CAT Model Paper 8 Questions and Answers with Explanation Part 1

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Answer the questions based on the information provided below.

In a country called Mehangistan, the food inflation is calculated based on the following five food items only (their weight ages are also given) .

Rice

Chicken

Sugar

Oil

Coriander

The table below gives the prices of these products in ₹ per kg or litre

The inflation index is set at as on 1^st Jan 2010 (base year) , and the inflation index in any other year is the sum-product of the prices multiplied by their respective weights.

Q: 1. If the Inflation Index becomes as on , then what is the approximate ₹ price of oil in per litre as on Jan 2012?

(A)

(B)

(C)

(D) Cannot be determined

Ans: C

Solution:

Let the blank cells be filled up by variables A, B, C, and D, as given in the table above.

For 2010, the inflation index is 100, which can be calculated by the sum-product of the prices with their respective weights.

We need to find the value of C, given that the inflation index is .

Hence,

Solving, we get

Q: 2. If Mr. Bandookwala wants to prepare Dhansak to celebrate New Year 2013, he will need of chicken and 2 litres of oil for the same. How much will it cost him to buy these items if inflation index is at on that day?

(A)

(B)

(C)

(D) Cannot be determined

Ans: A

Solution:

The correct choice is (A) . Let the blank cells be filled up by variables A, B, C and D, as given in the table above.

For 2010, the inflation index is , which can be calculated by the sum-product of the prices with their respective weights.

We need to find the value of A and B, given that the inflation index is .

Hence,

Or,

Or, .

Hence, .

Q: 3. The Inflation Index is 108 as on 1^st Jan 2011. Mr. Jagannath is allergic to coriander. What is the % change in his household expenditure from 2010 to 2011, given that the consumption of all food items is 1 unit and remains the same in the next year? Assume that he consumes all the items except coriander.

(A)

(B)

(C)

(D)

Ans: B

Solution:

Let the blank cells be filled up by variables A, B, C, and D, as given in the table above.

For 2010, the inflation index is 100, which can be calculated by the sum-product of the prices with their respective weights.

First we find out the value of D.

.

Let us assume that in both years, he consumes unit quantity of all items (except coriander)

In 2010, total value of consumption

In 2011, total value of consumption

Hence, the % change is

Q: 4. If the government starts regulating the price of oil in 2012 so that inflation does not go beyond , then what is the maximum permissible price of oil in per litre in that year?

(A) 100

(B) 110

(C) 115

(D) 120

Ans:

Solution:

The correct choice is (D) . Let the blank cells be filled up by variables A, B, C and D, as given in the table above.

For 2010, the inflation index is 100, which can be calculated by the sum-product of the prices with their respective weights.

We need to find the value of C, given that the inflation index does not exceed .

Hence,

Solving, we get

Q: 5. Ankuran is a sweetshop owner who sells sweets packed in different types of boxes. He planned to sell a minimum of rasgullas and gulabjamuns packing them in two different types of boxes A and B. In each box A, he packs 6 rasgullas and 4 gulabjamuns, whereas in each packet B he packs 9 rasgullas and 5 gulabjamuns. He sells box A for each box B for each. What could be the least amount realized by him by selling the boxes?

(A)

(B)

(C)

(D)

Ans: A

Solution:

The correct choice is (A) . To sell a minimum of 185 rasgullas and 111 gulabjamuns, Ankuran has to sell a minimum of 31 boxes of type A, or 23 boxes of type B, or some other combination of the two types. But since the total amount realized has to be minimum, the since the price of type A boxes is less than that of type B boxes the minimum amount be achieved if only boxes of type A are sold. Hence, if he sells boxes only of type A, he will realize an amount of .

Q: 6. How many real solutions does the equation have?

(A) Only one

(B) Only two

(C) More than two

(D) No solution exists

Ans: D

Solution:

The correct choice is (D) . Clearly it seems that the terms cancel out from both R. H. S. and L. H. S. and the number of solutions is one viz. . However this solution is not valid as the terms cancelled out contain in the denominator, and hence they . Hence the given equation has no solution.