4 : 9, 25 : 49, ?, 289 : 361
Pattern Recognition in Number Series
The question asks to find the missing number pair in a given series based on a pattern. The series is: 4 : 9, 25 : 49, ? : ?, 289 : 361.
Analyzing Number Pairs
Let's examine the relationship between the numbers in each pair:
- First pair: 4 and 9. Note that $4 = 2^2$ and $9 = 3^2$.
- Second pair: 25 and 49. Note that $25 = 5^2$ and $49 = 7^2$.
- Fourth pair: 289 and 361. Note that $289 = 17^2$ and $361 = 19^2$.
Identifying the Prime Number Sequence
The bases of these squares form a sequence: 2, 3, 5, 7, ?, ?, 17, 19.
Observing this sequence, we can identify it as the sequence of prime numbers.
Determining the Missing Numbers
The prime numbers between 7 and 17 are 11 and 13.
Therefore, the missing bases in the sequence are 11 and 13.
The missing number pair should be the squares of these prime numbers: $11^2$ and $13^2$.
Calculating the Missing Pair
- Calculate the square of 11: $11^2 = 121$.
- Calculate the square of 13: $13^2 = 169$.
The missing number pair is 121 : 169.
Matching with Options
Comparing this result with the given options:
- Option 1: 729 : 64 (Incorrect)
- Option 2: 225 : 245 (Incorrect)
- Option 3: 121 : 169 (Correct)
- Option 4: 49 : 216 (Incorrect)
The number set that correctly replaces the question mark is 121 : 169.
Similar Questions
- What should come in place of the question mark (?) in the given series?
3, −2, −12, −32, −72, ? - What should come in place of the question mark (?) in the given series?
512 513 505 532 468 ? - Identify the number that does NOT belong to the following series.
14, 19, 26, 35, 44, 59 - Select the number from among the given options that can replace the question mark (?) in the following series.
16, 25, 36, 49, ? Select the number from among the given options that can replace the question mark (?) in the following series.
5, 18, 39, 68, 105, ?
- Select the number that can replace the question mark (?) in the following series.
14, 2, 28, 3, 84, 4, ? - Select the number from among the given options that can replace the question mark (?) in the following series.
40, 36, 33, 31, ? - Select the number from among the given options that can replace the question mark (?) in the following series.
256, 625, 1296, 2401, ? - Select the number from among the given options that can replace the question mark (?) in the following series.
4, 6, 8, 18, 16, ? - Select the number from the given options that will come next in the following series.
0, 6, 24, 60, ______
Important Questions from Number Series
What will come in place of question mark (?) in the following number series?
2, 5, 11, 23, 44, 77, ?
What will come in place of question mark (?) in the following number series?
31, 32, 36, ?, 61, 86
What will come in the place of question mark (?) in the following number series?
3, 6, 18, ?, 630, 6930
What should come in place of the question mark ‘?’ in the following number series?
60, 40, 50, ?, 180, 460
A series is given with one term wrong. Select that wrong term from the given alternatives.
J12, M24, P48, S96, U192
