# CAT Model Paper 9 Questions and Answers with Explanation Part 1

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1. The area of regular hexagon ABCDEF is 144. What is the area of shaded region?

(A) 24

(B) 36

(C) 64

(D) 96

Solution:

Regular hexagon is the combination of 12 identical triangles, out of 12 three triangles are shaded. Thus the area of shaded region.

2. A palindrome is a positive integer which is unchanged if you reverse the order of its digits. If all palindromes are written in increasing order, how many possible prime values can the difference between successive palindromes take?

(A) 1

(B) 2

(C) 3

(D) None of these

Solution:

Let x be a palindrome and the next highest palindrome. It is obvious that all single digit numbers are palindromes

If then it is easy to see by inspection that so the only prime differences are 2 and 11.

Now, Let us assume . IF and have the same final digit, then their difference is divisible by 10 and hence not prime. So they must have different final digits. We have 2 cases to consider here: first case when and have different number of digits ,then the difference . Second case When have same number of digit but different final digit. Eg. Then. The difference,

So again only prime difference are 2 and 11.

3. Find the remainder when is divided by 17?

(A) 0

(B) 1

(C) -1

(D) 2

Solution:

This needs the application of basic remainder, Fermat theorem and frequency

Step 1 – Remainder when 400 is devided by 17 is 9

The Problem changes to

From Fermat theorem, the Euler’s number of 17 is 16

Problem now changes to

Going by frequency method, gives remainder -1

So will give remainder 1.

Alternate Solution:

We know that

4. Find the number of 6 letter words that can be formed using all letters of the English alphabet so that the words contain atheist 3 consonants and each letter of the word is unique in every case?

(A)

(B)

(C)

(D) None of these

Solution:

Option (b)

Total = 21 consonants and 5 vowels

Three cases

3 consonats & 3 vowels =

4 consonats & 2 vowels =

5 Consonants & 1 vowel =

6 Consonants & 0 vowels =

Arrangement = 6! In each case

5. A boy has to climb 10 steps. He tosses one coin. If head appears, he climbs a single step. If tail appears, he climbs 2 steps. In how many ways can climb 10 steps?

(A) 90

(B) 88

(C) 92

(D) 89