GATE ECE 2014 Set 3 | GA | Question: 4

Question

The next term in the series $81, 54, 36, 24, \dots$ is ________

Comments

I'm getting 15 by taking successive difference & forming its series.

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https://www.quora.com/What-is-the-next-number-in-the-series-81-54-36-24

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both 15 , 16 are the possible answers for this series

Answer 1

We get next term in sequence by $\left(\dfrac{X}{3}\right)\times 2$
$\dfrac{81}{3} =27\times 2 = 54$

$\dfrac{54}{3} =18\times 2 =36$

$\dfrac{36}{3} =12\times 2 = 24$

$\dfrac{24}{3} = 8\times 2 = 16$

Answer)16

Comments

9 is also a possible answer,

series given → 81 , 54 ,36 , 24

difference between first two terms( 81 – 54  = 27) then (54 – 36 = 18) then (36 – 24 = 12) see

27 = 3 * 9

18 = 3 * 6

12 = 3 * 4

now  take  9 , 6 , 4

difference between  first two  (9 – 6 = 3) then (6 – 4 = 2) so whats the next term?

it will be 1 right?

so means missing term will be 3 *3.

please check if anything is incorrect! not sure about this !

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Many answers are possible for such questions , GATE should avoid asking such questions . The only reason the best answer has 16 is because the GATE answer key had 16 as the answer for this question .

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81,54,36,24,_16

9.   ×     6    ×   4

Answer 2

ALTERNATE LOGIC (Look at the number of 2's)

$ 81 = 3 \times 3 \times 3 \times 3  $

$ 54 = 3 \times 3 \times 3 \times$$ 2  $

$ 36 = 3 \times 3 \times$$ 2 \times 2  $

$24= 3 \times$$ 2 \times 2 \times 2  $

$16=$ $2 \times 2 \times 2 \times 2  $

Comments

I am also getting 15 as the answer.

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What is the correct answer??15 or 16

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its 24=3*2*2*2

12=2*2*2*2=16

Answer 3

$81,54,36,24,$______

$\dfrac{81}{1.5} = 54$

$\dfrac{54}{1.5} = 36$

$\dfrac{36}{1.5} = 24$

$\dfrac{24}{1.5} = 16$

So, the correct answer is $16.$

Comments

Sir, you get these series assumption by intuition itself or there’s some trick or concept behind it?

Answer 4

By successive subtraction, I’m getting 15 as answer.