CAT 2003 Slot 1 — QA Question 50
Each question is followed by two statements, A and B. Answer each question using the following instructions
Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.
Let T be the set of integers {3, 11, 19, 27, ..., 451, 459, 467} and S be a subset of T such that the sum of no two elements of S is 470. The maximum possible number of elements in S is
Answer & solution
- A
32
- B
28
- C
29
30
The sum of the first and last terms in T is 470.
Likewise, the sum of the second and second-last terms is also 470.
In general the sum of the nth term from the beginning and the nth term from the end is 470.
∴ Only one of each of these pairs of terms will be in S. (For instance only one of 3 and 467 can be in S)
∴ The set S can have a maximum of half of the terms in T.
The terms in T are in A.P. with a common difference of 8.
Last Term = 467 = 3 + (n − 1) × 8
∴ n = 59
∴ Total number of terms in the set T = 59
∴ there are 29 pairs of numbers in T that add up to 470 and the 59th number is 235, which occurs in the middle of the series.
∴ S will be a set with 30 terms, with 29 terms which are from the pairs adding up to 470, and 235.
Hence, option (d).