Question

If the positive numbers a,b,c,d are in AP. Then, $abc, abd, acd, bcd$ are

• A. not in AP/GP/HP
• B. in AP
• C. in GP
• D. in HP

Answer 1

Answer: (D)

in HP

Answer 2

Since, a,b,c,d are in AP.
$\Rightarrow \, \, \frac{a}{abcd},\frac{b}{abcd},\frac{c}{abcd},\frac{d}{abcd}$ are in AP.
$\Rightarrow \, \, \frac{1}{bcd},\frac{1}{cda},\frac{1}{abd},\frac{1}{abc}$ are in AP.
$\Rightarrow \, \, bcd,cda,abd,abc$ are in HP.
$\Rightarrow \, \, abc,abd,cda,bcd$ are in HP.