# CAT Model Paper 6 Questions and Answers with Explanation Part 2

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Q: 9. A ladder consists of rungs, the lengths of which increase from the top to bottom. The topmost rung AB is 40 cm long. Every other rung is 5 cm longer than the rung immediately above it. The shortest distance between the topmost and the bottommost rung is 36 cm and the shortest distance between each rung is 3 cm. Find the sum of the lengths of all the rungs of the ladder.

(A)

(B)

(C)

(D)

Ans: B

Solution:

The correct choice is (B) . Let the rungs be named from the top to bottom and , , and so on. The distance between and each rung is apart. Hence, a total of rungs can be placed after the first rung. Therefore number of rungs .

The lengths of the rungs increase in an arithmetic progression. since) each rung is 5cm longer than the previous rung) .

Hence the rungs are of lengths .

Total length of all rungs

Hence option B

__Questions 10 to 12__:

__Answer these questions after going through the information given below__:

More, Fresh and Star Bazar are three super-markets that cater to the grocery requirements of people living in Powai, a locality in Mumbai. The number of people who do not purchase their groceries from any of the three super markets is equal to three-fourths of the number of people who purchase their groceries from More alone which in turn is double the number of people who purchase their groceries from Fresh and Star Bazar but not More. The number of people who purchase their groceries from both More and Star Bazar is three-and-a-half times the number of people who purchase their groceries from Fresh alone. The number of people who purchase their groceries from Star Bazar alone is a quarter more than the number of people who make their purchases from More and Fresh but not Star Bazar. The number of people who purchase from all three super markets is 50 percent more than the number of people who make their purchase from Fresh alone.

Q: 10. If the total number of people in the locality is , then what is the number of people who purchase from More but not from all three super markets?

(A)

(B)

(C)

(D) Cannot be determined

Ans: A

Solution:

The correct choice is (A) .

The number of people who do not purchase their groceries from any of the three super markets is equal to three-fourths of the number of people who purchase their groceries from MORE alone which in turn is double the number of people who purchase their groceries from FRESH and STAR BAZAR but not MORE.

Let h

The number of people who purchase their groceries from both MORE and STAR BAZAR is three-and-a-half times the number of people who purchase their groceries from FRESH alone.

The number of people who purchase their groceries from STAR BAZAR alone is a quarter more than the number of people who make their purchases from MORE and FRESH but not STAR BAZAR.

The number people who purchase from all three super markets is percent more than the number of people who make their purchase from FRESH alone.

Since .

The total number of people in the locality

Number of people who purchased from MORE but not all three super markets

Q: 11. The total number of people in the locality is and the number of people who purchase from More is more than the number of people who purchase from Fresh. Find the number of people who purchase from Star Bazar alone

(A)

(B)

(C)

(D)

Ans:

Solution:

The correct choice is (D) .

The number of people who do not purchase their groceries from any of the three super markets is equal to three-fourths of the number of people who purchase their groceries from MORE alone which in turn is double the number of people who purchase their groceries from FRESH and STAR BAZAR but not MORE.

Let

The number of people who purchase their groceries from both MORE and STAR BAZAR is three-and-a-half times the number of people who purchase their groceries from FRESH alone.

Let

The number of people who purchase their groceries from STAR BAZAR alone is a quarter more than the number of people who make their purchases from MORE and FRESH but not STAR BAZAR.

Let

The number people who purchase from all three super markets is percent more than the number of people who make their purchase from FRESH alone.

Since .

The total number of people in the locality Eqn (1)

The number of people who purchase from MORE is more than the number of people who purchase from FRESH.

Multiplying the above equation by Eqn (2)

Subtracting Eqn (2) from Eqn (1)

Q: 12. The number of people who purchase from none of the three super markets is twice the number of people who purchase from Star Bazar only while the number of people who purchase from Star Bazar only is one third the number of people who make their purchases from all the three super markets. If the number of people who make their purchase from both More and Star Bazar is , find the number of people who purchase groceries from at least one of the two super markets Star Bazar and Fresh

(A)

(B)

(C)

(D)

Ans: A

Solution:

The correct choice is (A) .

The number of people who do not purchase their groceries from any of the three super markets is equal to three-fourths of the number of people who purchase their groceries from MORE alone which in turn is double the number of people who purchase their groceries from FRESH and STAR BAZAR but not MORE.

Let

The number of people who purchase their groceries from both MORE and STAR

BAZAR is three-and-a-half times the number of people who purchase their groceries

from FRESH alone.

Let

The number of people who purchase their groceries from STAR BAZAR alone is a quarter more than the number of people who make their purchases from MORE and FRESH but not STAR BAZAR.

Let

The number people who purchase from all three super markets is 50 percent more than the number of people who make their purchase from FRESH alone.

Since .

The number of people who purchase from none of the three super markets is twice the number of people who purchase from STAR BAZAR only while the number of people who purchase from STAR BAZAR only is one third the number of people who make their purchases from all the three super markets.

and

Hence the . Let

Number of people purchasing from both MORE and STAR BAZAR 0

Hence .

The number of people who purchase groceries from at least one of the two super markets STAR BAZAR and FRESH