Free DI and LR - 20 Practice Test - CAT 

Question 1

Who among the following will fail to get an admission offer from any of the RECs?

A. Mohit
B. Darshan
C. Atul
D. Neil
E. Rohit

SOLUTION

Solution : A

Only Rohit clears the selection criteria for REC P.

Neil and Mohit fails to clear REC Q's criteria as well but all the students clear REC R's criteria but according to the condition given that this REC R will give admission only to top 3 students Neil managaes to clear the criteria with 2nd rank and thus Mohit fails to get any admission letter.

Question 2

If Anu also joins the list of probable students with scores of 96, 26, 34 and 31 in M, P, C and GK respectively, then how many final admission offers will Anu receive?

A. 0
B. 1
C. 2
D. 3
E. cannot be determined

SOLUTION

Solution : B

OPTION B

Here is the total score of all students:

Neil- 194

Rohit- 189

Mohit- 182

Darshan- 191

Atul- 197

Anu- 187

Anu fails to clear the selection criteria of REC P by failing in chemistry but she clears other two selection criterias.

REC Q gives offer letter to top 3 students and from the scores given it is clear that Neil Mohit and Rohit fails to clear REC Q's criteria and thus ANU gets the call from REC Q.

Also everyone clears REC R's criteria thus the top 3 gets the admission call and hence ANU being on 5th position fails to achieve it.

So answer is B.

Question 3

Out of the following, by how much and in which test Neil can improve his score in order to secure an admission offer from REC P?

A. 1 mark in Physics
B. 4 mark in Chemistry
C. 2 marks in GK
D. any one of a,b,c
E. none of these

SOLUTION

Solution : B

OPTION d

Neil needs 4 marks in chemistry to clear the selection criteria for REC P.

Question 4

On the basis of the weights of the selection tests of the RECs, the average total marks of the five students expressed as a percentage of the maximum possible score is highest for which of the following RECs? 

A. REC P
B. REC Q
C. REC R
D. REC P& Q are equal
E. Data insufficient

SOLUTION

Solution : C

OPTION C

Question 5

At least what percentage of those scoring 75% or above in the J A T will fail to make it to the interview in Ostentia University?

A. 90%
B. 87%
C. 85%
D. 88%
E. 92%

SOLUTION

Solution : A

Ans. (a)

Ostentia’s JAT/GD cut-off figure is (125/60). The last row total of 1075 represents the number who score 75 % of 200 i.e. 150 and above in the JAT. Of these, 109 score 60 and above in GD and therefore qualify for interview if their academics conform to Ostentia. How many among these will actually qualify cannot be established, but (1075 – 109) will fail as they do not clear the GD cut-off. Hence minimum percentage disqualified for interview among those who quality in the JAT = (1075 – 109) * 100/1075 = 90%

Question 6

70 % of those who clear the JAT in the highest marks category (150 and above) in second table, have over 80 % marks in their academic grades and are also in the highest marks category for GD. What percentage of such students will qualify for the interview at Utopia?

A. 26%
B. 10%
C. Not less than 10%
D. 20%
E. Cannot be determined

SOLUTION

Solution : E

Ans. (d)

Since Utopia’s cut-off for JAT/GD is (180/80), we cannot determine the required percentage from the highest marks category data.

Question 7

If 20 % of those in the highest marks category for GD obtain 100 % marks in GD and 10 % of those who are in the highest marks category for the JAT, score 180 and above in JAT, how many will be eligible for the interview in the Utopia University? 

A. 260
B. 107
C. 367
D. 300 
E. Cannot be determined

SOLUTION

Solution : E

Ans. (d)

We do not know if these students met the cut-off for academics grade. Hence, this cannot be determined.

Question 8

The Ostentia University wanted to admit 30 candidates without altering its requirement standards. All candidates who qualified the JAT and GD cut-off requirements for this University, met the required academic cut-off of that University, out of which 90 % secured and accepted admission into Universities another than Ostentia. What percentage of seats went vacant in Ostentia?

A. 5 to 10
B. 20 to 25
C. 26 to 30
D. 10 to 12
E. 31 to 35

SOLUTION

Solution : C

Ans. (c)

First find how many of the 6875 conform to Ostentia requirements of 125/60. By this standard (104 + 109) = 213 qualify. 10 % of these can appear for interview. 10 % of 213 = 21.3 which implies 21 or 22. Equivalent percentage values (30-22)/30*100 = 26% to (30-21)/30*100 = 30%. Hence 26% to 30%.

Question 9

At least what percentage of those scoring 62.5% or above in JAT will fail to make it to the interview at Ambrosia university?

A. 45.2%
B. 25.6%
C. 54.3%
D. 63.5%
E. none of these

SOLUTION

Solution : D

Ans. (d)

Ambrosia’s JAT/GD score cut-off is (125/40). The last two rows of the second table show the number (654+1075= 1729) which represents those who score > 62.5% on 200.

To find the minimum number of people who won’t make it to the interview round, we will eliminate all those who get a score < 40 in the GS round in both the rounds. This amounts to (92+198+100+163+247+298= 1098). Therefore minimum percentage = 1098/1729*100= 63.5%

Question 10

Minu wants to have 2 phones. What would be the number of minutes of usage at which it would be economical for her to buy the second phone, such that the number of minutes she uses on each phone are equal?

A. 1650
B. 1950
C. 2550
D. 2600
E. not possible

SOLUTION

Solution : C

Ans: Extra cost of the other phone = Rs 330. When she buys a second phone she saves 275*0.8 = Rs 220. the overheads are 330-220=Rs 110.

For each minute above 2000, she will save 20 paise. So by using for 550 minutes, Rs 110 will be saved. Thus at 2550 minutes, both costs are equal. Answer is option (c)

Question 11

What would the telephone bill be if the user has used his phone for 6000 minutes? 

A. Rs. 5630
B. Rs 5960
C. Rs 6250
D. Rs 6996
E. Rs 7486

SOLUTION

Solution : B

as;6000 minutes can be calculated as

(1725*0.8)+(3000*1)+(1000*1.25) = Rs 5960. option (b)

Question 12

What is the difference in the telephone bill over 4 months, if the number of minutes for the first period is 4000 and the number of minutes for the second period is 2500?

A. 1668
B. 1500
C. 1800
D. 1750
E. none of these

SOLUTION

Solution : B

as; 4000 minutes can be calculated as (1725*0.8)+(2000) = Rs 3380

2500 minutes can be calculated as (1725*0.8)+(500) = Rs 1880

Difference = 3380-1880 = 1500

Question 13

Anu wants to have a phone booth wherein she charges Rs.1 per minute. At what number of minutes, would she neither make a profit nor have a loss (over a two month period). Handset cost not taken into account?

A. 550
B. 1000
C. 300
D. 750
E. 1256

SOLUTION

Solution : A

as;Going from answer options.

Assuming answer option (a)

Number of minutes = 550. free minutes = 275. total calculated minutes = 275*0.8 = Rs 220

220+330=550 which is the number of minutes at which she would neither make a profit nor have a loss. Answer is option (a)

Question 14

The government has changed and the rates are revised. The fixed rental is raised to Rs 400 for every two months; but the number of free minutes is increased to 300. The slabs of charge remain the same. What would be the increase or decrease in telephone bill for a user who is talking for 1600 minutes?

A. Rs 50
B. Rs 60
C. Rs 70
D. Rs 80
E. Rs 90

SOLUTION

Solution : A

as;When number of minutes =1600

Old scheme:-

Rental = 330. bill = 1325*0.8 + 330= Rs 1390

New scheme:-

Rental= 400. bill=1300*0.8 + 400 = Rs 1440. Increase = Rs 50. Answer is option (a)

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