# CAT Model Paper 7 Questions and Answers with Explanation Part 1

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Q: 1. During the rainy season, the Indian Statistical Institute made the following observations regarding the weather at Kolkata. A total of “Y” days were under observation. The following points were noted:

(a) It rained on 14 days either in the morning or in the evening.

(b) Whenever it rained in the morning, it did not rain in the evening.

(c) It did not rain on 7 mornings.

(d) It did not rain on 9 evenings.

Find the value of y.

(A)

(B)

(C)

(D)

Ans: B

Solution:

The correct choice is (B). Number of days with rain in the morning

Number of days with rain in the evening

Total number of days it rained, morning or evening

Hence,

Q: 2. Ranjit bought a special plan from Airbel Mobile that was newly introduced in the market. It had a combination of talk time and data plan with a rental of per month.

Ranjit bought the plan since it was looking attractive because it offered 2 hours of talk time and 2 GB of data download absolutely free. Ranjit estimated a usage of 6 hours of talk time and 2 GB of data throughout the month. While using the same, he was given to understand some more info on the plan almost at the end of the 1st billing cycle. Beyond two hours, for the 1^{st} minutes, call charges were /minute, beyond that for next minutes, the call charges were 2/minute, and then the call charges were minute for next 5 minutes. For every minutes beyond this, call charges will drop by paisa per minute, till a total of 100 minutes of chargeable talk time, and then there will be a flat rate of 20 paisa per minute. Moreover, for data usage, beyond, each download will be charged at paisa/mb. That is not all; the bill will also include of service tax on the total amount. Ranjit was shocked and confused! He sat back and started calculating his usage. He found out that though his talk time usage is 15 minutes less than his estimate, still, total data usage has exceeded by. If he stops using the service from then on, what will be the bill amount at the end of 1st month of usage? []

(A)

(B)

(C)

(D) None of these

Ans: C

Solution:

Total Talk time mins

Down load.

Time | Cum time | Charge per min | Total Charge (Rs.) |

00.00 | |||

15.00 | |||

20.00 | |||

10.50 | |||

97.50 | |||

25.00 | |||

Extra usage | 192.00 | ||

Rental | 200.00 | ||

Total | 560.00 | ||

Tax | 70.00 | ||

Bill Amount | Rs. 630.00 |

Q: 3. My phone, an Indian mobile company introduced a new model called Bobby Dalaxy in the market, which they sell at profit. They import the body and LCD screen from USA and Japan respectively. The body and LCD form and of the total production cost. Recently, cost of the Japanese Yen increased by and that of the US dollar increased by If due to market conditions the selling price cannot be increased beyond , then what is the maximum gain that can be made by My phone by selling Bobby Dalaxy?

(A)

(B)

(C)

(D)

Ans: C

SOLUTION

Let the prices of body & LCD be before the hike, thus total cost. New prices of body & LCD are respectively. Thus total cost will increase by 20, i.e. it becomes . SP can’t exceed.

Thus maximum gain

Q: 4. Find the units digit of .

(A)

(B)

(C)

(D)

Ans: D

Solution:

Since there is at least one 2 and at least one 5 in the multiplication, the unit’s digit will always be 0.

Q: 5. Sambhu sent his assistant to buy some apples, banana and hot-dogs for his friends. He instructed him to buy a minimum of apples, bananas and 3 hot-dogs. His assistant bought the maximum possible number of apples. How many bananas were purchased by him if a total of was spent and each apple costs 21, each banana, and each hot-dog?

(A)

(B)

(C)

(D) More than one value possible

Ans: C

Solution:

The cost of minimum items instructed is

Hence (where A, B, C are number of apple, banana, hot dogs more than the minimum number mentioned)

To satisfy maximum number of apples, number of hot dogs will be minimum.

If solution with integral values of A and B not possible.

If then, Hence

Then total value of

Q: 6. Mohammad was hired to dig cylindrical holes in the ground of radius 3 cm and height 3 cm but because of some hearing impairment, he misheard the shape of the holes as hemispherical of radius 3 cm and number of holes as instead of . He was supposed to finish the work in 10 days and was entitled to get for the work. While working he realised that he has been working much harder than estimated to finish the work in time. Later on he realises that he had done extra work because of hearing the shape and number of holes wrongly. What is the additional entitlement he should ask for the work done by him?

(A)

(B)

(C)

(D)

Ans: D

Solution:

The work done will here be proportional to the volume of the holes dug

The volume of cylindrical holes will be So,

By mistake he dug 200 hemispherical with the same radius 3 cm. So the volume he dug was

Clearly

So, Mohammad dug more than he was asked to. So he should ask for more entitlement. He was entitled to get initially so he should ask for an additional entitlement of or or

Q: 7. The average weight of a group of “N”men is 64 kg. Three men with weights and 66 kg join the group and two men with weights in between 54 kg and 60 kg individually (both inclusive), leave the group. The average of the group now goes up by 2 kg. What is the average weight of the two men who left the group, if it was given that, the initial number of men in the group was a multiple of 5?

(A)

(B)

(C)

(D) Cannot be determined

Ans: A

Solution:

Let the weights of the 2 men who left be x and y kg respectively.

Hence, the equation is as follows:

Solving, we get, .

Now, given N is a multiple of 5 and the average age of the two men who left must be , only one value of N i.e. satisfies the given equation. Hence,

Q: 8. Mother Annette leaves a certain number of candies in a bag to be distributed in a n slum. At night four kids named Abdul, Brij, Chandan and Danish steal some candies in the following way. Abdul enters first and divides the candies into seven equal parts and is left with one extra candy. He takes one part and the extra candy. Brij enters next and in turn divides the remaining candies into seven equal parts and is left with one extra candy. He also takes one part and the extra candy. Same actions are repeated by Chandan and Danish. If the initial number of candies is between and , what is the number of candies Mother Annette had left in the bag?

(A)

(B)

(C)

(D)

Ans: D

Solution:

Let us assume that initially the number of candies available were N0 which was divided into 7 equal parts each of which is denoted by N1. So,

(1)

Now Abdul takes candies and leaves. Let’s assume the rest were divided into equal parts each of which is denoted by. So,

(2)

Similarly, . . . (3)

and, . (4)

Clearly from equation (4),

Putting the value of in equation (3),

Similarly,

For