# Official Quant Thread for CAT 2021

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This is the Official CAT 2021 Quantitative preparation group. Solve questions & discuss answers/solutions shortcuts & tips with other CAT aspirants.

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CAT 2019 (70%) : CAT 2020 (90%) : CAT 2021 (PREP)
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Three friends A, B and C play a game in a pub. The rules are simple. Whenever there is a contest between any two of them, the one who has a higher percentage alcohol should pour 200 ml of his wine into the one having lower percentage alcohol. The game starts as a contest between A and B, then B and C and then C and A. Post this, the game continues in the same cycle on and on. If a player has emptied all his alcohol, then the remaining two play the game with the same rules. If two players have the alcohol of the same percentage level, the younger one pours 200 ml of his alcohol into the elder one’s glass. All three of them start the game with 600 ml of wine. A’s wine has 60% alcohol, B’s has 48% alcohol and C’s has 50% alcohol. They take 3 minutes to play one round of this game. D, a fourth friend leaves the pub immediately after the game begins, returns after an hour and drinks wine from the person who has the highest alcohol percentage. What is the concentration of the alcohol that D had?

A)51.5%

B)52.67%

C)53%

D)Cannot be determined

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A merchant decides to sell off 100 articles a week at a selling price of Rs. 150 each. For each 4% rise in the selling price he sells 3 less articles a week. If the selling price of each article is Rs x, then which of the below expression represents the number of articles sold by the merchant in that week?

1. 175 - x2x2
2. x3x3 + 156
3. 350 - x22x22
4. x2 - 2x + 75
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Ramesh takes 6.5 hours to go from city A to city B at 3 different speeds 30 kmph, 45 kmph, and 60 kmph covering the same distance with each speed. The respective mileages per liter of fuel are 11 km, 14 km and 18 km for the above speeds. Ramesh's friend Arun is an efficient driver and wants to minimise his friend's car's fuel consumption. So he decides to drive Ramesh's car one day from city A to city B. How much fuel will he be able to save?

A)4.2 liters

B)4.5 liters

C)0.7 liters

D)0.3 liters

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Anyone know how to solve question no. 4 ?

@CAT_Ayan  ·  38 karma
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@IIMC_PK  ·  1 karma

@Soundaryas Observe options carefully.

P cannot be equal to Q

and then use trail and error method

Let's assume P=2 and Q=1, then only option B satisfies .

You can take P=1 and Q=2 also

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@Charitarth  ·  1 karma

@FMSDB Option b?

@FMSDB  ·  4 karma

@Charitarth Nope brother

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@FMSDB  ·  4 karma
@Charitarth  ·  1 karma

640 Km? you should apply the concept of "Infinite GP". you can calculate distance travelled by the sparrow from H to B, B to H, H to B and B to H. you will observe two infinite GP series. use the formula and calculate the distance. I am not sure if there is any shortcut to solve this question, You can explore alternate method if interested. Do share if you find any.

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Traffic NH4, Chennai Bangalore highway moves at a constant speed of 90kms per hour in both directions.A Bangalore bound driver passes 20 Chennai bound vehicle in a 2 minute interval.assume that the vehicle on the Chennai bound lane are equally spaced.which of the following options is closest to the number of Chennai bound vehicle in a 90km stretch of the highway?

@Dwightschrute  ·  567 karma

@FMSDB I still feel it should be 300. What does the solution say?

@FMSDB  ·  4 karma

@Dwightschrute Sorry, It is 300

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Raju is a driver who has to transport 4500 products from Pali to Girdwala, Rajasthan. The distance between them is 1500 km. The truck can carry a maximum of 1200 products in each trip. He is short of cash and hence for every 1 km he travels towards Girdwala, 1 product is taken by the tax officer. However, if Raju is returning from Girdwala to Pali, he does not have to pay any taxes. How many maximum number of products can Raju deliver from Pali to Girdwala?