MU-NLPC/Calc-aqua_rat huggingface dataset:
Which of the Conclusion is true fof the below statement
Statement : D @ M, M $ B, B ☆ R, R % T
Conclusion:
I. B ☆ D
II. B @ D
III. T ☆ M Choose the correct choice from the following options:
A) Only I is true
B) Only II is true
C) Only III is true
D) Only either I or II is true
E) None is true

Solution: Only either I or II is true=M, M>B, B<r, r="">T Only either I or II is true</r,>=M>=B<r>T   B @ Only either I or II is true True   T ☆ M True   Option Only either I or II is true</r>
Answer: D
Anu can do a work in 6 days and Binu alone in 9 days. Anu and Binu undertook to do it for Rs.4200. With help of Minu, they completed the work in 3 days. How much is to be paid to Minu and Anu?	Answers
A) s.700, Rs.2100	B) s.2000, Rs.750	C) s.750, Rs.2000	D) s.800, Rs.1250	E) s.1000, Rs.1250

Solution: Minuâ€™s one dayâ€™s work = 1/3 - 1/6 + 1/9= 1/3 - 5/18 = 1/18   s.700, Rs.2100nuâ€™s wages: Binuâ€™s wages: Minuâ€™s wages = 1/6 : 1/9 : 1/18 = 6: 4: 2   Minuâ€™s share = Rs.4200* 2/12 = Rs.700   s.700, Rs.2100nuâ€™s share = Rs.4200* 6 /12= 
.4200* 6 /12 = 0.21
Rs.2100   s.700, Rs.2100NSWER:s.700, Rs.2100
Answer: A
A Prototype fuel-efficient car (P-Car) is estimated to get 85% more miles per gallon of gasoline
than does a traditional fuel-efficient car (T-Car). However, the P-Car requires a special type
of gasoline that costs 20% more per gallon than does the gasoline used by a T-Car. If the two
cars are driven the same distance, what percent less than the money spent on gasoline for the
T-Car is the money spent on gasoline for the P-Car?
Choose the correct option
A) 16 2/3%
B) 35.13 %
C) 50%
D) 60%
E) 66 2/3 %

Solution: Assumption   Miles/Gallon   T = 100   P = 185 ( 85% more)   $/gallon   T = 100   P = 120 (20% more)   Miles   100 for both   Cost = (Miles X $/ Gallon)/ M/gallon   T = 100   P = 64.86   Hence 100 - 64.86 =35.13%   Ans 35.13 %
Answer: B
A and B start walking towards each other at 1pm at speed of 5kmph and 7kmph. They were initially 24km apart. At what time do they meet?	Choose the most appropriate option:
A) 4pm B) 6pm C) 3pm D) 10pm E) 5pm

Solution: Time of meeting = distance / relative speed = 24/7+5 = 24/12= 
24/12 = 2
2 hrs after 1pm= 3pm   Answer is 3pm
Answer: C
P and Q started a business investing Rs.85,000 and Rs.15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?  Choose the correct choice from the following options:
A) 3 : 4
B) 3 : 5
C) 15 : 23
D) 17 : 3
E) None

Solution: Solution   P : Q	= 85000 : 15000   =85 : 15   =17 : 3   Answer 17 : 3
Answer: D
6 25 64 81 32 ?
Find The Last Number In the Series ? Pick one
A) 5 B) 4 C) 1 D) 2 E) 7

Solution: 1   The answer is 1   6 {6^1}   25 {5^2}   64 {4^3}   81 {3^4}   32 {2^5}   1 {1^6}
Answer: C
2 dice are tossed. What is the probability that the total score is a prime no. is?  Choose the most appropriate option:
A) 3/14
B) 5/12
C) 5/13
D) 7/11
E) 7/12

Solution: 5/12   5/12
Answer: B
The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product?
Select the correct option.
A) 12% B) 12.5% C) 12.9% D) 12.11% E) 13.5%

Solution: X Rate = Price   1 x 1 = 1   0.7 x 1.25 = 0.875   Decrease in price = (0.125/1) × 100 = 12.5%   12.5%)
Answer: B
A circular rim 14 inches in diameter rotates the same number of inches per second as a circular rim 21 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?	Choices:
A) 48pi/x	B) 40x	C) 48x	D) 24x	E) x/75

Solution: Let's try the explanation. We have two wheels. One with 14pi and the other one with 21pi. They have the same speed. In the smaller wheel it's 14pi*x, which must be equal to the speed of the bigger one (21pi*a number of revolutions).They are asking that number of revolutions (but in minutes, which makes the question even harder).   Anyway, we have 14pi*x=21pi*a.   (14pi*x)/(21pi). As I said, that's in seconds. So, to convert it to minutes we multiply by 60 and we get the result, 40x.   Ans : 40x
Answer: B
The ratio between the perimeter and the width of a rectangle is 5 : 1. If the area of the rectangle is 150 sq. cm, what is the width of the rectangle?
Pick one:
A) 10 cm	B) 12 cm	C) 14 cm	D) 16 cm	E) 18 cm

Solution: 2L+2W = 5W   L = 3W/2   W*L = 150   3W^2/2 = 150   W^2 = 100   W = 10   The answer is 10 cm.
Answer: A
'a' and 'b' are positive integers such that their LCM is 20 and their HCF is 1. What is the difference between the maximum and minimum possible values of 'a + b'?	Select
A) 0
B) 12
C) 13
D) 9
E) 11

Solution: a = 4, b = 5 as they have to co-primes (HCF being 1 and LCM = 20)   So 0+B = 9 is their max and min value   hence Difference = 0   0nswer - 0
Answer: A
If the average (arithmetic mean) of (2a+16) and (3a-8) is 74, what is the value of a? Choose the correct choice:	A) 25	B) 30	C) 28	D) 36	E) 42

Solution: ((2a+16) + (3a-8)) / 2 = (5a+8)/2 = 74   a= 28   The answer is 28.
Answer: C
A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt? Pick.
A) 187 ways  B) 176 ways  C) 166 ways  D) 108 ways  E) 181 ways

Solution: The boy can select one trouser in nine ways.   The boy can select one shirt in 12 ways.   The number of ways in which he can select one trouser and one shirt is   9 * 12= 
  9 * 12 = 108
108 ways.   Answer: 108 ways
Answer: D
A certain car uses 12 gallons of gasoline in traveling 180 miles. In order for the car to travel the same distance using 10 gallons of gasoline, by how many miles per gallon must the car’s gas mileage be increased?	Choose the correct choice from the following options:
A) 2  B) 3  C) 6  D) 8  E) 10

Solution: 180/10= 
180/10 = 18
18. The difference is  18 - 15= 
 18 - 15 = 3
3.   Answer 3
Answer: B
The total of the ages of Jayant, Prem and Saransh is 93 years. Ten years ago, the ratio of their ages was
2 : 3 : 4. What is the present age of Saransh?	Options:
A) 24 years B) 32 years C) 34 years D) 38 years E) None

Solution: Solution   Let the ages of Jayant, Prem and Saransh 10 years ago be 2x, 3x and 4x years respectively. Then,   (2x + 10)+(3x + 10)+(4x + 10)	= 93.   ‹=›9x = 63   x = 7.   ∴ Saransh's present age = 4x + 10 = 38 years.   Answer 38 years
Answer: D
If A,B,C are three integers and AB+C is even ; which of the following must be true? A)C is even B)B is Odd C)AB is Odd Select:
A) I only B) II only C) None of the above D) II,III only E) III only

Solution: If AB is Odd then C will not even. O+E = O   If AB is even then C will not be odd.   If B is even AB is even always. But If C is Odd E+O = O   If B is Odd AB is even or odd depends on A   None of the above are true.   Answer : None of the above
Answer: C
The ratio of boys to girl in a school is 5:4. If there are 1500 boys in the school, how many girls are there?  Choose the correct choice from the following options
A) 300	B) 1200	C) 1500	D) 1800	E) 2000

Solution: Think of the ratio as 5 parts: 4 parts.   Divide 1500 by 5 to find 1 "part" of the ratio.   1500/5= 
1500/5 = 300
300   Multiply this by 4 to get 4 "parts" of the ratio.   300*4= 
300*4 = 1_200
1200   There are 1200 girls in the school.   The answer is 1200
Answer: B
A and B together can do a work in 3 days. If A alone can do it in 12 days. In how many days can B alone do it?	Select
A) 4	B) 6	C) 8	D) 10	E) 25

Solution: 4   4   1/3 â€“ 1/12 = 1/4 => 4
Answer: A
The population of a town is 10000. It increases annually at the rate of 10% p.a. What will be its population after 2 years?
Choose one
A) 12100	B) 14400	C) 14500	D) 14600	E) 14700

Solution: Formula :   10000 × 110/100 × 110/100 = 12100   12100nswer : 12100
Answer: A
Jim takes a seconds to swim z meters at a constant rate from point P to point Q in a pool. Roger, who is faster than Jim, can swim the same distance in b seconds at a constant rate. If Jim leaves point P the same time that Roger leaves point Q, how many fewer meters will Jim have swum than Roger when the two swimmers pass each other?
Options.
A) c(b-a)/ a+b	B) c(a-b)/a+b	C) c(a+b)/a-b	D) ab(a-b)/a+b	E) z(a-b)/a+b

Solution: Both JimRoger are travelling at constant speedin opposite direction:   So, speed of Jim = z/a speed of Roger = z/b   Let say Jim travelled distance x from P where it met Roger, it means that Roger travelled (z-x) from point Q   [x would be less than (z-x) as Jim is travelling slow]   From above, time taken by Jim to travel x = xa/z....................... (1)   Also, time taken by Roger to travel (z-x) = (z-x)b/z.....................(2)   Time taken by both JimRoger is same, so (1) = (2)   xa/z = (z-x)b/c,   Solving further, x = bz/(a+b).................... (3)   We require to find how many fewer meters will Jim have swum i.e   additional distance travelled by Roger = (z - x) - x   = z-2x   Substituting value of x from (3)solving the equation further, we get Answer = z(a-b)/a+b   Answer = (z(a-b)/a+b)
Answer: E
Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $8.91 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discount rates is 22 percent, what is the discount rate on Pony jeans?
Choose the correct choice from the following
A) 9% B) 10% C) 11% D) 12% E) 15%

Solution: Let x be the discount on Pony jeans. Then 0.22-x is the discount on Fox jeans.   3(0.22-x)(15) + 2x(18) = 8.91   9.9 - 45x + 36x = 8.91   9x = 0.99   x = 0.11   The answer is 11%.
Answer: C
For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [9]*[10] equivalent to?	Choose the correct choice from the following choices: A) [25] B) [135] C) [30] D) [90] E) [45]

Solution: [9]*[10] = 27*5= 
27*5 = 135
135= 3*45 = [45]   The answer is [45].
Answer: E
If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 27 more than n. What is y in terms of x ?	Choices:
A) x-3
B) x+3
C) x+5
D) x-10
E) x-7

Solution: Original Digits=xy i.e. Number=10x+y   After reversing the digits:   Digits=yx i.e. Number=10y+x   10y+x is 27 more than 10x+y   10x+y+27=10y+x   10x-x+27=10y-y   9x+27=9y   x+3=y   OR   y=x+3   Answer : x+3
Answer: B
One pump drains one-half of a pond in 7 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone? Choose the correct choice from the following options.
A) 1 hour  B) 1.1 hour  C) 3 hours  D) 5 hours  E) 6 hours

Solution: First pump drains 1/2 of the tank in 7 hours   so 14 hours it will take to drain the full tank.   Let, 2nd pump drains the full tank in a hours   so both together can drain (1/14+1/a) part in 1 hour   son in 1/2 hour they drain 1/2*(1/14+1/a) part of the tank   given that in 1/2 hour they drain 1/2 of the tank   hence we can say   1/2*(1/14+1/a) = 1/2   solving u get a = 14/13=1.1   Hence answer is 1.1 hour
Answer: B
A shopkeeper buys mangoes at the rate of 9 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?	Choose the correct choice from the following answers:	A) 33 4/3 %	B) 33 1/7 %	C) 200/3 %	D) 32 1/3 %	E) 33 2/3 %

Solution: The total number of mangoes bought by the shopkeeper be 27.   If he buys 9 a rupee, his 200/3 %P = 3   He selling at 3 a rupee, his SP = 9   Profit = SP - 200/3 %P = 9 - 3= 
9 - 3 = 6
6   Profit Percent= 6/9 * 100 = 200/3 %   Answer:200/3 %
Answer: C
The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
Choose the correct choice from the following options
A) 17 kg B) 20 kg C) 26 kg D) 31 kg E) 35 kg

Solution: Let A, B, C represent their respective weights. Then, we have:   A + B + C = (45 x 3) = 135 .... (i)   A + B = (40 x 2) = 80 .... (ii)   B + C = (43 x 2) = 86 ....(iii)   Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)   Subtracting (i) from (iv), we get : B = 31.   B's weight = 31 kg.   Answer: Option 31 kg
Answer: D
A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?
Options.
A) 3.34
B) 3.349
C) 3.348
D) 3.37
E) 3.248

Solution: 3.34rea of the path = 3.34rea of the outer circle - 3.34rea of the inner circle = ∏{4/2 + 25/100}2 - ∏[4/2]2   = ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }   = (3.14)(1/4)(17/4) = 53.38/16 = 3.34 sq m   3.34nswer: 3.34
Answer: A
[1/(1.2.3)] + [1/(2.3.4)] + [1/(3.4.5)] + [1/(4.5.6)] is equal to
Choose the correct choice:
A) 7 / 30
B) 11 / 30
C) 13 / 30
D) 17 / 30
E) None

Solution: Answer   Given Exp. = [(4 x 5 x 6) + (5 x 6) + (2 x 6) + (2 x 3)] / [(2 x 3 x 4 x 5 x 6)]   = 168 / (24 x 30)   = 7 / 30   Correct Option: 7 / 30
Answer: A
Luke purchased a used car for a price of H dollars, which he took to a garage where he bought a new windshield for L dollars, and four new wheels for J dollars per wheel. He then sold the car to a friend for K dollars.
How much profit did he make?
Choices.
A) (K+H)-(L-J)  B) (K-H)-(L+J)  C) (K-J)+(L+H)  D) (K+H)-(L-4J)  E) (K-H)-(L+4J)

Solution: The cost for the new wheels= 4J dollars   Then the cost price=H+L+4J dollars   The selling price= K dollars   Hence, the profit= K-(H+L+4J)   = K-H-L-4J dollars   The correct answer is (K-H)-(L+4J)!!
Answer: E
A man purchased a fan and a tv for Rs. 5000 &Rs. 10000 respectively. He sold the fan at a loss of 6% and the tv at a profit of 12%. Overall how much he make a profit. Choices.
A) 100	B) 300	C) 900	D) 600	E) 400

Solution: Let the SP of the fan and the tv be Rs. r and Rs. m respectively.   r = 5000(1 - 6/100) = 5000 - 300   m = 10000(1 + 12/100) = 10000 + 1200   Total SP - Total CP = r + m - (15000 + 8000) = -300 + 1200 = Rs. 900   As this is positive, an overall profit of Rs. 900 was made.   900
Answer: C
Java House charges $3.25 for a cup of coffee that costs a total of $2.85 to make. Cup'O'Joe charges $2.80 for a cup that costs $2.65 to make. If Java House sells 24,000 cups of coffee, how many must Cup'O'Joe sell to make at least as much in total gross profit as its competitor does?	Choose the most appropriate option.
A) 7,858
B) 8,301
C) 14,667
D) 64,000
E) 146,667

Solution: Java: Profit/Cup = 3.25-2.85= 
3.25-2.85 = 0.4
0.4   : No of Cups= 24,000   : Gross Profit = 24,000*0.4 = 9,600   Joe: Profit/Cup = 0.15   : Gross Profit = 9,600   : No of Cups = 9,600/0.15 = 64000   Answer 64,000
Answer: D
Tickets numbered from 1 to 27 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bears a number which is a multiple of 3?
Choose the most appropriate option:
A) 1/3	B) 2/5	C) 3/10	D) 3/7	E) 1/7

Solution: Here, S = [1, 2, 3, 4, …., 19, 20, 21, 22, 23, 24, 25, 26, 27]   Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18, 21, 24, 27]   P (E) = n (E) / n (S) = 9 / 27 = 1/3   The answer is 1/3.
Answer: A
If a man walks to his office at 5/4 of his usual rate, he reaches office 30 minutes early than usual. What is his usual time to reach office. Choose the correct choice from the following answers:
A) 2 hrs
B) 2 1⁄2 hrs
C) 1 hr 50 min
D) 2 hrs 15 min
E) None of these

Solution: usual time × (4⁄5 - 1) = -30⁄60   ⇒ usual time = 1⁄2 × 5 = 21⁄2 hrs   Answer 2 1⁄2 hrs
Answer: B
A bag contains 4 white,5 red and 6 blue balls.Three balls are drawn at random from the bag.the probability that all of them are red are????
Choose one.
A) 1/91
B) 3/91
C) 4/91
D) 2/91
E) 6/91

Solution: 5c3/15c3=455/10=2/91   ANSWER:2/91
Answer: D
The average of six numbers is 3.55. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers ?	Choose the correct choice from the following answers
A) 4.7 B) 4.6 C) 4.2 D) 3.4 E) 4.9

Solution: Explanation:   Sum of the remaining two numbers = (3.55 * 6) - [(3.4 * 2) + (3.85 * 2)]   = 21.30 - (6.8 + 7.7) = 21.30 - 14.5 = 6.8.   Required average = (6.8 / 2) = 3.4.   Answer: 3.4) 3.4
Answer: D
An army’s recruitment process included N rounds of selection tasks. For the first A rounds, the rejection percentage was 60 percent per round. For the next B rounds, the rejection percentage was 50 percent per round and for the remaining rounds, the selection percentage was 70 percent per round. If there were 100000 people who applied for the army and 245 were finally selected, what was the value of N? Choose the correct choice from the following options.
A) 4	B) 5	C) 6	D) 8	E) 9

Solution: fastly i reduce 60% till it gets closer to our required 2000 candidates   step(1) 40000 accepted.   step(2) another 40%of 40000=16000 accepted.   here it is quiet observable that if we further deduct candidate by 60% it would change our probablity of easy going 2000 candidate.   so i would get to second stage of recruitment where 50 % is accepted   step(3) 50% of 16000=8000   step(4) 50% of 8000=4000   Step(5) 50% of 4000=2000   Step(6) 50% of 2000=1000   Step(7) 50% of 1000=500   Step(8) 70% of 500=350   Step(9) 70% of 350=245(our target)   total 9 steps required.   Ans 9
Answer: E
The distance between two stars is 1.8 × 10^7 light years. What is the distance between the two stars in parsecs? (1 parsec = 3.26 light years)
Pick:	A) 1.1 x 10^2	B) 2.2 x 10^3	C) 3.3 x 10^4	D) 4.4 x 10^5	E) 5.5 x 10^6

Solution: 1.8 × 10^7 ly / (3.26 ly/parsec) = (1.8/3.26) x 10^7 = 0.55 x 10^7 = 5.5 x 10^6 parsec   The answer is 5.5 x 10^6.
Answer: E
A group of five girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 8 theatre-goers?	Select:  A) 8! – 2!3!2!  B) 8! – 6!3!  C) 8 × 2!3!2!  D) 8! – 5!3!  E) 2!3!2!

Solution: There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM.   Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 8 persons without restriction. Thus we'll get the # of arrangements asked in the question.   1. Total # of arrangements of 8 is 8!.   2. # of arrangements when 3 boys are seated together, like MMM;   Among themselves these 3 boys can sit in 3! # of ways,   Now consider these 3 boys as one unit like this {MMM}. We'll have total of 6 units: {MMM}{W}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!.   Hence total # of arrangements when 3 men sit together is: 3!6!.   # of arrangements when 3 boys do not sit together would be: 8!-3!6!.   Answer: 8! – 6!3!).
Answer: B
20 men can complete a piece of work in 30 days. In how many days can 25 men complete that piece of work? Choose the correct choice:
A) 23	B) 27	C) 24	D) 27	E) 11

Solution: 20 * 30 = 25 * x => x = 24 days   Answer:24
Answer: C
A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number? Choose the correct choice from the following answers:  A) 3.5  B) 6  C) 8  D) 7  E) 4

Solution: Let the number be x. Then,   3(2x + 9) = 75   2x = 16 => x = 8   ANSWER:8
Answer: C
If,
1 * 3 * 5 = 16
3 * 5 * 7 = 38
Then find,
5 * 2 * 9 =? Choose the correct choice
A) 65
B) 68
C) 72
D) 23
E) 77

Solution: (9 * 2) + 5= 
(9 * 2) + 5 = 23
23   23
Answer: D
On a certain road, 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 40% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on that road exceed the posted speed limit?	Answers
A) 10.5% B) 12.5% C) 16.7% D) 25% E) 30%

Solution: suppose there are X motorists.   10% of them exceeded the speed limit and received the ticket, i.e. X/10.   Again, suppose total no. of motorists who exceeded the speed limit are Y.   40% of Y exceeded the speed limit but didn't received the ticket, i.e. 2Y/5.   it means 3Y/5 received the ticket.   hence, 3Y/5 = X/10   or Y/X=1/6   or Y/X * 100= 1/6 * 100= 16.7%   16.7%
Answer: C
Look at this series: V, VIII, XI, __, XVII, XX, ... What number should fill the blank? Choose the correct choice from the following answers:	A) IX	B) XXIII	C) XV	D) XIV	E) None

Solution: Explanation: This is a simple addition series; each number is 3 more than the previous number.   Answer: XIV
Answer: D
When the price of sugar was increased by 32%, a family reduced its consumption in such a way that the expenditure on sugar was only 10% more than before. If 30 kg were consumed per month before, find the new monthly consumption.
Choose the correct choice from the following options:
A) 20 kg B) 25 kg C) 30 kg D) 35 kg E) None of these

Solution: Since, expenditure = price × consumption   ∴ 110% of 30 = 132⁄100 × new consumption   ⇒ 110⁄100 × 30 = 132⁄100 × new consumption   ⇒ New consumption = 25 kg   Answer 25 kg
Answer: B
An article is bought for Rs.805 and sold for Rs.900, find the gain percent?
Pick one:
A) 12.8%	B) 17.8%	C) 15.8%	D) 11.8%	E) 14.8%

Solution: 805 ---- 95   100 ---- ? => 11.8%   Answer:11.8%
Answer: D
a person travels from his house to office from 11:10am to 12:10 am and covers a distence of 15.4km. find the average speed of the person. Choose one
A) 20.1km/h	B) 15.4km/h	C) 21.1km/h	D) 22.1km/h	E) 20.9km/h

Solution: time=12:10-11:10=1 hour   distance = 15.4 km   speed=15.4*1= 
15.4*1 = 15.4
15.4 km/h   ANSWER:15.4km/h
Answer: B
Two trains of equal length, running with the speeds of 60 and 60 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?	Pick.
A) 1.0  B) 8.2  C) 7.7  D) 2.6  E) 8.3

Solution: RS = 60 -40= 
60 -40 = 20
20 * 5/18= 100/18   T = 50   D = 50 * 100/18 = 2500/9   RS = 60 + 60= 
60 + 60 = 120
120* 5/18   T= 2500/9 * 18/600 = 8.3 sec.Answer: 8.3
Answer: E
In a class, the average age of 45 boys is 10 years and the average of 15 girls is 10 years. what is the average age of the whole class?	Select.
A) 12 Years
B) 12.3 Years
C) 10 Years
D) 13 Years
E) 15 Years

Solution: Total age of 60 students   (45X 10+15 X 10) = 630   Average = 600/60= 
600/60 = 10
10 Years   10 Years
Answer: C
If 2x + y = 7 and x + 2y = 8, then (x + y)/3 = Choose one:	A) 1	B) 4/3	C) 17/5	D) 18/5	E) 5/3

Solution: We have two equations:   2x + y = 7   x + 2y = 8   Notice that something nice happens when we ADD them. We get:   3x + 3y = 15   Divide both sides by 3 to get:x + y = 5   So, (x + y)/3 =5/3   Answer: 5/3
Answer: E
Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder	Choose the correct choice from the following:
A) 1000
B) 1100
C) 1230
D) 1350
E) 1635

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Large number = 270+1365= 
270+1365 = 1_635
1635   1635
Answer: E
Ten years ago, the age of Peter was one-third the age of Jacob at that time. The present age of Jacob is 12 years more than the present age of Peter. Find the present age of Peter?	Choose one
A) 15 B) 11 C) 18 D) 16 E) 20

Solution: D   16   Let the present ages of Peter and Jacob be 'a' and 'b' respectively.   a - 10 = 1/3 (b - 10) --- (1)   b = a + 12   Substituting b = a + 12 in first equation,   a - 10 = 1/3 (a + 2) => 3a - 30 = a + 2= 
+ 2 = 2
> 2a= 32 => a = 16.
Answer: D
There are 3 couples. If they will sit 6 chairs in a row such that each couple sits side by side, how many possible cases are there?
Choose the correct choice from the following answers
A) 48
B) 240
C) 1,200
D) 2,460
E) 3,840

Solution: Tie the couples. Then we have 3 persons that have to be arranged in 3 places. 3! ways.   Now the couples can change position with each other. 2! ways.   3! * (2!)^3 = 6*8= 
6*8 = 48
48   48nswer is 48.
Answer: A