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|.
Answer: D.
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