcl=ldl
Could someone help me?
Thanks

Given: (i) $$\frac{a}{b}=\frac{c}{d}$$ and (ii) $$\frac{a}{d}=\frac{b}{c}$$.

Now, from (i) $$a=\frac{bc}{d}$$ and substituting $$a$$ in (ii) you'll get $$\frac{bc}{d^2}=\frac{b}{c}$$ --> $$c^2=d^2$$ --> $$|c|=|d|$$ (so you are right), but this option is not listed among answer choices and you should try to get the one which is listed.

Again, from (i) $$c=\frac{ad}{b}$$ and substituting $$c$$ in (ii) you'll get $$\frac{a}{d}=\frac{b^2}{ad}$$ --> $$a^2=b^2$$ --> $$|a|=|b|$$.

_________________
Re: Test 16   [#permalink] 30 Jan 2011, 14:21
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# Test 16

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