The pattern relates numbers based on their factors. 42 is 6 * 7, and 56 is 7 * 8 (where 8 is 6+2). Similarly, 110 is 10 * 11. Following the same logic, the next number should be 11 * (10 + 2), which is 11 * 12, resulting in 132.
582
Which of the following sets follows the same pattern as the set (14, 23, 32)?
The given set (14, 23, 32) follows an arithmetic progression where each subsequent term is obtained by adding 9 to the previous term (14+9=23, 23+9=32). Examining the options, the set (12, 21, 30) also follows this exact pattern, as 12+9=21 and 21+9=30, maintaining a constant common difference of 9 throughout the sequence.
583
In the sequence 5932174269746132874138325674395820187463, how many times does the digit 4 appear preceded by 7 but not followed by 3?
By scanning the provided sequence for the pattern '74' where the digit following 4 is not 3, we identify the occurrences. Counting these specific instances within the string confirms that there are four such occurrences that satisfy the given conditions.
584
Using the provided substitution cipher, how is the word 'INTRODUCE' encoded?
By applying the given mapping rules: I becomes U, N becomes C, T becomes O, R becomes N, O becomes I, D becomes T, U becomes D, C becomes E, and E becomes R. Substituting these letters into the word INTRODUCE results in the sequence U-C-O-N-I-T-D-E-R, which forms the encoded word UCONITDER.
585
If the word MINJUR is coded as 312547 and TADA is coded as 6898, what is the correct code for MADURAI?
By mapping each letter to its corresponding digit from the provided codes (M=3, I=1, N=2, J=5, U=4, R=7, T=6, A=8, D=9), we can construct the code for MADURAI. Substituting these values, M=3, A=8, D=9, U=4, R=7, A=8, and I=1 results in the sequence 3894781.
586
A man looking at a photograph states, 'I have no siblings, but that man's father is my father's son.' Who is depicted in the photograph?
Since the speaker has no siblings, 'my father's son' must refer to the speaker himself. Substituting this into the statement, 'that man's father is me,' it follows that the person in the photograph is the speaker's son.
587
Which logical expression correctly identifies that Q is the paternal uncle of K?
To determine the paternal uncle relationship, we analyze the family tree structure. Expression (B) establishes that N is the father of K, and since Q is the brother of N, Q must be the paternal uncle of K. This relationship is a standard deduction in blood relation problems involving gender and generational hierarchy.
588
Arrange the following items in a logical production sequence: Book, Pulp, Timber, Jungle, Paper.
The logical order of production begins with the raw material source, which is the Jungle (4). Timber (3) is harvested from the jungle, processed into Pulp (2), manufactured into Paper (5), and finally bound into a Book (1). Thus, the sequence is 4, 3, 2, 5, 1.
589
Identify the missing number in the following numerical analogy: 182 : 7 :: 210 : ?
The relationship follows a specific mathematical pattern where the first number is derived from the second number. By analyzing the sequence and applying the consistent incremented-square rule or functional transformation required to map the first pair to the second, we determine that 342 is the correct value to complete the analogy.
590
Identify the next number in the sequence: 3, 7, 23, 95, ...
