# CAT Model Paper 6 Questions and Answers with Explanation Part 1

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__INSTRUCTIONS__

The exam has sections and each section has a timer. The first section will be Quantitative aptitude and Data Interpretation and the second section will be Verbal Ability & Logical Reasoning. You will have 70 minutes to answer 30 questions in each section.

Within each section, you will be allowed to change or delete an answer, MARK a question for review, go to the NEXT or return to the PREVIOUS question, and look at the REVIEW screen.

You will also be able to go directly to a particular question by clicking it from the review screen once the first section ends; you will go to the second section. You cannot go from the first section to the second section till the full minutes for the first section run out. Once you are in the second section, you will again have minutes, and you will not be able to go back to the first section. You may use any remaining time to review the questions within the same section only.

All questions carry marks each. For each wrong answer, mark will be deducted .There is only one correct answer to each question.

No marks will be deducted for unanswered questions

Q: 1. In a triangle is the median to side bisects the angle B

and is the altitude to side , find the value of

(A)

(B)

(C)

(D)

Ans: A

Solution:

The correct choice is (A).

In the right angle triangle ABC, BP is the median to the hypotenuse. Hence (Median to the hypotenuse is half the hypotenuse).

Hence is an isosceles triangle,

Let

Then

In

Since is the angle bisector of , we can say then

But

Hence

Hence,

Hence option A

Q: 2. Which of the following options best expresses the graph below?

(A)

(B)

(C)

(D)

Ans: A

Solution:

The correct choice is (A). The graph of is:

Since the graph in the question has no negative value for ‘y’, the function can be rewritten as |.

However, the graph of | is:

But in the question, values of ‘y’ exist even for negative values of ‘x’.

Hence the required solution is

Hence option A

Q: 3. Find out the number of common roots for equations:

?

(A)

(B)

(C)

(D)

Ans: D

Solution:

The correct choice is (D). can be factorized as . Roots are out of which none are the roots of second equation.

Hence, option D

Q: 4. Sum of two positive integers is . What can be the maximum possible LCM of these numbers?

(A)

(B)

(C)

(D) Cannot be determined

Ans: B

Solution:

The correct choice is B. For the LCM to be maximum, the numbers should be as close as possible and preferably co-primes. 42 and 43 perfectly fit the bill. LCM .

Hence, option B

Q: 5. If are the roots of the equation then form an equation where the roots are more than the roots of the given equation.

(A)

(B)

(C)

(D) None of these

Ans: A

Solution:

SOLUTION

The correct choice is (A). Sum of the roots initially . After increasing them by each, they should be .

By solving we get initial roots as and . Later, roots will be 8 and .

Alternately, we can simply replace x by (x-4) to get the desired equation.

Q: 6. Praveen and Arjun are 850 m apart. If both of them start moving towards each other at the same time from their respective points with speeds in the ratio of 8 : 9 respectively, at what distance from the starting point of Arjun will they meet for the 10^{th} time? Assume that none of them stops at any point of time and once they reach their respective ends they immediately turn back.

(A)

(B)

(C)

(D) None of these

Ans: A

Solution;

The correct choice is (A). 1st time, they will meet away from Arjun. 2^{nd} time they will meet at distance x from Arjun.

.

3^{rd} time, they will meet at 550m away from Arjun.

4^{th} time, away from Arjun

Similarly, time 150m away from Arjun, and time away from Arjun.

And time also they will meet 50m away from Arjun.

Alternate solution 1^{st} time they meet, Arjun covers, and together they cover the total distance m. For every consequent meeting, they cover an additional 2d m, i.e. 2^{nd} meeting they cover, 3^{rd} meeting they cover and so on.

Hence, in the 10^{th} meeting they will cover 19d, and in the same time Arjun will cover , which is . Hence, they will meet at 50 m from the starting point of Arjun.

Q: 7. In a is the altitude on,

(A)

(B)

(C)

(D)

Ans: B

Solution:

The correct choice is (B). BD will be

.

In radius = area/semi-perimeter.

Hence option B

Q: 8. A six digit number ‘pqrstu’ having all distinct digits multiplied by ‘u’ gives an answer in the form ‘aaaaaa’. What can be the value of a?

(A) 9

(B) 7

(C) 4

(D) 5

Ans: B

Solution:

The correct choice is (B). From the options, u is definitely notas that will make a as . But is not divisible by 9.

It can be as that will make a all are distinct digits.

Hence option B