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If $2\times 8=4$;$3\times 27=9$; $6\times 24=4$, then $5\times 40=?$
A. 12
B. 10
C. 8
D. 6
E. 100

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Last updated date: 20th Jul 2024
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Answer
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Hint: These types of questions are completely logic based, these cannot be done through knowing a one or two formula, but if you have practice on these types of questions then you can solve them easily. Rather than simple calculation as these questions look, they have some hidden applied trick while doing calculation which we had to know. However, we will go through the problem and see the different possibilities that will be there which will satisfy the condition of the question, the same we will apply to the unknown one, which we had to know then we will get the answer.

Complete step by step answer:
Moving further with the question we had$2\times 8=4$;$3\times 27=9$; $6\times 24=4$,
Focusing on the first condition of question i.e. $2\times 8=4$, in actual $2\times 8=16$, but now it is giving 4, so seeing 16, we can get 4 when we find square root of 16 which is 4 or through dividing 16 by 4, which is the square of first term i.e. 2.
Now these two cases we will apply and see on another given condition in question, that whether they will satisfy them or not, whichever case will satisfy them will also satisfy the other condition of which we had to know the answer.
So in the second given condition i.e. $3\times 27=9$, in actual $3\times 27=81$, but now it is giving 9, so seeing 81, we can get 9 when we find square root of 81 which is 9, or through dividing 16 by 9, which is the square of first term i.e. 3. As this given condition satisfies both the cases, so now we will move to the third condition.
So, in the third condition i.e. $6\times 24=4$, in actual $6\times 24=144$, but now it is giving 4, so seeing 144, we can get 4 when we divide 144 by 36, which is the square of first term i.e. 6. And if we find the square root of 144 as we did in the above given condition then we will get 12, which is wrong. So the correct case will be the second one. That is dividing the actual answer by the square of the first term of the given condition will give our answer.
Now applying it to $5\times 40$of which we had to know the value, by going with the second case, as in actual$5\times 40=200$. And second case says to divide this answer by the square of first term, which is ‘5’ here so by second case
$\dfrac{200}{25}=8$

So, the correct answer is “Option C”.

Note: If in the above example if the two cases which we applied in the given condition seem to fail, then we had to go with some other logic/case which looks like to be applied. To be perfect in the type of question you had to practice such a type of question, as there is no particular formula for solving them.