Unraveling the Complexity: Aptitude Questions to Challenge Your Mind
Question 1: The Cryptic Sequence
Find the next term in the following sequence:
2, 12, 36, 80, 150, ?
Answer 1:
To decipher this sequence, let's break it down:
2 * 3 + 6 = 12
12 * 3 - 12 = 36
36 * 3 + 8 = 80
80 * 3 - 30 = 150
Following this pattern, the next term would be:
150 * 3 + 52 = 502
So, the next term in the sequence is 502.
Question 2: The Conundrum of Cubes
If the length, width, and height of a cuboid are increased by 50%, 40%, and 30% respectively, by what percentage will its volume increase?
Answer 2:
Let's assume the original dimensions of the cuboid are \( l \), \( w \), and \( h \) respectively.
So, the original volume (\( V_1 \)) would be \( lwh \).
After the increase, the new dimensions become \( 1.5l \), \( 1.4w \), and \( 1.3h \) respectively.
The new volume (\( V_2 \)) would then be \( (1.5l)(1.4w)(1.3h) \).
Now, let's calculate the percentage increase:
\[ \text{Percentage Increase} = \left( \frac{{V_2 - V_1}}{{V_1}} \right) \times 100\% \]
\[ = \left( \frac{{(1.5l)(1.4w)(1.3h) - lwh}}{{lwh}} \right) \times 100\% \]
\[ = \left( \frac{{(1.5 \times 1.4 \times 1.3) - 1}}{{1}} \right) \times 100\% \]
\[ = \left( \frac{{2.94 - 1}}{{1}} \right) \times 100\% \]
\[ = 1.94 \times 100\% \]
\[ = 194\% \]
So, the volume of the cuboid will increase by 194%.
Question 3: The Enigmatic Series
Find the missing number in the series:
1, 8, 27, 64, ?
Answer 3:
The given series consists of perfect cubes of consecutive natural numbers.
1 = \( 1^3 \)
8 = \( 2^3 \)
27 = \( 3^3 \)
64 = \( 4^3 \)
Following this pattern, the next term would be \( 5^3 = 125 \).
So, the missing number in the series is 125.
These aptitude questions serve as mental gymnastics, challenging you to think critically and creatively. Embrace the challenge, for it is through overcoming such obstacles that our minds grow sharper and more resilient. Keep exploring, keep learning, and keep pushing the boundaries of your intellect.
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