SRCC GBO 2023

Out of the total Employees enrolled, E, F and G had total share of 8+12+16 = 36%
So the total number of employess enrolled from these three were, $$0.36\times\ 23550$$

Of all the employees who passed the exam, E, F, and G had a total share of 9+15+12 = 36%
So the total number of employees who passed from these three were, $$0.36\times\ 3700$$

Therefore the percentage of employees who passed from E, F and G were $$\frac{0.36\times\ 3700}{0.36\times\ 233550}\times\ 100=15.711\%$$

Number of employees who enrolled from E and C were, 8+10= 18% of 23550
Which is equal to 4,239

Number of employees who passed from D and A were, 16 + 18 = 34% of 3700
Which is equal to 1,258

The difference would be 4239-1258 = 2981
Therefore, Option A would be the correct answer. 

Since the values are given as percentages of the same numbers and we only have to find the highest and not the exact values, we can find the ratio between all of the options and see which is the highest value. 

C: 13% of passed/ 10% of enrolled
F: 15% of passed/ 12% of enrolled 
B: 17% of passed/ 16% of enrolled
E: 9% of passed/ 8% of enrolled

we can take passed/enrolled as constant K since they are same in all of the calculations, this would give us

C: 1.3 K
F: 1.25 K
B: 1.0625 K
E: 1.125 K

As we can see, C has the highest percentage of employees passed to enrolled ratio. 

The number of employees enrolled from A and E together are : 22+8 = 30% of 23550
The number of employees passed from A and G together are: 18+12 = 30% of 3700

The required ratio is $$\frac{23550}{3700}=\frac{471}{74}$$
Therefore, Option D is the correct answer. 

Average list price of the first four years: $$\frac{3+6+8+7}{4}=6$$
Average list price of the last four years: $$\frac{5+9+8+10}{4}=8$$
Increase = 2
percentage increase : $$\frac{2}{6}\times\ 100=\frac{100}{3}$$  {x}

Average net price of the first four years: $$\frac{2000+5000+7000+5000}{4}=\frac{19000}{4}$$
Average net price of the last four years: $$\frac{3000+6000+5000+8000}{4}=\frac{22000}{4}$$
Increase = $$\frac{3000}{4}$$
Percentage increase: $$\frac{3000}{4}\times\ \frac{4}{19000}\times\ 100=\frac{300}{19}$$  {y}

Putting these values in the given term we get:
$$\sqrt{\left(\ 3\times\ \frac{100}{3}\right)+\left(19\times\ \frac{300}{19}\right)}$$
$$\sqrt{\ 400}=20$$

Therefore, Option A is the correct answer. 

The question had an error in the original question paper, where the ratio $$\left(5+\frac{1}{p}+\frac{1}{p^{2}}\right) \frac{75}{131} : 1$$ was given as $$5\left(5+\frac{1}{p}+\frac{1}{p^{2}}\right) \frac{75}{131} : 1$$.

The sum of the product's net prices in 2015, 2016 and 2017 is $$7000+5000+3000=15000$$ million
The products list price in year 2017 is 5 billion, which is equivalent to 5000 million.
The ratio of the sum of net prices to the list price would be 15000:5000 = 3:1

Equating this with the ratio we are given, we get
$$\left(5+\frac{1}{p}+\frac{1}{p^2}\right)\ \frac{75}{131}:1\ =\ 3:1$$
$$\frac{\left(5p^2+p+1\right)}{p^2}\times\ \frac{75}{131}=3$$

131 is a prime number and in order to cancel it out from the denominator, we would require 131 in the numerator as well. 
At this point, we can try putting in the options to see if we can get 131 in the numberator.

putting p=5, we get $$\left(5(5)^2+(5)+1\right)$$ as 131
Using 5 as the value of p, we get:
$$\ \frac{131}{25}\times\ \frac{75}{131}=3$$

Therefore, Option C is the correct answer. 

(A) In 2020, The list price was 8000 Million or 8 Billion, which is more than the total list price in 2013.
Therefore, statement A is correct. 

(B) The highest net price was in year 2020 of 8000 Million or 8 Billion while the lowest list price was in year 2013 of 3 Billion. 
Therefore, statement B is correct. 

(C) Let's take the total market to be of 100 price units. 25 price units were from routers and 15 price units were from switches. After decreasing the router's price by 10% is comes down to 22.5 units and increasing the switches prices by 10% it come sup to 16.5%
The routers are still higher than the switches, therefore, statement C is incorrect. 

The average product net price would be: $$\frac{2000+5000+7000+5000+3000+6000+5000+8000}{8}=5125$$
The average of product prices less than this average price: 
$$\frac{2000+5000+5000+3000+5000}{5}=4000$$

The average product price greater than this average price would be:
$$\frac{7000+6000+8000}{3}=7000$$

The difference between these two averages would be 7000 - 4000 = 3000 million dollars. 
Hence, Option C is the correct answer. 

After reading the chart, we can get the data:

School   Total    Passed  Distinction  Without distinction     
A            800      640          300              340
B           1050     840          350              490
C           1200     920          450              470
D            750      600          260              340
E            900      750          330              420
F           1500     1000         450              550

Finding the percentage of students who passed without distinction to the total number of students who appeared we get:
A = $$\frac{340}{800}\times\ 100=42.5\%$$
B = $$\frac{490}{1050}\times\ 100=46.67\%$$
C = $$\frac{470}{1200}\times\ 100=39.1667\%$$
D = $$\frac{340}{750}\times\ 100=45.33\%$$
E = $$\frac{420}{900}\times\ 100=46.667\%$$
F = $$\frac{550}{1500}\times\ 100=36.67\%$$

We can see that B and E have the same percentage which aligns with option B. 
Therefore, Option B will be the correct answer. 

For this part, we will also have to calculate the number of students who failed in each school. 
adding that to our previous data table we get:

School    Total     Passed    Distinction     Without distinction    Failed
A              800          640            300                      340                   160
B             1050         840            350                      490                   210
C             1200         920            450                      470                   280
D              750          600            260                      340                   150
E              900          750            330                      420                   150
F             1500        1000           450                       550                   500


Calculating the students who passed with distinction as a percentage of students who failed for the given options we see, 
Option A: $$\frac{470}{280}\times\ 100\approx\ 170\%$$
Option B: $$\frac{420}{150}\times\ 100\approx\ 280\%$$
Option C: $$\frac{490}{210}\times\ 100\approx\ 230\%$$
Option D: $$\frac{550}{500}\times\ 100\approx\ 110\%$$

We can see that Option D or School F has the least percentage in this category. 
Therefore, Option D is the correct answer.