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# GATE Numerical Reasoning Aptitude (Analytical) Questions - 1

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GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 1

### 40% of deaths on city roads may be attributed to drunken driving. The number of degree needed to represent this as a slice of a pie chart is

Detailed Solution for GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 1

40% of 360o = (40/100) * 360o =144o
Therefore Number of degrees needed to represent, 40% in a pie chart is 144o

GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 2

### Fatima starts from point P, goes North for 3 km, and then East for 4km to reach point Q. She then turns to face point P and goes 15km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P?

Detailed Solution for GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 2

GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 3

### The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 is

Detailed Solution for GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 3

We have total 900 three digit numbers from 100-999.
We have numbers in which 1 is immediate right to 2 are 210-219, 121, 221, 321, 421, 521, 621, 721, 821, 921.
So we have numbers in which 1 is never immediate right of 2 = 900 - 19 = 881 numbers

GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 4

A person moving through a tuberculosis prone zone has a 50% probability of becoming infected.However, only 30% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease?

Detailed Solution for GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 4

Probability of being infected = 0.5
Probability of developing disease = 0.3
Only when a person develops disease he will show symptoms of it and whenever a disease is developed we can expect symptoms to be shown.
So, Probability of not showing symptoms = 1 − 0.3 = 0.7
Probability of being infected and not showing any symptoms = 0.5 × 0.7 = 0.35
(or)
P(infected) = 0.5,
P(No.of disease / Infected) = 0.7 × 0.5 = 0.35

GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 5

P, Q, R and S are working on a project. Q can finish the task in 25 days, working alone for 12hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave in the beginning for two days. R worked 18 hours a day on all days. What is the ratio of work done by Q and R after 7 days from the start of the project?

Detailed Solution for GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 5

Q's one hour work =
R's one hour work =
Since Q has taken 2 days sick leave, he has worked only 5 days on the end of seventh day.
Work completed by Q on 7th day= (5x12)
Work completed by R on 7th day=(7x18)
Ratio of their work
=

GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 6

If logx (5/7) = -1/3, then the value of x is

Detailed Solution for GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 6

5/7 = x-1/3 ⇒ 7/5 = x1/3

⇒ x = (7/5)3 = 343 / 125

GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 7

A rule states that in order to drink beer one must be over 18 years old. In a bar, there are 4 people. P is 16 years old, Q is 25 years old, R is drinking milkshake and S is drinking beer. What must be checked to ensure that the rule is being followed ?

Detailed Solution for GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 7

In this question the rule states that "in order to drink beer the person must be over 18 years of age". So we will consider the following options according to the rule:
For P it is given that his/her age is 16 years and since he/she is below 18 years of age, they cannot have beer so we have to check P's drink to see if the rule is followed.
For Q it is given that his/her age is 25 years and the rule states nothing about what anyone above 18 years cannot drink therefore there is no restriction on him/her. We do not need to check his/her drink.
For R it is given that he/she is having a milkshake. Now for milkshake also the rule puts no restriction therefore there is no need to check his/her age.
and finally for S it is given that he/she is having a beer and now since the rule clearly states that if anyone is having beer then he/she must be over 18 years of age therefore we need to check S's age.
So the correct option is Option B) We need to check P's drink and S's age

GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 8

500 students are taking one or more courses out of Chemistry, Physics, and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329). Physics (186).Mathematics (295). Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects?

Detailed Solution for GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 8

Method 1
There are 500 students in total.
Only Chemistry: 329 - ( 217 + 83 ) = 29
Only Mathematics : 295 - ( 217 + 63 ) = 15
Only Physics : 186 - ( 83 + 63 ) = 40
Finally :
500 - ( 29 + 15 + 40 + 83 + 63 + 217 ) = 500 - 447 = 53 students.
Method 2
Total number of students
= n(P) + n(C) + n(M) − n(P∩C) − n(P∩M)− n(C∩M) + n(P∩C∩M)
⇒ 500  =329 + 295 + 186 − 217 − 83 − 63 + x
⇒ x = 53.

GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 9

A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25m intervals in this plot.

Q. Which of the following is the steepest path leaving from P?

Detailed Solution for GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 9

Form the given Locations and contour lines
Path from P to Q = 575 to 500 = 75 m deep
Path from P to R = 575 to 425 = 150 m deep
Path from P to S = 575 to 525 = 25 m deep
Path from P to T = 575 to 525 = 25 m deep
Therefore P to R is the steepest path 62 among all the paths

GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 10

If, the value of abc is _____

Detailed Solution for GATE Numerical Reasoning Aptitude (Analytical) Questions - 1 - Question 10

Given,

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