Hello CAT 2022 Aspirants!
Here is the question for today, please solve it and let us know your approach. Don’t forget to post your answer in the comments section
A computer is sold either for Rs.19200 cash or for Rs.4800 cash down payment together with five equal monthly instalments. If the rate of interest charged is 12% per annum, then the amount of each instalment (nearest to rupee) is:
A. Rs.2880
B. Rs.2965
C. Rs.2896
D. Rs.2990
Please do add your answers in the comment section. Answers would be provided to you soon.
CATKing Team
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Hello Aspirants!
Here is the question for today, please solve it and let us know your approach and answer in the comments section.
Suppose, C1, C2, C3, C4, and C5 are five companies. The profits made by C1, C2, and C3 are in the ratio 9 : 10 : 8 while the profits made by C2, C4, and C5 are in the ratio 18 : 19 : 20. If C5 has made a profit of Rs 19 crore more than C1, then the total profit (in Rs) made by all five companies is:
- A. 438 Crore
- B. 435 Crore
- C. 348 Crore
- D. 345 Crore
Hopefully you are enjoying the process of learning
Regards
CATKing Team
Dear Aspirants!
Answer is option B
If ₹ 4800 cash down payment is made, remaining amount = ₹ 19, 200 - 4800 = ₹ 14,400
Debt amount = Rs. 14,400 + SI on 14,400 for 5 months at the rate of 12% per annum = 14,400 + 720 = Rs. 15,120
Let’s say the amount of each instalment is Rs. x.
Now, debt = 5x + SI on Rs. x for (1+2+3+4) months at the rate of 12% per annum
Or, 15120 = 5x + SI on Rs x for 10 months ⇒ 15120 = 5x + (12 * x * 10 / 100 * 12) ⇒ 15120 = 5x + x/10 ⇒ x = 151200/51 ⇒ x ~ 2965
Hoping you are enjoying the process of learning.
Regards
CATKing Team
Hello Aspirants!
Here is the question for today, please solve it and let us know your approach and answer in the comments section.
x, y, z are integer that are side of an obtuse-angled triangle. If xy = 4, find z.
- A.2
- B.3
- C.1
- D. More than one possible value of z exists
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Regards
CATKing Team
Dear Aspirants!
Answer is option B
Checking out the possibilities of the third side will give the answer.
xy = 4
xy could be 2 *2 or 4 * 1
221
222 These are the possible triangles.
223
441
22x will be a triangle if x is 1, 2 or 3 (trial and error).
44x is a triangle only if x is 1.
- 221 is acute. 12 + 22 > 22
- 222 is equilateral. So acute.
- 223 is obtuse. 22 + 22 < 32
- 144 is acute. 12 + 42 > 42
The question is " x, y, z are integer that are side of an obtuse-angled triangle. If xy = 4, find z."
And so, the third side has to be 3
Hence, the answer is 3.
Hoping you are enjoying the process of learning.
Regards
CATKing Team
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Hello Aspirants!
Here is the question for today, please solve it and let us know your approach and answer in the comments section.
Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is
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Regards
CATKing Team
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Dear Aspirants!
Answer is option B
Given that ABCDEF be a regular hexagon with each side of length of 1 cm.
We have to find the area of a square with AC as one side.
ABO is the equilateral triangle with each side having length of 1 cm and ABCO is the rhombus.
Altitude of an equilateral triangle = √32 a
So AP = √32 × 1
Where AP = PC
⟹ AC = AP + PC
⟹ AC = √32 × 2
⟹ AC = √3
Area of a square = a2 sq.units
Area of the square with AC as one side = √3 × √3 = 3 sq.units
The question is “Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is”
Hence, the answer is 3
Hoping you are enjoying the process of learning.
Regards
CATKing Team
Hello Aspirants!
Here is the question for today, please solve it and let us know your approach and answer in the comments section.
The local office of the APP-CAB company evaluates the performance of five cab drivers, Arun, Barun, Chandan, Damodaran, and Eman for their monthly payment based on ratings in five different parameters (P1 to P5) as given below:
P1: timely arrival
P2: behaviour
P3: comfortable ride
P4: driver’s familiarity with the route
P5: value for money
Based on feedback from the customers, the office assigns a rating from 1 to 5 in each of these parameters. Each rating is an integer from a low value of 1 to a high value of 5. The final rating of a driver is the average of his ratings in these five parameters. The monthly payment of the drivers has two parts – a fixed payment and final rating-based bonus.
If a driver gets a rating of 1 in any of the parameters, he is not eligible to get bonus. To be eligible for bonus a driver also needs to get a rating of five in at least one of the parameters. The partial information related to the ratings of the drivers in different parameters and the monthly payment structure (in rupees) is given in the table below:
The following additional facts are known.
- Arun and Barun have got a rating of 5 in exactly one of the parameters. Chandan has got a rating of 5 in exactly two parameters.
- None of drivers has got the same rating in three parameters.
Q1. If Damodaran does not get a bonus, what is the maximum possible value of his final rating?
- A. 3.4
- B. 3.6
- C. 3.8
- D. 3.2
Q2. If Eman gets a bonus, what is the minimum possible value of his final rating?
- A. 3.4
- B. 3.2
- C. 3.0
- D. 2.8
Q3. If all five drivers get bonus, what is the minimum possible value of the monthly payment (in rupees) that a driver gets?
- A. 1600
- B. 1700
- C. 1740
- D. 1750
Q4. If all five drivers get bonus, what is the maximum possible value of the monthly payment (in rupees) that a driver gets?
- A. 1960
- B. 1950
- C. 1900
- D. 2050
Hoping you are enjoying the process of learning.
Regards
CATKing Team
Dear Aspirants!
Answer for Question 1
Answer - B
If Damodaran does not get a bonus , it means he must get at least 1 rating in one parameter .
Now he has rating 3 in P2. So in rest 4 parameter he should get rating 1 in one parameter and to maximize his overall rating he must get 5 rating in 2 other parameters and 4 in the rest parameters.
So maximum possible rating = (3+5+5+4+1)/5 = 18/5 = 3.6
Hoping you are enjoying the process of learning.
Regards
CATKing Team
Dear Aspirants!
Answer for Question 2
Answer - C
As Eman has got rating 2 in P5. He gets bonus so he should get at least one 5 rating . Also he shouldn’t get ration 1 in any parameters.
Now as no one gets same rating in three parameters, to minimize Eman’s rating , he should get rating 2 in 2 parameters and rating 3 in other 2 parameters .
Final Rating = (2+2+3+3+5)/5 = 15/5 = 3.0
Hoping you are enjoying the process of learning.
Regards
CATKing Team
Dear Aspirants!
Answer for Question 3
Answer - B
To minimize the monthly payment , we need to minimize the final rating as we did in question 2.
As everyone is getting bonus , so no one will get rating 1 in any parameter.
Also Arun and Barun has got rating 5 in exactly one parameters and Chandan has got rating 5 in exactly two parameters.
Minimum possible final rating of Arun = (5+4+2+2+3)/5 =16/2 = 3.2
Salary of Arun = 1000 + 2503.2 = Rs 1800
Minimum possible final rating of Barun = (5+3+2+2+3)/5 = 15/5 = 3.0
Salary of Barun = 1200+2003.0 = Rs 1800
Minimum possible final rating of Chandan = (5+5+2+2+3)/5 = 17/5 = 3.4
Salary of Chandan = 1400 + 1003.4 = 1740
Minimum possible final rating of Damodaran = (5+3+2+2+3)/5 = 15/5 = 3
Salary of Damodaran = 1300 + 1503 = Rs 1750
Minimum possible final rating of Eman = (5+3+2+2+3)/5 = 15/5 = 3
Salary of Eman =1100 + 200*3 = Rs 1700
So minimum possible salary = 1700
Hoping you are enjoying the process of learning.
Regards
CATKing Team
Dear Aspirants!
Answer for Question 4
Answer - A
This question is similar to previous question , in this question we have to maximize the final rating for maximum possible salary . Taking those points in mind given in point 1 and point 2.
As everyone is getting bonus , so no one will get rating 1 in any parameter.
Also Arun and Barun has got rating 5 in exactly one parameters and Chandan has got rating 5 in exactly two parameters.
Maximum possible final rating of Arun = (5+4+4+3+3)/5 =19/2 = 3.8
Salary of Arun = 1000 + 2503.8 = Rs 1950
Maximum possible final rating of Barun = (5+3+4+4+3)/5 = 19/5 = 3.8
Salary of Barun = 1200+2003.8 = Rs 1960
Maximum possible final rating of Chandan = (5+5+2+4+4)/5 = 20/5 = 4.0
Salary of Chandan = 1400 + 1004.0 = 1800
Maximum possible final rating of Damodaran = (5+3+4+4+5)/5 = 21/5 = 4.2
Salary of Damodaran = 1300 + 1504.2 = Rs 1930
Maximum possible final rating of Eman = (5+2+5+4+4)/5 = 20/5 = 4.0
Salary of Eman =1100 + 200*4 = Rs 1900
So Maximum possible salary = 1960
Hoping you are enjoying the process of learning.
Regards
CATKing Team
Hello Aspirants!
Here is the question for today, please solve it and let us know your approach and answer in the comments section.
The figure below shows the street map for a certain region with the street intersections marked from a through l. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections. For example, a person standing at intersection g can see all people standing at intersections b, c, e, f, h, and k. In particular, the person standing at intersection g can see the person standing at intersection e irrespective of whether there is a person standing at intersection f.
Six people U, V, W, X, Y, and Z, are standing at different intersections. No two people are standing at the same intersection.
The following additional facts are known.
- X, U, and Z are standing at the three corners of a triangle formed by three street segments.
- X can see only U and Z.
- Y can see only U and W.
- U sees V standing in the next intersection behind Z.
- W cannot see V or Z.
- No one among the six is standing at intersection d.
1- Who is standing at intersection a?
2- Who can V see?
- A. U, W and Z only
- B. U and Z only
- C. Z only
- D. U only
3- What is the minimum number of street segments that X must cross to reach Y?
4- Should a new person stand at intersection d, who among the six would she see?
- A. V and X only
- B. U and Z only
- C. U and W only
- D. W and X only
Hoping you are enjoying the process of learning.
Regards
CATKing Team
Dear Aspirants!
Answer for Question 1
Answer - C
X,U,Z are at ends of a triangle so they can be at any of b,c,f,g intersections.
Now X cannot be at g since he sees only 2 people.
UZV have to be in a straight line and x sees only U and z thus
X must be at b, V at e, Z at f, U at g.
Since Y can see W and W cannot see either V or Z thus
Y must be at k and W must be at at l.
– V –
X Z –
– U Y
– – W
Now all questions can be answered.
Hoping you are enjoying the process of learning.
Regards
CATKing Team
Dear Aspirants!
Answer for Question 2
Answer - B
X,U,Z are at ends of a triangle so they can be at any of b,c,f,g intersections.
Now X cannot be at g since he sees only 2 people.
UZV have to be in a straight line and x sees only U and z thus
X must be at b, V at e, Z at f, U at g.
Since Y can see W and W cannot see either V or Z thus
Y must be at k and W must be at at l.
– V –
X Z –
– U Y
– – W
Now all questions can be answered.
Hoping you are enjoying the process of learning.
Regards
CATKing Team
Dear Aspirants!
Answer for Question 3
Answer - B
X,U,Z are at ends of a triangle so they can be at any of b,c,f,g intersections.
Now X cannot be at g since he sees only 2 people.
UZV have to be in a straight line and x sees only U and z thus
X must be at b, V at e, Z at f, U at g.
Since Y can see W and W cannot see either V or Z thus
Y must be at k and W must be at at l.
– V –
X Z –
– U Y
– – W
Now all questions can be answered.
Hoping you are enjoying the process of learning.
Regards
CATKing Team
Dear Aspirants!
Answer for Question 4
Answer - D
X,U,Z are at ends of a triangle so they can be at any of b,c,f,g intersections.
Now X cannot be at g since he sees only 2 people.
UZV have to be in a straight line and x sees only U and z thus
X must be at b, V at e, Z at f, U at g.
Since Y can see W and W cannot see either V or Z thus
Y must be at k and W must be at at l.
– V –
X Z –
– U Y
– – W
Now all questions can be answered.
Hoping you are enjoying the process of learning.
Regards
CATKing Team
Hello Aspirants!
Here is the question for today, please solve it and let us know your approach and answer in the comments section.
The sum of the factors of a number is 124. What is the number?
- A. Number lies between 40 and 50
- B. Number lies between 50 and 60
- C. Number lies between 60 and 80
- D. More than one such number exists
Hopefully you are enjoying the process of learning
Regards
CATKing Team
Answer - D
In some situations, going back would be really difficult.
Any number of the form paqbrc will have (a + 1) (b + 1)(c + 1) factors, where p, q, r are prime. (This is a very important idea)
For any number N of the form paqbrc, the sum of the factors will be (1 + p1 + p2 + p3 + …+ pa) (1 + q1 + q2 + q3 + …+ qb) (1 + r1 + r2 + r3 + …+ rc).
Sum of factors of number N is 124. 124 can be factorized as 22 * 31. It can be written as 4 * 31, or 2 * 62 or 1 * 124.
2 cannot be written as (1 + p1 + p2 + p3 + …+ pa) for any value of p.
4 can be written as (1 + 3)
So, we need to see if 31 can be written in that form.
The interesting bit here is that 31 can be written in two different ways.
31 = (1 + 21 + 22 + 23 + 24)
31 = ( 1 + 5 + 52)
Or, the number N can be 3 * 24 or 3 * 52. Or N can be 48 or 75
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