CAT Model Paper 5 Questions and Answers with Explanation Part 1

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Q: 1. Find the number of zeroes at the end of

(A)

(B)

(C)

(D)

Ans: A

Solution:

We have to consider the zeroes at the end of as they will be less compared to those at the end of. Zeroes at the end of.

Q: 2. The sum of the first terms of an AP is . The sum of the 37th term and the 84th term of the AP is zero. What is the sum of the first 40 terms of the AP?

(A)

(B)

(C)

(D)

Ans: A

Solution:

Let the first term of the A.P be ‘a’ and the common difference be‘d’.

Sum of the first 80 terms,

Eqn (1)

Eqn (2)

Solving Eqn (1) and Eqn (2)

Sum of the first 40 terms,

Hence option A

Q: 3. A manufacturer estimates that of the articles he produces will be rejected. He has an order to sell items at each. If the estimated profit on his outlay including the cost of production of rejected articles is, find the cost of producing each article.

(A)

(B)

(C)

(D)

Ans: B

The correct choice is (B). Number of articles he had to produce.

Money he gets from transaction

As his profit is, his cost of manufacturing.

Cost of production of each article.

Hence option (B)

Q: 4. A piece of string is 66cm long. It is cut into four pieces such that the second piece is twice the length of the first, the third piece is thrice the length of the second and the fourth piece is four times the length of the third. If sum of the lengths of any two pieces is taken and compared with sum of other two pieces, what can be the minimum possible difference between these sums?

(A)

(B)

(C)

(D)

Ans: C

Solution:

The correct choice is (C). If first piece is x, second piece is , third piece is , fourth piece is , then sum of all pieces.

. The lengths are, and . To get the minimum possible difference between sums, group them as. Difference.

Hence option C

Start Passage

Directions for questions 5 to 7:

The graph below gives details about the price of per square foot of an apartment in Marathalli - Bangalore and Hinjewadi - Pune over a period of 6 years.

Q 5-to-7 Chart of Price of One Square Foot

Q 5-to-7 Chart of Price of One Square Foot

Q: 5. Raju had bought an square-feet apartment in either Marathalli or Hinjewadi in one of the years from and sold it after a year. If Raju made the highest percentage profit possible that one could have made in the given period, then in which of the following years should he have bought the apartment?

(A) 2008

(B) 2009

(C) 2010

(D) None of the above

Ans: B

Solution:

The correct choice is (B). Apartment prices in Marathalli:

Q_5_Table of Apartment Prices in Marathalli
Q_5_Table of Apartment Prices in Marathalli

Buying year

Price of a square foot bought (in Rs.)

Selling year

Price of a square foot sold (in Rs.)

Profit per square foot (in Rs.)

Profit per percent

2007

5500

2008

7000

1500

2008

7000

2009

6500

-500

2009

6500

2010

7500

1000

2010

7500

2011

8000

500

2011

8000

2012

10000

2000

Apartment prices in Hinjewadi

Q_5_1_Table of Apartment Prices in Hinjewadi
Q_5_1_Table of Apartment Prices in Hinjewadi

Buying year

Price of a square foot bought (in Rs.)

Selling year

Price of a square foot sold (in Rs.)

Profit per square foot (in Rs.)

Profit per percent

2007

4500

2008

6000

1500

2008

6000

2009

4500

-1500

2009

4500

2010

6500

2000

2010

6500

2011

8000

1500

2011

8000

2012

9000

1000

Raju would make the highest possible profit if he buys an apartment in Hinjewadi in 2009 and sold it in 2010.

Q: 6. Due to lack of demand, apartment prices in Marathalli fell by 10 percent in 2013 compared to the previous year. To stimulate demand, Alacrity Developers, an apartment builder in Marathalli, decided to offer a discount to prospective buyers where the ninth square foot was given free of cost for every eight square feet bought. Ms. Monisha bought a 900 square feet apartment from Alacrity Developers in 2013. of the cost of her apartment was funded by loans from a bank while of the apartment cost come from her personal funds. Monisha sell her ancestral property for?

(A)

(B)

(C)

(D)

Ans: D

Solution:

Apartment prices in Marathalli in

Alacrity Developers offers a square foot free for every eight square foot bought. Hence, by paying for eight square feet, the buyer gets nine square feet. In other words, a buyer gets an apartment for eight-ninths its price

Hence, if Monisha buys a square feet apartment, she is paying for only square feet.

Price of the square-feet apartment Cost of square feet

of the apartment cost is funded by sale of ancestral property.

Selling price of ancestral property

Q: 7. In the given period , Mr. Rakesh invested lakh in an apartment in Marathalli and sold it after two years. What is the highest possible profit he could have made given that apartment prices remained flat after 2012?

(A)

(B)

(C)

(D)

Ans: A

Solution:

The table below gives details about the profits made per square foot by Mr. Rakesh for every possible case where he sold the apartment 2 years after purchasing it. Since, apartment prices remained flat after , the price of a square foot in 2013 and 2014 is

Q_7_1_Table of Details About the Profits Made Per Square Foot
Q_7_1_Table of Details About the Profits Made per Square Foot

Buying year

Price of a square foot bought (in Rs.)

Selling year

Price of a square foot sold (in Rs.)

Profit per square foot (in Rs.)

Profit per percent

2007

5500

2009

2008

7000

2010

2009

6500

2011

2010

7500

2011

8000

2013

10000

2000

2012

10000

2014

10000

0

The profit percent made is the highest if Mr. Rakesh bought the apartment in 2010 and sold in 2012. Hence, for an investment of 60 lakh, he would have made a profit of lakh.

End Passage

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