# Model Test Paper - 27

Question 1: The ratio between the present ages of A and B is 8 : 9. If B is 5 years old than A, what will be the ratio of the ages of A and B after 5 years.

Options
(a) 1 : 3
(b) 2 : 3
(c) 9 : 10
(d) 10 : 13

Answer: Let A's age and B's age be 8x year and 9x year respectively

then, 9x - 8x = 5 ⇔ x = 5.

So, Required ratio = (8x + 5) : (9x + 5) ⇒ 45 : 50 ⇒ 9 : 10

Question 2: Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:

Options
(a) 36
(b) 48
(c) 45
(d) 49

Answer: Relative speed = (60+ 90) km/hr

$\left (150\times\frac{5}{18}\right )m/sec=\left (\frac{125}{3}\right )m/sec$

Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.

Required time =$\left (2000\times\frac{3}{125}\right )m/sec=48 \, \,sec$

Question 3: An express train runs an average speed 100 kmph stopping 3 minutes after 75 km. A local train runs at a speed of 50 kmph, stopping for 1 minute after every 25 km. If the train began running at the same time, how many kilometers did the local train run in the time it took the express train to run 600 km?

Options
(a) 307.5 km
(b) 900 km
(c) 1200 km
(d) 1000 km

Answer: For express train : time to run 600 km = 6hrs. But this also includes 7 stoppages of 3 minutes each. Hence total time = 6 hrs 21 minutes or (381 minutes)

The local train covers 25 km in every 31 minutes.

$\frac{381}{31} \approx 12.29.....$

This mean train has covered $25 \times 12 km\:(300 km)\:in\:12 \times 31\:minutes\:(372 minutes)$

still 9 minutes are left.

The train covers another $\frac{9}{60} \times 50 km =7.5 km$

Hence total distance travelled = 307.5 km.

Question 4: The average of 3, 8, 9 and x is 6 and the average of 17, 2, 5, x and y is 10. What is the value of y ?

Options
(a) 4
(b) 7
(c) 11
(d) 13

Answer: We have $\frac{3+8+9+x}{4}$ x= 4
Also$\frac{17+2+5+x+y}{5}$ y= 11

Question 5: Two dice are rolled, find the probability that the sum is

Options
(a) equal to 1
(b) equal to 4
(c) less than 13
(d) none of these

Answer: The sample space S of two dice is shown below.

S = { (1,1),(1,2),(1,3),(1,4),(1,5),(1,6)

(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)

(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)

(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)

(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)

(6,1),(6,2),(6,3),(6,4),(6,5),(6,6) }

Let E be the event "sum equal to 1". There are no outcomes which correspond to a

sum equal to 1, hence

P(E) = $\frac{n(E)}{ n(S)} =\frac{0}{36}= 0$

Three possible outcomes give a sum equal to 4: E = {(1,3),(2,2),(3,1)}, hence.

P(E) = $\frac{ n(E)}{n(S)} =\frac{3}{36}= \frac{1}{12}$

All possible outcomes, E = S, give a sum less than 13, hence.

P(E) = $\frac{n(E)}{n(S)} =\frac{36}{36}$ = 1

Question 6: Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is

Options
(a) 2:5
(b) 3:5
(c) 4:5
(d) 6:5

Answer: Let the third number be x.

First Number $(\frac{120}{100})\times x = \frac{6x}{5}$

Second Number $(\frac{150}{100})\times x = \frac{3x}{2}$

Ratio = $\frac{6x}{5}:\frac{3x}{2}$

= 4:5

Question 7: Find the H.C.F and L.C.M of 2, 8, 16 and 10.398127

Options
(a) $\frac{3}{82},\frac{80}{3}$
(b) $\frac{5}{86},\frac{82}{3}$
(c) $\frac{7}{89},\frac{80}{2}$
(d) $\frac{2}{80},\frac{80}{5}$

Answer: H.C.F of given fractions =$\frac{HCF 2,8,16,10}{LCM OF 3,9,81,27} =\frac{2}{81}$

LCM of given fractions =$\frac{LCM OF 2,8,16,10}{HCF OF 3,9,8127} =\frac{80}{3}$

Question 8: How many times in a day, are the hands of a clock in straight line but opposite in direction ? (R.R.B.2003)

Options
(a) 10
(b) 22
(c) 33
(d) 47

Answer: The hands of a clock point in opposite directions (in the same straight line)11 times in every 12 hours (Because between 5 and 7 they point in opposite directions at 6 o'clock only). So, in a day, the hands point in the opposite directions 22 times.

Question 9: If the difference between the simple and the compound interest earned on a sum of money at the rate of 5% per annum for 2 yr is Rs. 21, find the principal.

Options
(a) Rs. 8000
(b) Rs. 8250
(c) Rs. 8400
(d) Cannot be determined
(e) None of these

Answer: Let the principal be Rs. x

$\therefore\, \, \,21=x\left ( \frac{5}{100}\right )^{2}$

$\Rightarrow x = \frac{21 \times100 \times100}{5 \times5} = Rs. 8400$

Question 10: List price of an audio cassette is Rs. 80. A dealer sells 4 audio cassettes for Rs. 272 after allowing discount a certain rate. The discount allowed is

Options
(a) 22.5%
(b) 15%
(c) 7.5%
(d) 12.5%

Answer: MP = $80 \times 4 = Rs. 320$

D% = $\frac{320-272}{320} \times 100\%=15\%$

Question 11: The persons who are (1)/ suffering from diabetes are (2)/advised to substitute(3)/ saccharine by sugar. (4)/ No error(5).

Options
(a) The persons who are
(b) suffering from diabetes are
(d) saccharine by sugar.
(e) No error

Answer: Change 'by' to 'for' .

Question 12: According to corporate circles data is pushing through the merger to create financially ________ company in the processed foods business, the group's thrust area for the 1990's

Options
(a) powerful
(b) straight
(d) acceptable

Question 13: Find the correctly spelt words.

Options
(a) Velnerable
(b) Vulnarable
(c) Vulnerable
(d) Valnerable

Question 14: P: We must read
P : if we want to absorb the fruits of great literature
Q : but with concentration
R : them not as we do cricket stories
S : undefined
The Proper sequence should be:

Options
(a) PSQR
(b) PRQS
(c) QPSR
(d) PRSQ

Question 15: Because of his mastery in this field, his suggestions are wide accepted.

Options
(a) are prepared
(b) have prepared
(c) are preparing
(e) No correction required

Question 16: No sooner he had returned home then his mother felt happy.

Options
(a) had he returned home when
(b) he had returned home than
(c) did he return home than
(d) No improvement

Answer: did he return home than

Question 17: (solve as per the direction given above)

Options
(a) rules
(b) belongs
(c) grew
(d) elects

Question 18: What needs to be set right is our approach to work. It is a common sight in our country of employees reporting for duty on time and at the same time doing little work. If an assessment is made of time they spent in gossiping, drinking tea, eating "pan" and smoking cigarettes, it will be shocking to know that the time devoted to actual work is negligible. The problem is the standard which the leadership in administration sets for the staff. Forgot the ministers because they mix politics and administration. What do top bureaucrats do? What do the below down officials do? The administration set up remains week mainly because the employees do not have the right example to follow and they are more concerned about being in the good books of the bosses than doing work.

Options
(a) sets a fine example to the employees
(b) is of a reasonably high standard
(c) is composed of idealists
(d) is of a very poor standard

Answer: is of a very poor standard

Question 19: A person not sure of the existence of god

Options
(a) Cynic
(b) Agnostic
(c) Atheist
(d) Theist

Question 20: The doctor advised the patient not to eat rice.

Options
(a) The patient has been advised not to eat rice by the doctor.
(b) The patient was advised by the doctor that he should not eat rice.
(c) The patient was advised by the doctor not to eat rice.
(d) The patient was being advised by the doctor that he should not rice by the doctor.

Answer: The patient was advised by the doctor not to eat rice.

Question 21: 2, 15, 41, 80, ?

Options
(a) 100
(b) 120
(c) 132
(d) 150

Answer: Given solution is + 13, + 26, + 39, .....

So, missing term = 80 + 52 = 132.

Question 22: Itinerary

Options
(a) travel
(b) route
(c) guidebook
(d) map

Answer: An itinerary is a proposed route of a journey. A map (choice a) is not necessary to have a planned route. Travel (choice c) is usually the outcome of an itinerary, but not always. A guidebook (choice d) may be used to plan the journey but is not essential.

Question 23: Statements: All young scientists are open-minded. No open-minded men are superstitious.
Conclusions:
1. No scientist is superstitious.
2. No young people are superstitious.

Options
(a) Only conclusion 1 follows
(b) Only conclusion 2 follows
(c) Either 1 or 2 follows
(d) Neither 1 nor 2 follows
(e) Both 1 and 2 follow

Answer: The subject in both the conclusions is vague. The true conclusion is 'No young scientist is superstitious'. Thus, neither 1 nor 2 follows,

Question 24: During the past year, Josh saw more movies than Stephen. Stephen saw fewer movies than Darren. Darren saw more movies than Josh.
If the first two statements are true, the third statement is

Options
(a) True
(b) False
(c) Uncertain
(d) None of these

Answer: Because the first two sentences are true, both Josh and Darren saw more movies than Stephen. However, it is uncertain as to whether Darren saw more movies than Josh.

Question 25: Statement: Like a mad man, I decided to follow him.
Assumptions:
1. I am not a mad man.
2. I am a mad man.

Options
(a) Only assumption 1 is implicit
(b) Only assumption 2 is implicit
(c) Either 1 or 2 is implicit
(d) Neither I nor II is implicit
(e) Both 1 and 2 are implicit

Answer: The words 'Like a mad man' show that either a person is really mad or he is not mad but acted like mad. So, either 1 or 2 is implicit.

Question 26: Statement: Many medical and engineering graduates are taking up jobs in administrative services and in banks.
Courses of Action:
1. All the professionals should be advised to refrain from taking up such jobs.
2. The government should appoint a committee to find out the reasons for these professionals taking up such jobs and to suggest remedial measures.

Options
(a) Only 1 follows
(b) Only 2 follows
(c) Either 1 or 2 follows
(d) Neither 1 nor 2 follows
(e) Both 1 and 2 follow

Answer: Following course 1 would be an infringement of the right to freedom of individuals. However, if the lacking of their respective fields are found out and removed, the professionals would surely give up the idea of opting for other jobs. Hence, only course 2 follows.

Question 27: All beggars are poor.

Options
(a) If A is a beggar, then A is not rich.
(b) If A is not rich, then A is not a beggar.
(c) All those who are poor are beggars.
(d) If A is rich, then A is not a beggar.

Answer: If A is rich, then A is not a beggar.

Question 28: A Tiebreaker is an additional contest or period of play designed to establish a winner among tied contestants. Which situation below is the best example of a Tiebreaker?

Options
(a) At halftime, the score is tied at 28
(b) The referee tosses a coin to decide which team will have possession of the ball first.
(c) The Sharks and the Bears each finished with 14 points, and they are now battling it out in a five-minute overtime.
(d) Mary and Megan have each scored three goals in the game.

Answer: This is the only choice that indicates that an additional period of play is taking place to determine the winner of a game that ended in a tie.

Question 29: If ROBUST is coded as QNATRS in a certain language, which word would be coded as ZXCMP?

Options
(a) YYBNO
(b) AWDLQ
(c) AYDNQ
(d) none of these

Answer: Each letter of the word is one step ahead of the corresponding letter of the code.

Question 30: Authoritative behavior involves setting clear boundaries appropriate for the child's age and development, which the children are expected to follow. It is when the parents are in total control, and the children are expected to obey without question. Children from authoritarian parents can become aggressive and rebellious, and they often have problems with self-esteem. In uninvolved parenting, the parents are permissive and do not have any boundaries or rules because they do not have much interest in their children's lives. There is no real discipline because the parents do not care .The parents may be emotionally detached from their children.

The passage best supports the statement that:

Options
(a) The effect of visual media on the social behavior of children
(b) The Effect of Parent Behavior on Children's Discipline.
(c) Emotional Attachment of Parents with their Job not with Children.
(d) Challenges of Effective Discipline in the Parents.

Answer: The Effect of Parent Behavior on Children's Discipline.

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