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CAT Practice Test: Month (February) - CAT MCQ


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30 Questions MCQ Test Daily Test for CAT Preparation - CAT Practice Test: Month (February)

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CAT Practice Test: Month (February) - Question 1
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Find the principal if the interest compounded at the rate of 10% per annum for two years is ₹ 420.

Detailed Solution for CAT Practice Test: Month (February) - Question 1

Solve using options. Thinking about option (a): 2000 → 2200 (after 1 year) → 2420 (after 2 years) which gives us an interest of ₹420 as required in the problem. Hence, this is the correct answer.

CAT Practice Test: Month (February) - Question 2
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What is the difference between compound interest and simple interest for the sum of ₹ 20,000 over a 2 year period if the compound interest is calculated at 20% and simple interest is calculated at 23%?

Detailed Solution for CAT Practice Test: Month (February) - Question 2

Simple interest @ 23% = 4600 x 2 = 9200 Compound interest @ 20% 

→ ₹ 8800 compound interest. Difference = 9200 – 8800 = ₹ 400. 

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CAT Practice Test: Month (February) - Question 3
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The SBI lent ₹ 1331 to the Tata group at a compound interest and got ₹ 1728 after three years. What is the rate of interest charged if the interest is compounded annually?

Detailed Solution for CAT Practice Test: Month (February) - Question 3

1331 x 1.090909 x 1.090909 x 1.090909 = 1331 x 12/11 x 12/11 x 12/11 = 1728. Hence, the rate of compound interest is 9.09%.

CAT Practice Test: Month (February) - Question 4
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A is proportional to B. B is inversely proportional to C. C is proportional to the square of D. D is directly proportional to the cube root of E. Assuming positive integers, if A increases then E
Detailed Solution for CAT Practice Test: Month (February) - Question 4

Given,
A ∝ B
B ∝ (1/C)
C ∝ D2
D ∝ ∛E
When A increases ⇒ B also increases ⇒ C decreases
Decrease in C results in decrease in D and decrease in D results decrease in E.

CAT Practice Test: Month (February) - Question 5
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After how many years will a sum of ₹ 12,500 become ₹ 17,500 at the rate of 10% per annum?
Detailed Solution for CAT Practice Test: Month (February) - Question 5

12500 @ 10% simple interest would give an interest of ₹ 1250 per annum. For a total interest of ₹ 5000, it would take 4 years.

CAT Practice Test: Month (February) - Question 6
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In what ratio must water be mixed with milk to gain on selling the mixture at cost price?
Detailed Solution for CAT Practice Test: Month (February) - Question 6

Let the C.P. of 1 litre milk be Re. 1. 
S.P. of 1 litre of mixture = Re. 1
Gain = 
C.P. of 1 litre of mixture = (100 x 3/350 x 1) = Rs. 6/7 
So, 6/7 litres of milk is present in 1 litre of mixture. 
Hence, ratio of water to milk = 1/7 : 6/7 = 1 : 6 
Alternate Solution:
To make a profit of 16.67% we need to add 16.67% water.
i.e. we need to add water in milk in the ratio 1 : 6.

CAT Practice Test: Month (February) - Question 7
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A giant watermelon weighs 30 kg, of which 90% is water. After remaining in the sun for one hour, some of the water evaporates such that water makes up 80% of the weight. What is the weight of the watermelon now?  
Detailed Solution for CAT Practice Test: Month (February) - Question 7

Water portion of the watermelon weighs 90% of 30 = 27 kg.
Solid portion of the watermelon weighs 30 - 27 = 3 kg.
When water is 80%, solid portion = 20% 
As 20% = 3 kg; 
Total weight = 3 x 5 = 15 kg

CAT Practice Test: Month (February) - Question 8
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What is the simple interest on a sum of  ₹700 if the rate of interest for the first 3 years is 8% per annum and for the last 2 years is 7.5% per annum?
Detailed Solution for CAT Practice Test: Month (February) - Question 8

8% @ 700 = ₹ 56 per year for 3 years 7.5% @ 700 = ₹ 52.5 per year for 2 years Total interest = 56 x 3 + 52.5 x 2 = 273.

CAT Practice Test: Month (February) - Question 9
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A wholeseller supplies few chips to a retailer every year. Each chip costs Rs 10,000 to the wholeseller. 5% of the chips are defective and they are to be replaced without charging anything extra. If the wholeseller still makes a profit of 20%, at what price is he selling it to retailer?
Detailed Solution for CAT Practice Test: Month (February) - Question 9

Let No. of chips supplied = 100

For whole seller, Net CP = (10000 x 100 + 5 x 10000) = Rs 1050000

CAT Practice Test: Month (February) - Question 10
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A milkman has 48 litres of mixture of milk and water in the ratio 5 : 1, respectively. He withdraws some amount of the mixture from the vessel and replaces it with milk. The ratio of the mixture of milk and water now becomes 7 : 1. What amount of the mixture is withdrawn?
Detailed Solution for CAT Practice Test: Month (February) - Question 10

Capacity = 48 litres
Amount of milk = 5/6 x 48 = 40 litres
Amount of water =1/6 x 48 = 8 litres
Let the amount withdrawn be x.
Thus, 
⇒  x = 12 litres

CAT Practice Test: Month (February) - Question 11
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Two liquids A and B are in the ratio 5 : 1 in container X and in the ratio 1 : 3 in container Y. In what ratio should the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio 1 : 1?  
Detailed Solution for CAT Practice Test: Month (February) - Question 11

Let X units of liquid be taken from container X.
So, liquid A taken = (5/6)X
Liquid B taken = (1/6)X
Let Y units of liquid be taken from container Y.
So, liquid A taken = (Y/4)
Liquid B taken = (3/4)Y
So, as the ratio is 1 : 1, we get
(5/6)X + (Y/4) = (X/6) + (3/4)Y
Or X/Y = 3/4
Hence, the required ratio is 3 : 4.
Thus, option d is correct.

CAT Practice Test: Month (February) - Question 12
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Two horses cost as much as 5 dogs, 6 dogs as much as 8 oxen, 10 oxen as much as 50 sheep, 14 sheep as much as 9 goats. If the price of one goat is Rs 70, how much will one horse cost?
Detailed Solution for CAT Practice Test: Month (February) - Question 12

► Price of one goat = Rs 70 ⇒ Price of 9 goats = 9 x 70 = Rs 630
► Price of 14 sheeps = Rs 630 
⇒ Price of 1 sheep = Rs 630/14 = Rs 45 ⇒ Price of 50 sheep = Rs 45 x 50 = Rs 2250
► Price of 10 oxen = 2250 ⇒ Price of 1 oxen = 225 ⇒ Price of 8 oxen  = 1800
► Price of 6 dogs = 1800 ⇒ Price of 1 dog = 300 ⇒ Price of 5 dog = 1500
► Price of two horses = 1500 ⇒ Price of one horse = 750

CAT Practice Test: Month (February) - Question 13
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The first, second and third class fares between two railway stations, Patna and Lucknow were 10:8:3 and the number of first, second and third class passengers between the two stations was is 3:4:10. If total sales of the ticket is Rs 16,100, find the money obtained by the sales of second class tickets.
Detailed Solution for CAT Practice Test: Month (February) - Question 13

► Let the fare of 1st, 2nd and 3rd class be 10x, 8x, and 3x respectively.
► Let the no. of passengers of 1st, 2nd and 3rd class be 3y, 4y and 10y respectively. 
Then 30xy + 32xy + 30xy = 16100
⇒ 92xy = 16100
Hence xy = 175
Required amount = 32xy = 32 x 175 = 5600 

CAT Practice Test: Month (February) - Question 14
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CP of 40 articles is equal to the SP of 30 articles. What is the profit/loss percentage?
Detailed Solution for CAT Practice Test: Month (February) - Question 14

CP of 1 article = Re 1

CP of 40 articles = Rs 40

SP of 30 articles = Rs 40

CAT Practice Test: Month (February) - Question 15
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In what proportion must wheat at Rs. 1.8 per kg be mixed with wheat at Rs. 2.5 per kg to get a mixture worth Rs. 2.0 per kg?
Detailed Solution for CAT Practice Test: Month (February) - Question 15

Applying the rule of alligation:

⇒ Required ratio = 5 : 2

CAT Practice Test: Month (February) - Question 16
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What is the angle in degrees made by a sector, the ratio of whose area with the area of the semicircle is equal to 1:10?
Detailed Solution for CAT Practice Test: Month (February) - Question 16

Area of semicircle = (1/2)πr2
Area of sector = (θ/360)πr2

CAT Practice Test: Month (February) - Question 17
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A supplier sells 20 pencils at the marked price of 16 pens to a retailer. The retailer, in turn, sells them at the marked price. What is the percentage profit or percentage loss of the retailer?
Detailed Solution for CAT Practice Test: Month (February) - Question 17

CAT Practice Test: Month (February) - Question 18
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Sum of CP’s of two cows is Rs 13,000. Both the cows are sold at a profit of 20% and 40% respectively with their SP’s being the same. What is the difference of CPs of both the cows?
Detailed Solution for CAT Practice Test: Month (February) - Question 18

CAT Practice Test: Month (February) - Question 19
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A shopkeeper sells his goods at its CP only. But he uses 750 grams weight at the place of 1000 gms weight for a kg. What is his net profit percentage?
Detailed Solution for CAT Practice Test: Month (February) - Question 19

CAT Practice Test: Month (February) - Question 20
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The value of a diamond varies directly as the square of its weight. If a diamond worth Rs 10,000 is divided into 2 pieces in the ratio of 4:6, what is the loss in value?
Detailed Solution for CAT Practice Test: Month (February) - Question 20

V ∝ W2, V = KW2
Where, V = Value of diamond, W = weight of diamond and K = constant
⇒ 10000 = K.(10)2
⇒ K = 100
Hence, V = 100 x 42 = 1600
also, V = 100 x 62 = 3600
Net loss = Rs.(10000 - 5200) = Rs 4800 i.e., 48%

CAT Practice Test: Month (February) - Question 21
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After how many years will a sum of ₹ 12,500 become ₹ 17,500 at the rate of 10% per annum?
Detailed Solution for CAT Practice Test: Month (February) - Question 21

12500 @ 10% simple interest would give an interest of ₹ 1250 per annum. For a total interest of ₹ 5000, it would take 4 years.

CAT Practice Test: Month (February) - Question 22
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What is the simple interest on a sum of  ₹700 if the rate of interest for the first 3 years is 8% per annum and for the last 2 years is 7.5% per annum?
Detailed Solution for CAT Practice Test: Month (February) - Question 22

8% @ 700 = ₹ 56 per year for 3 years 7.5% @ 700 = ₹ 52.5 per year for 2 years Total interest = 56 x 3 + 52.5 x 2 = 273.

CAT Practice Test: Month (February) - Question 23
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What is the difference between compound interest and simple interest for the sum of ₹ 20,000 over a 2 year period if the compound interest is calculated at 20% and simple interest is calculated at 23%?
Detailed Solution for CAT Practice Test: Month (February) - Question 23

Simple interest @ 23% = 4600 x 2 = 9200 Compound interest @ 20% 

→ ₹ 8800 compound interest. Difference = 9200 – 8800 = ₹ 400. 

CAT Practice Test: Month (February) - Question 24
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Find the principal if the interest compounded at the rate of 10% per annum for two years is ₹ 420.
Detailed Solution for CAT Practice Test: Month (February) - Question 24

Solve using options. Thinking about option (a): 2000 → 2200 (after 1 year) → 2420 (after 2 years) which gives us an interest of ₹420 as required in the problem. Hence, this is the correct answer.

CAT Practice Test: Month (February) - Question 25
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The SBI lent ₹ 1331 to the Tata group at a compound interest and got ₹ 1728 after three years. What is the rate of interest charged if the interest is compounded annually?
Detailed Solution for CAT Practice Test: Month (February) - Question 25

1331 x 1.090909 x 1.090909 x 1.090909 = 1331 x 12/11 x 12/11 x 12/11 = 1728. Hence, the rate of compound interest is 9.09%.

CAT Practice Test: Month (February) - Question 26
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If the hour-hand and the minute-hand of a clock coincide every 64 minutes, how much does the clock gain or lose everyday?
Detailed Solution for CAT Practice Test: Month (February) - Question 26

55 min spaces are covered in 60 min
60 min. spaces are covered in

Loss in 64 min

Loss in 24 hrs

CAT Practice Test: Month (February) - Question 27
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At what time will the hands of a clock be together between 3 o'clock and 4 o'clock?
Detailed Solution for CAT Practice Test: Month (February) - Question 27

Using direct formula,
where m - minutes and h - hours
Time, between 3 o'clock and 4 o'clock, at which the hands will be together = 
minutes past 3 o'clock

CAT Practice Test: Month (February) - Question 28
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A defective watch which gains uniformly, is 5 minutes slow at 8 o'clock in the morning on Sunday and it is 5 minutes 48 seconds fast at 8 pm on following Sunday. When was it correct?
Detailed Solution for CAT Practice Test: Month (February) - Question 28

Sunday 8 am to next Sunday 8 pm time duration 24 × 7 + 12 = 180 hrs.
In 180 hrs total gain = 10 min 48 s = 648 s
Gain of 5 min = 300 s will be obtained in  

Hence, Sunday 8 am + 83 h 20 min = Wednesday 7 : 20 p.m.

CAT Practice Test: Month (February) - Question 29
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How many times are the hands of a clock at right angles in a day?  
Detailed Solution for CAT Practice Test: Month (February) - Question 29

Hands will be at right angle twice every hour except from 2 to 4 and 8 to 10 where hands will be at right angle only thrice instead of four times.
Thus, hands will be at right angle 22 times in 12 hours or 44 times in 24 hrs.

CAT Practice Test: Month (February) - Question 30
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At what time between 4 and 5 will the hands of a watch point in the opposite directions?
Detailed Solution for CAT Practice Test: Month (February) - Question 30

Hands are pointing in opposite directions. It means hands are 180° apart or they are 30 minutes apart.
Required time = (5x + 30) × 12/11 minutes past x

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