In the following question, you are given the base word INFORMATION. From the listed options, select the word which cannot be formed using the letters of INFORMATION, assuming that no letter is used more times than it appears in INFORMATION.

Introduction / Context:
This question asks you to identify which word cannot be constructed from the letters of the base word INFORMATION. The rule is that each letter in INFORMATION can be used at most as many times as it appears there, and no new letters may be added. Problems of this type are designed to check your precision when comparing letter sets and are a staple in verbal and logical reasoning sections of many aptitude examinations.

Given Data / Assumptions:

• Base word: INFORMATION.
• Letters available: I, N, F, O, R, M, A, T, I, O, N (with I, O and N appearing more than once).
• Options: NATION, INFRA, RATION, MATER.
• Letters can be rearranged, but no extra letters can be introduced and frequency limits must be respected.

Concept / Approach:
The standard approach is to examine the distinct letters of the base word to see which alphabet characters are available. Then, for each option, we confirm whether every letter is contained in this pool and whether the number of times it appears is not more than the available count. If any option uses a new letter that does not occur in INFORMATION or demands a letter more frequently than allowed, that option cannot be formed and becomes the correct answer. Particular attention should be given to letters like E, L or D, which do not appear in the base word but could appear in the options.

Step-by-Step Solution:
Step 1: From INFORMATION, list the distinct letters: I, N, F, O, R, M, A, T. Note that there is no letter E in this set. Step 2: Check NATION. Its letters are N, A, T, I, O, N. All occur within the base set and the repetition of N and I is supported by their multiple occurrences in INFORMATION. Therefore NATION can be formed. Step 3: Check INFRA. Its letters are I, N, F, R, A. Each one of these letters is clearly present in INFORMATION, so INFRA can be formed. Step 4: Check RATION. Its letters are R, A, T, I, O, N. All of these letters appear in INFORMATION within the available frequencies, so RATION can also be formed. Step 5: Check MATER. Its letters are M, A, T, E, R. While M, A, T and R all appear in INFORMATION, the letter E does not occur in the base word. Because E is required for MATER but is not available, MATER cannot be formed.

Verification / Alternative check:
A quick verification is to write the base word INFORMATION and search visually for each letter needed in the options. Doing this, you can see that all letters for NATION, INFRA and RATION are present. However, when you look for E in INFORMATION to build MATER, you will not find it. Since adding new letters is not allowed, this immediately disqualifies MATER as a valid formation. Rechecking the other options confirms that none of them require any letter outside the base set, reinforcing that MATER is uniquely impossible to form.

Why Other Options Are Wrong:
NATION uses N, A, T, I and O, all of which are available, with the repeated letters supported by the base word. INFRA uses I, N, F, R and A, which are clearly present. RATION draws on R, A, T, I, O and N, again all included in INFORMATION. Since each of these words can be assembled from the given letters without violating frequency limits, they do not satisfy the requirement of being impossible to form and cannot be correct answers.

Common Pitfalls:
Many test takers concentrate on the overall appearance of the words and neglect to verify each individual letter. Under time pressure, it is easy to assume that a common word like MATER must be valid, or to confuse similar-looking letters such as I and E. To avoid these mistakes, always start by listing the distinct letters available in the base word and then scan each option carefully, specifically checking for any letter that is not in that list. This simple discipline helps you avoid nearly all errors in this type of question.

Final Answer:
Since INFORMATION does not contain the letter E, the word MATER cannot be formed from its letters, while all other options can. Therefore MATER is the correct answer.