# CAT Model Paper 6 Questions and Answers with Explanation Part 3

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Q: 13. If and then between

(A) 2 and 4

(B) 3 and 5

(C) 4 and 6

(D) 5 and 7

Ans:

Solution:

The correct choice is (D). On solving for x, y, z we get x would lie between 5 and 7.

Q: 14. If and and are real numbers, then which of the following statements is true?

(A)

(B)

(C)

(D)

Ans: A

Solution:

The correct choice is (A).

Rewriting the above equation, Eqn.(1)

Using component do – dividend rule

Eqn (1) can be written as,

Hence

Since

Hence Option A

Q: 15. How many integers that are greater than but less than can be formed using the digits ?

(A)

(B)

(C)

(D)

Ans: B

Solution:

The correct choice is (B). 3 digit

4 digit numbers =

Thousands digit must be 4. Hundreds digit can be chosen in 6 ways, tens digit in 6 ways and units digit in 6 ways. Total numbers possible

.

Hence option B

Q: 16. If

(A)

(B)

(C)

(D)

Ans: B

Solution:

The correct choice is 362916.

Q: 17. Raghu sells an item at profit to Devansh who sells it to Girish for 250. Girish sells it to Pranav for a loss who sells it to Raghu at a 20% profit. Assume that there is no deprecation of the article from the time Raghu sold it to the time Raghu bought it. If Raghu made a profit of 50 on the transaction, what is the cost price of Raghu when he bought the item for the first time and the percentage profit or loss made by Devansh?

(A)

(B)

(C)

(D)

Ans: B

Solution:

The correct choice is (B). Girish sold to Pranav for who sold it to Raghu for

So initially Raghu must have bought the item for x. He sold it for .

As Raghu made profit of

Devansh got it for 290 but sold it for loss

Q: 18. Taman can do a piece of work in 10 days. After the 1^{st} day, he fell sick and his efficiency decreased by so he hired Viru to help him. Viru has half the normal efficiency of Taman. After four more days, Viru too felt sick and his efficiency decreased by What is the total number of days in which the work will be completed?

(A) days

(B) days

(C) days

(D) None of these

Ans: A

Solution:

The correct choice is (A). Work done on day

Work done on day

Work done on day

Work done on 4^{th} day

Work done on 5^{th} day

Work done in first 5 days

Work done on 6^{th} day

Work done on7th day

Work done on 8^{th} day

In 8 days, work done

Total work will be done in days

Q: 19. Find the remainder when is divided by 82

(A)

(B)

(C)

(D)

Ans: C

Solution:

The correct choice is (C).

The above gives a remainder of 2. Hence, the actual remainder is 4