MU-NLPC/Calc-aqua_rat huggingface dataset:
Recently, I decided to walk down an escalator of a tube station. I did some quick calculation in my mind. I found that if I walk down twenty " six steps, I require thirty seconds to reach the bottom. However, if I am able to step down thirty " four stairs, I would only require eighteen seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time I step off the last step at the bottom?	Choose the correct choice from the following
A) 43  B) 44  C) 45  D) 40  E) 46

Solution: 26 steps 30 seconds and for 34 steps only 18 seconds left to reach botto.   Means he covered 8 steps (i.e.34-26) in 12 (i.e 30-18)seconds   The spped of the boy is 8 steps in 12 seconds   after further simplyfy..2 steps in 3 seconds   After 34 steps only 18 seconds, means 12 more steps are left   Total Steps are 34+12= 
34+12 = 46
46   ANSW46R:46
Answer: E
A person bought 114 glass bowls at a rate of Rs. 13 per bowl. He sold 108 of them at Rs. 17 and the remaining broke. What is the percentage gain for A?
Choose the correct choice from the following answers:
A) 40  B) 3000/11  C) 5900/247  D) 2790/11  E) 2709/8

Solution: 5900/247P=114*13= 
114*13 = 1_482
1482 and SP=108*17= 
108*17 = 1_836
1836   Gain %= 100*(1836-1482)/1482= 5900/247   ANSWER:5900/247
Answer: C
A man can hit the target once in four shots. If he fires four shots in succession, what is the probability that he will hit the target?
Choose the correct choice from the following: A) 1 B) 1/256 C) 81/256 D) 175/256 E) 185/256

Solution: In four shots he can hit once,twice,thrice,all hit   the probability of hitting the target isp(1hit out of 4)+P(2hit out of 4)+p(3hit out of 4)+p(All hit)   it is total probability-probability of not hitting yhr target   =>1-(3/4*3/4*3/4*3/4)   =>175/256   ANSWER:175/256
Answer: D
When x is multiplied by 3, the result is 18 more than the result of subtracting x from 26. What is the value of x?  Pick:
A) -4
B) -2
C) 11
D) 13
E) 22

Solution: The equation that can be formed is:   3x-18=26-x   or, 4x=44   or, x=11.   11 answer.
Answer: C
Among a group of 2,500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from the 2,500 people, what is the probability that the person selected will be one who invests in municipal bonds but NOT in oil stocks?	Choose the correct choice from the following.
A) 9/50
B) 7/25
C) 7/20
D) 21/50
E) 27/50

Solution: Among a group of 2,500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks.   As per the attached venn diagram, we have to find the number of people in shaded portion.   =35%-7%=28%   Thus, probability 35 -7= 
35 -7 = 28
28%   Thus, probability= 0.28 = 7/25   (2,500 people, 18 percent invest in oil stocks is not required.)   Answer is (7/25)
Answer: B
If x and y are different integers and x^2 = xy, which of the following must be true ?
I. x = 2
II. y = 0
III. x = 0	Pick one:
A) I only  B) II only  C) III only  D) I and III only  E) I, II, and III

Solution: Answer choice A is correct.   The question gives you x^2=xy   you can simplify that as x^2-xy=0   x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer.   Answer III only
Answer: C
Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. if he sells the scooter for Rs. 5800, his gain percent is :  Choose the correct choice from the following answers.
A) 4 4/7&	B) 5 5/11%	C) 10%	D) 12%	E) 15%

Solution: Cost price (C.P)= 4700+800= 
4700+800 = 5_500
5500   selling price (S.P)= 5800   Gain = (S.P) - (C.P)=5800-5500= Rs. 300, Gain %= (300/5500*100)%= 5 5/100%   Correct Answer : (5 5/11%)
Answer: B
If Friday occurred on 21th January 2005. What was the day of the week on 21th January 2004?	Choose the correct answer:
A) Sunday B) Wednesday C) Friday D) Monday E) Tuesday

Solution: There are 2 odd days in the year 2004   So, the day on 21th January 2005 will be two days beyond the day on 21th January 2004   On 21th January 2004, it was Wednesday   Answer: Wednesday
Answer: B
The difference between the ages of two persons is 10 years. Fifteen years ago, the elder one was twice as old as the younger one. The present age of the elder person is?
Choose the correct answer
A) 35yr B) 25yr C) 20yr D) 30yr E) 40yr

Solution: Let their ages be x years and (x+10) years   Then, (x+10) - 15 = 2(x-15)   x - 5 = 2x-30   x = 25   Present age of the elder person = 25+10= 
25+10 = 35
35 years   35yrnswer is 35yr
Answer: A
How many triangles can be formed by joining the vertices of an octagon? Choose the correct option.
A) 50  B) 56  C) 23  D) 12  E) 89

Solution: Here n = 8   Hence, the number of triangles that can be formed by joining the vertices of an octagon   =n(n−1)(n−2)/6=8(8−1)(8−2)/6=8.7.6/6=56   Anwer is 56
Answer: B
In the equation m = 36.12n, n and m are integers. If m/n leaves a remainder of r, which of the following must divide into r? Choose the correct choice from the following answers
A) 2 B) 3 C) 4 D) 6 E) 12

Solution: 1) It says it is a equation, so m=36.12n should be 36.12 * n..   2) It says n is an integer, again it means 36.12 * n..   Otherwise n would be just a digit and it would be mentioned..   Although not clearly mentioned that 36.12n is actually 36.12 * n, BUT entire info points towards that..   and that is why I have taken m/n = 36.12
Answer: B
Hector runs a one-product widget shop. Each month, his fixed costs, whether he produces anything or not, amount to x dollars. The marginal cost of producing and selling one widget is a constant y dollars, regardless of the number he produces. He generally can sell widgets for p dollars each. What is the minimum number of widgets he must produce, assuming he sells every widget he produces, to break even (neither make a profit nor incur a loss) in a given month?	Choose one:
A) x/(y - p)  B) x/(p - y)  C) x  D) x/p  E) x/y

Solution: Two ways...   1) let t be the total number, so cost = t*y+x and selling price=t*zp..   No profit no loss....t*y+x=t*p.....T=x/(p-y)...   x/(p - y)
Answer: B
In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by:	Choose the correct choice:	A) 33	B) 25	C) 88	D) 29	E) 10

Solution: A : B = 200 : 169.   A : C = 200 : 182.   \inline \fn_jvn {\color{Black} \frac{C}{B}=\left ( \frac{C}{A}\times \frac{A}{B} \right )=\left ( \frac{182}{200}\times \frac{200}{169} \right )=182:169}   When C covers 182 m, B covers 169 m.   When C covers 350 m, B covers \inline \fn_jvn {\color{Black}\left ( \frac{169}{182}\times 350 \right )m} = 325 m   Therefore, C beats B by   (350 - 325)= 
  (350 - 325) = 25
25 m.   Answer: 25) 25 m
Answer: B
Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:	Choose the correct choice from the following answers:	A) Rs. 169.50	B) Rs. 170	C) Rs. 175.50	D) Rs. 180	E) Rs. 190

Solution: Explanation:   Since first and second varieties are mixed in equal proportions.   So, their average price = Rs. 126 + 135 = Rs. 130.50   2   So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.   x - 153/22.50=1   x - 153 = 22.50   x = 175.50   ANSWER IS Rs. 175.50
Answer: C
Find the largest 4 digit number which isexactly divisible by 88?
Pick
A) 4567	B) 3588	C) 9944	D) 5465	E) 6784

Solution: Largest 4 digit number is 9999   After doing 9999 ÷ 88 we get remainder 55   Hence largest 4 digit number exactly divisible by 88 = 9999 - 55= 
9999 - 55 = 9_944
9944   9944
Answer: C
Angelina walked 180 meters from her home to the grocery at a constant speed. She then walked 240 meters to the gym at double the speed. She spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?
Choices.
A) 2
B) 3
C) 4
D) 6
E) 12

Solution: let the speed be X...   so time taken from home to grocery= 180/x..   the speed to gym = 2x..   so time taken = 240/2= 
240/2 = 120
120/x..   its given 180/x-120/x=40..   60/x=40 => 40x = 60 => x =60/40= 
60/40 = 3/2 = around 1.5
1.5m/secs..   so grocery to gym=2*1.5= 
2*1.5 = 3
3m/s...   Answer : 3
Answer: B
A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the total share of A & B in profit of Rs.12100 after a year?
Choose the correct answer.
A) Rs.6030
B) Rs.4050
C) Rs.6050
D) Rs.7050
E) Rs.6080

Solution: 6300:4200:10500   3:2:5   A'share =3/10 * 12100= 
3/10 * 12100 = 3_630
3630   B's share=2/10*12100= 
2/10*12100 = 2_420
2420   Required total share= 3630 + 2420= 
3630 + 2420 = 6_050
6050   Answer : Rs.6050
Answer: C
One fourth of a solution that was 12% sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?  Choose the correct choice from the following choices:  A) 34%  B) 28%  C) 22%  D) 18%  E) 8.5%

Solution: Instead of using complex calculations and remembering formulae, why dont u directly get to weighted average.   3 parts of 12% + 1 part of x (unknown) % = 4 parts of 16%   => x% = 64%-36% = 28%   ans 28% it is.64 -36= 
64 -36 = 28
28%   ans 28% it is.
Answer: B
Nathan took out a student loan for 1200$ at 10 percent annual interest, compounded annually. If he did not repay any of the loan or interest during the first 3 years, which of the following is the closest to the amount of interest he owed for the 3 years.
Choose the correct choice from the following
A) 360	B) 390	C) 400 dollars	D) 410	E) 420

Solution: A straight Q requiring direct formulae..   when compounded annually the final amount= P(1+ r/100)^n..   here P=1200, r=10 and n=3..   1200(1+ 10/100)^3..   1200*1.1^3=1597.2   interest =1597-1200= 
1597-1200 = 397
397, which is nearly 400 in the choices given   ANSWER:400 dollars
Answer: C
In a race with 30 runners where 5 trophies will be given to the top 9 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?	Choose the correct option
A) 9^5 ways B) 8^9 ways C) 7^8 ways D) 8^7 ways E) 8^6 ways

Solution: 9 people can be prized with 5 distinct prizes in 9^5 ways   9^5 waysNSWER:9^5 ways
Answer: A
Look at this series: 65, 77, 84, __, 91, 98, 65, 105, ... What number should fill the blank?  Choose the correct choice from the following answers
A) 60  B) 70  C) 82  D) 77  E) 65

Solution: 65   65   In this series, 7 is added to the previous number; the number 65 is inserted as every third number.
Answer: E
What will come in place of the x in the following Number series? 1, 2, 4, 7, 12, 19, X	Choose the correct choice from the following answers.
A) 23
B) 30
C) 31
D) 41
E) 29

Solution: There is one series here   (the numbers are being increased by prime numbers 1, 2, 3, 5, 7, 11....)   1 + 1= 
1 + 1 = 2
2   2 + 2= 
2 + 2 = 4
4   4 + 3= 
4 + 3 = 7
7   7 + 5= 
7 + 5 = 12
12   12 + 7= 
12 + 7 = 19
19   Hence 19 + 11= 
19 + 11 = 30
30   The correct choice is 30
Answer: B
If soundharya rows 49 km upstream and 77 km down steam taking 7 hours each, then the speed of the stream	Choose the correct choice from the following:  A) 6 kmph  B) 5 kmph  C) 2 kmph  D) 3 kmph  E) 4 kmph

Solution: Speed upstream = 49/7= 
49/7 = 7
7 kmph   Speed down stream= 77/7= 
77/7 = 11
11kmph   Speed of stream= ½ (11-7) = 2 kmph   ANSWER:2 kmph
Answer: C
In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let M be the average rental price for all apartments in the building. If M is $1,500 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $6,000 higher that M, then what percentage of apartments in the building are two-bedroom apartments?	Pick one:	A) 40%	B) 35%	C) 30%	D) 20%	E) 28%

Solution: Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 1500 : 6000 -----> 1 : 4   Let total number of Apartments be X   No. of 2 Bedroom Apartment = (1 / 5) * X   percentage of apartments in the building are two-bedroom apartments ---->   (1/5) * 100 ---> 20%   Answer : 20%
Answer: D
The sum W of the arithmetic sequence a, a+d, a+2d,..., a+(n-1)d is give by Wn = (n/2)*(2a + n-1)d. What is the sum of the integers 1 to 100 inclusive, with the even integers between 25 and 63 omitted.
Choose the correct choice from the following choices:
A) 4345  B) 4302  C) 4258  D) 4214  E) 4170

Solution: a method to do it under one minutes is to take advantage of the choices given...   lets work on the last digit as we have different units digit in each choice...   total sum of 1 to 100 inclusive will have 0 as the last digit..   this is so because the resultant will be 10*(sum of all single digits)... and since we are multiplying by 10,units digit will be 0...   now for single digit in sum W of even number from 25 to 63..   25 to 65 will have 4 times sum of single digit even int, 4*(2+4+6+8+0)=4*20..   here too the units digit is 0, but 64 has to be excluded from the total..   two ways from here on..   1) we are subtracting 0 from 0   so units digit should be 0, but we have to add 64..   so last/units digit =4..   2)we subtract 64 from sum of even int..   so units digit=80-4=76..   or units digit =6...   so our answer should have units digit as 10-6=4..   only D has 4 as units digit..   ans 4214
Answer: D
o mow a grass field a team of mowers planned to cover 15 hectares a day. After 4 working days they increased the daily productivity by 33×13%33×13%, and finished the work 1 day earlier than it was planned.
A) What is the area of the grass field?
B) How many days did it take to mow the whole field?
C) How many days were scheduled initially for this job?	Choose one
A) 387  B) 39  C) 37  D) 20  E) 28

Solution: Hint: See problem 20 and solve by yourself.   Answer: A) 120 hectares; B) 7 days; C) 8 days.   Answer:20
Answer: D
When p is divided by 9, the remainder is 4. All of the following are possible values of p, except for which of the following?	Choose the correct option
A) 13	B) 31	C) 49	D) 53	E) 67

Solution: If a number is divisible by 9, the sum of its digits must be divisible by 9. --> If a number leaves a remainder 4 when divided by 9 the sum of its digits must be 4.   53   Answer: 53
Answer: D
A cube of side 1.5 meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?  Select
A) 2878	B) 3375	C) 1000	D) 2997	E) 2701

Solution: Along one edge, the number of small cubes that can be cut   = 150/10= 
150/10 = 15
15   Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut= 15 * 15 * 15= 
15 * 15 * 15 = 3_375
3375   Answer: 3375
Answer: B
The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.5 years, The ratio of the number of boys to the number of girls in the class is Choose the correct choice from the following:  A) 1 : 2  B) 2 : 3  C) 9 : 3  D) 6 : 3  E) 2 : 5

Solution: Explanation:   Let the ratio be k : 1. Then,   k * 16.4 + 1 * 15.5 = (k + 1) * 15.8   <=> (16.4 - 15.8) k = (15.8 - 15.5) <=> k = 0.3/0.6 = 1/2.   Required ratio = 1/2 : 1 = 1 : 2.   1 : 2nswer: 1 : 2
Answer: A
Each customer of a networking company subscribes to one of two plans: Plan A or Plan B. Plan A costs $50 per month and Plan B costs $150 per month per customer. If the company’s average revenue per customer per month is $100, then what percent of the company's revenue comes from customers with Plan A? Choose the correct choice from the following choices:  A) 25%  B) 50%  C) 37.5%  D) 56.25%  E) 75%

Solution: We can show this algebraically:   If there are A customers with plan A, and B customers with plan B, then the total revenue is $50A + $150B.   Since the average customer pays $100, we know that   $100 = ($50A + $150B) / (A + B)   $100(A + B) = ($50A + $150B)   $100A + $100B = $50A + $150B   $50A = $50B   A = B.   Since there are Equal times as many $50 clients as $150 clients, for every $150 received from Plan B customers, $50 is received from Plan A customers, and the percent of revenue from customers with Plan A is:   $50/($50 + $150) = $50/$200 = 25%.   The correct answer is choice (25%).
Answer: A
There are 456 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 8 : 11, then how many nurses are there in the hospital?  Choose the correct choice.
A) 264
B) 209
C) 57
D) 171
E) 181

Solution: Given,   The ratio of the doctors to the nurses is 8 : 11   Number of nurses = 11/19 x 456 = 264   264NSWER:264
Answer: A
The true discount on a bill of Rs. 540 is Rs. 90. The Banker’s discount is	Select the correct option.
A) Rs. 60 B) Rs. 108 C) Rs. 110 D) Rs. 112 E) None of these

Solution: Answer B   Solution   P.W. = Rs. (540-90) = Rs. 450.   ∴ S.I on Rs. 450 = Rs. 90   S.I on Rs. 540 = Rs. (90/450x540 ) = Rs. 108.   ∴ B.D. = Rs. 108 Answer Rs. 108
Answer: B
(1/34)+(1/35)+……+(1/64)+(1/65) is including in which of the following ranges?
Choices
A) 1/2~1  B) 1  C) 2  D) 3  E) 4

Solution: Number of terms in the given series = 32.   The lowest term is 1/65 , the largest being 1/34.   Thus, the sum of the given series will be more than   1/65 + 1/65.....1/65 (32 times)   ---> 32*(1/65) = 32/65 and   less than 1/34 + 1/34...... 1/34 (32 times)   ---> 32*(1/34) = 32/34 = 1 (approx)   1/2~1ns 1/2~ 1   1/2~1
Answer: A
The S.I. on a certain sum of money for 2 years at 4% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?
Pick:
A) 5250	B) 1267	C) 5750	D) 2267	E) 5262

Solution: Explanation:   C.I. = [4000 * (1 + 10/100)2 - 4000]   = (4000 * 11/10 * 11/10 - 4000) = Rs. 840.   Sum = (420 * 100)/(3 * 8) = Rs. 5250   5250nswer:5250
Answer: A
The speed of a boat in still water is 90kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?	Choose the most appropriate option.
A) 40, 68 kmph  B) 110, 70 kmph  C) 90, 60 kmph  D) 40, 60 kmph  E) 20, 60 kmph

Solution: Speed downstream = 90 + 20= 
90 + 20 = 110
110 kmph   Speed upstream= 90 - 20= 
90 - 20 = 70
70 kmph   Answer: 110, 70 kmph
Answer: B
If A speaks the truth 80% of the times, B speaks the truth 60% of the times. What is the probability that they tell the truth at the same time Choices
A) 0.49
B) 0.48
C) 0.41
D) 0.482
E) 0.411

Solution: Explanation:   Probability that A speaks truth is 80/100= 
80/100 = 4/5 = around 0.8
0.8   Probability that 0.48 speaks truth is   60/100= 
  60/100 = 3/5 = around 0.6
0.6   Since both A and 0.48 are independent of each other   So probability of A intersection 0.48 is P(A) × P(0.48)=0.8 × 0.6 = 0.48   Answer: 0.48
Answer: B
In the third grade of Windblown School there are 78 students, one third of them failed the math test and 1/6 failed that literature test. At least how many students failed both tests?  Choose the correct choice from the following choices:  A) 0.  B) 6.  C) 8.  D) 10.  E) 12.

Solution: Total = 78   failed in math = 78/3= 
78/3 = 26
26   failed in literature=78/6= 
78/6 = 13
13   the least failed in both can be 0   while max can be 13   0.nswer 0.
Answer: A
If 1535/1038 = a+1/[b+1 /{c+(d+1/e)}]. Find a*b*c*d*e?	Choices:	A) 165/2	B) 175/2	C) 178/3	D) 187 by 2	E) 197/2

Solution: by expanding 1535/1038 make form like a+1/[b+1/{c+(d+ 1/e)}   =1+(497/1038) now a=1   =1+{1/(1038/497)}   =1+{1/(2+42/497)}   =1+{1/(2+1/(497/42)} now b= 2 similarly expand   c=11 d= 1 e=34/8   finally a*b*b*c*d*e   1*2*11*1*34/8   187/2   ANSWER:187 by 2
Answer: D
Which of the following numbers is divisible by 11?
Choose the correct choice from the following.
A) 4424  B) 2232  C) 1522  D) 8524  E) 9515

Solution: 9515. This is the only option with last two digits divisible by 11   Answer:9515
Answer: E
A no. Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that |X|<3?  Choose the most appropriate option.
A) 1/5
B) 2/5
C) 3/7
D) 3/11
E) 2/7

Solution: |X||X| can take 7 values.   To get |X|<2|X|<2 ( i.e., −2<x<+2−2<x   ⇒ P(|X|<2)= Favourable 3/7asesTotal 3/7asesP(|X|<2)= Favourable 3/7asesTotal 3/7ases   = 3/7   3/7
Answer: C
Cecilia, Robbie, and Briony all bought stamps. The number of stamps Cecilia purchased was equal to a single digit. The number of stamps only one of them purchased was divisible by 2. The number of stamps one of them bought was an even number. Which of the following could represent the numbers of stamps each purchased?
Choose one.
A) 3, 8, 24 B) 7, 9, 17 C) 6, 9, 12 D) 5, 15, 18 E) 9, 10, 13

Solution: I didnt get your point on eliminating B.   The number of stamps only one purchased was divisible by 2.Could that not be Cecilia with 7 stamps.   I choose this and marked 7, 9, 17.
Answer: B
Two partners in a business (James and Kelly) invested $900 and $1600 in a business respectively. At the end of the year they made a profit of $950. Find share of each partner?  Choose the correct answer:
A) $352,$657
B) $392,$608
C) $342,$408
D) $342,$608
E) $347,$608

Solution: A:B = 900:1600   A:B = 9 : 16   A's share = 950*9/25= 
950*9/25 = 342
$342   B's share= 950*16/25= 
950*16/25 = 608
$608   Answer is $342,$608
Answer: D
Jason flips a coin three times. What is the probability X that the coin will land on the same side in all three tosses? Choose the correct option:
A) 1/16
B) 1/8
C) 1/4
D) 1/3
E) 1/2

Solution: Total outcome is 2^3=8   Favorable cases HHH or TTT   Therefore, probability X is 2/8 or 1/4.1/4
Answer: C
The 30 members of a club decided to play a badminton singles tournament. Every time a member loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that must be played to determine the winner ?	Pick:
A) 15	B) 29	C) 64	D) 39	E) 35

Solution: 29 matches   because each match will result in removing a player.   ANSWER:29
Answer: B
A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?	Choose the most appropriate option:  A) 228  B) 240  C) 887  D) 166  E) 1811

Solution: Speed = 54 * 5/18= 
54 * 5/18 = 15
15 m/sec.   Length of the train= 15 * 20= 
15 * 20 = 300
300 m.   Let the length of the platform be x m . Then,   (x + 300)/36= 15 => x = 240 m.   Answer: 240
Answer: B
IN Common Wealth Games an athlete runs 200 meters in 30 seconds. Hisspeed is ?	Choose the correct choice
A) 24 km/hr	B) 27 km/hr	C) 30 km/hr	D) 32 km/hr	E) None of these

Solution: Explanation :   (200/1000)/(30/3600)= 
(200/1000)/(30/3600) = 24
24 km/hr   24 km/hrnswer : 24 km/hr
Answer: A
Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Children A & B must sit next to each other, and child C must be somewhere to the right of A & B. How many possible configurations are there for the children?  Choose the correct choice from the following options.
A) 600	B) 720	C) 1440	D) 4320	E) 4800

Solution: First, consider the restriction of A & B. As with problem #1 above, there are 12 possibilities for A & B, counting both position and order.   Now, put the other five in any order — that’s 120 possibilities, for a total number of configurations of 1440. That number does not take into account the restriction with C.   Think about those 1440 configurations. In exactly half of them, C will be to the right of A & B, and exactly half, C will be to the left of A & B. Therefore, in  (1/2)*1440= 
 (1/2)*1440 = 720
720 configurations, C will be to the right of A & B.   Answer= 720
Answer: B