MU-NLPC/Calc-aqua_rat huggingface dataset:
If x and y are integers such that x^2-4x+2y+6=2x^2-5x+y-6, we can deduce that y is Choose one:  A) not an even  B) an even  C) a perfect square  D) an odd  E) a prime

Solution: x^2 - 4x + 2y + 6 = 2x^2 - 5x + y - 6   y = x^2 - x - 12   y = (x-4)(x+3) (Note that one factor is even and one factor is odd.)   Then y must be even.   The answer is an even.
Answer: B
If 5th March, 2009 is Tuesday, what was the day of the week on 5th March, 2008?	Choices
A) Sunday  B) Saturday  C) Tuesday  D) Wednesday  E) Monday

Solution: Solution   The year 2008 is a leap year. So, it has 2 odd days.   But, Feb 2008 not included because we are calculating from March 2008 to March 2009. So it has 1 odd day only.   The day on 5th March, 2009 will be 1 day beyond the day on 5th March, 2008. Given that, 5th March, 2009 is Tuesday.   5th March, 2008 is Monday (1 day before to 5th March, 2009)   Answer Monday
Answer: E
If (a-b) is 6 more than (c+d) and (a+b) is 3 less than (c-d), then (a-c)  Choices:
A) 0.25  B) 1.5  C) 2  D) 2.5  E) 3

Solution: (a-b)-(c-d)=6 and (c-d)-(a+b)=3   (a-c)-(b+d)=6 and (c-a)-(b+d)=3   (b+d)= (a-c)-6 and (b+d)=3-(c-a)   2(a-c)=3   (a-c)=1.5   ANSWER 1.5 1.5
Answer: B
If x is less than y by 50% then y exceed x by: Choose the correct choice from the following
A) 33.33%
B) 100%
C) 75%
D) 66.66%
E) None of these

Solution: Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 25%)   => 50(100-50)*100   =100%   ANSWER:100%
Answer: B
Given that a/b < 1, and both a and b are positive integers, which one of the following must be greater than 1?	Options:
A) a/b^2	B) a^2/b	C) a^2/b^2	D) b/a	E) √(a/b)

Solution: Since a/b is a fraction b must always be > 1   Given -   Which one of the following must be greater than 1   We can get the result one only when the denominator in a/b ( Which is less than 1 ) becomes numerator..   Among the given options only (D) has the required characteristic we are looking for...   Hence answer will be (b/a)
Answer: D
What is the HCF of 2/3, 4/9 and 6/5  Choose the correct option:
A) 7/45
B) 2/45
C) 4/15
D) 8/45
E) 9/45

Solution: Explanation:   HCF of Fractions = HCF of Numerators/LCM of Denominators   = (HCF of 2, 4, 6)/(LCM of 3, 9, 5) = 2/45   Answer: Option 2/45
Answer: B
P, Q and R have Rs.9000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?	Choose the correct choice from the following choices
A) Rs.3000
B) Rs.3600
C) Rs.2400
D) Rs.4000
E) None of these

Solution: Let the amount with R be Rs.r   r = 2/3 (total amount with P and Q)   r = 2/3(9000 - r) => 3r = 18000 - 2r   => 5r = 18000 => r = 3600.   ANSWER:Rs.3600
Answer: B
Three small cruise ships, each carrying 7 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random and each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out? Choose the correct choice from the following options
A) 4328
B) 5382
C) 6174
D) 7690
E) 8436

Solution: The number of ways for the ships to go to the ports is 3! = 6.   At Port A, the number of ways to choose two winners is 7C2 = 21.   At Port B, the number of ways to choose one winner is 7.   At Port C, the number of ways to choose one winner is 7.   The total number of ways to give out gift certificates is  6*21*7*7= 
 6*21*7*7 = 6_174
6174   The answer is 6174.
Answer: C
Calculate the average of all the numbers between 11 and 27 which are divisible by 2.  Choose the correct option
A) 11  B) 10  C) 18  D) 19  E) 21

Solution: Explanation:   numbers divisible by 2 are 12,14,16,18,20,22,24,26,   Average = (12+14+16+18+20+22+24+26, ) / 8 = 152/8= 
152/8 = 19
19   ANSWER: 19
Answer: D
Every day Daniel drives 120 miles back from work. On Sunday, Daniel drove all the way back from work at a constant speed of x miles per hour. On Monday, Daniel drove the first 32 miles back from work at (2x) miles per hour, and the rest of the way at (x/2) miles per hour. The time it took Daniel to drive back from work on Monday is longer than the time it took him to drive back from work on Sunday by what percent?  Pick
A) 10% B) 20% C) 30% D) 40% E) 60%

Solution: Let's TEST X = 4....   On Sunday, Daniel drove 120 miles at 4 miles/hour.   D = (R)(T)   120 = (4)(T)   120/4= 
120/4 = 30
30= T   It takes 30 hours to drive home   On Monday, Daniel drove the first 32 miles at (2)(4) = 8 miles/hour and the rest of the way (88 miles) at  4/2= 
 4/2 = 2
2 miles/hour   D= (R)(T)   32 = (8)(T)   32/8= 
32/8 = 4
4= T   It takes 4 hours for the first part   D = (R)(T)   88 = (2)(T)   88/2= 
88/2 = 44
44= T   It takes 44 hours for the second part   Total time to drive home on Monday = 4+44= 
4+44 = 48
48 hours   We're asked by what percent 48 hours is greater than 30 hours.   48/30= 
48/30 = 8/5 = around 1.6
1.6, so it is 60% greater.   answer:60%
Answer: E
A box contains 12 mangoes out of which 4 are spoilt. If four mangoes are chosen at random, find the probability that Exactly three are not spoiled. Choose the most appropriate option:
A) 116/495
B) 224/495
C) 129/495
D) 187/495
E) 197/495

Solution: equired probability = 8C3 . 4C1/12C4 = 56 x 4/495   = 224/495.   ANSWER:224/495
Answer: B
At a meeting, 8 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?	Answers:
A) 12
B) 72
C) 120
D) 1440
E) 5040

Solution: The number of arrangements of n distinct objects in a row is given by n!   The number of arrangements of n distinct objects in a circle is given by (n−1)!   "The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:   R=n!-n=(n−1)!   (n−1)!=(8−1)!=5040   Answer: 5040
Answer: E
A train 120 m long crosses a platform 220 m long in 20 sec; find the speed of the train?
Select:
A) 87 kmph B) 65 kmph C) 54 kmph D) 61 kmph E) 18 kmph

Solution: 61 kmph = 120 + 220= 
120 + 220 = 340
340   T= 20   S = 340/20 * 18/5 = 61 kmph   Answer:61 kmph
Answer: D
Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?	Pick:
A) 2318  B) 2380  C) 1277  D) 2662  E) 1321

Solution: Kamal : Sameer = (9000 * 12) : (8000 * 7)   = 108:56 = 27:14   Sameer's share = 6970 * 14/41 = Rs. 2380.   Answer: 2380
Answer: B
A man buys a cycle for Rs. 1800 and sells it at a loss of 25%. What is the selling price of the cycle?	Choose the correct choice:
A) s. 1090
B) s. 1160
C) s. 1190
D) s. 1350
E) s. 1256

Solution: S.P. = 75% of Rs. 1800 = Rs.75/100x 1800	= Rs. 1350   ANSWER :s. 1350
Answer: D
Milk contains 5% water. What content of pure milk should be added to 10 liters of milk to reduce this to 2%?
Choose the correct choice from the following answers:
A) 10liters  B) 15liters  C) 20liters  D) 18liters  E) 22liters

Solution: Quantity of water in 10 liters = 5% of 10 liters = 0.5 liters   Let x liters of pure milk be added.   Then, 0.5/(10+x) = 2/100   2x = 30   x=15 liters   Answer is 15liters
Answer: B
Two pipes A and B can fill a tank is 8 minutes and 14 minutes respectively. If both the pipes are opened simultaneously, and the pipe A is closed after 3 minutes, then how much more time will it take to fill the tank by pipe B?
Pick:
A) 5 minute 25 second  B) 5 minute 45 second  C) 5 minute 35 second  D) 6 minute 45 second  E) 7 minute 45 second

Solution: Part filled by pipe A in 1 minute =1/8   Part filled by pipe B in 1 minute =1/14   Part filled by pipe A and pipe B in 1 minute =1/8+1/14=11/56   Pipe A and B were open for 3 minutes.   Part filled by pipe A and 5 minute 45 second in 3 minute=3 Ã— 11/56=33/56   Remaining part =1-33/56=23/56   Time taken by pipe 5 minute 45 second to fill this remaining part=(23/56)/(1/14)=23/4   =5 3/4 minutes   =5 minute 45 second   Answer is 5 minute 45 second
Answer: B
If x > 3000, then the value of (x)/(2x-42) is closest to?
Pick:
A) 1/6  B) 1/3  C) 10/21  D) 1/2  E) 3/2

Solution: assume x = 3002   (x)/(2x-42) = 3002 / (3002*2-42)   =3002 / 5962   = = 1/2   Ans - 1/2
Answer: D
In a mixture of milk and water, the proportion of milk by weight was 90%. If, in a 120-gram mixture, 30 grams of pure milk is added, what would be the percentage of milk in the resulting mixture? Choose the correct option
A) 91.4%  B) 91.6%  C) 91.8%  D) 92.0%  E) 92.2%

Solution: The amount of milk is 0.9(120) + 30 = 138 grams.   The proportion is 138/150= 
138/150 = 23/25 = around 0.92
0.92 which is 92%   The answer is 92.0%.
Answer: D
Farm Tax is levied on the 75% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. william. Mr. william paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is :
Choose the correct choice:
A) 15%
B) 25%
C) 0.125%
D) 0.2083%
E) 16.667%

Solution: This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms.   But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/75) = 16.667%   The correct answer is (16.667%).
Answer: E
If (a-7)(b-2) =0, which of the following must be true ?
I. a=7 and b=2
II. if a is not 7, then b=2
III. if a=7, then b is not=2  Choose one
A) I only
B) II only
C) III only
D) I and II
E) II and III

Solution: (a-7)(b-2)=0   So either a=7 or b=2 or both. It is 'or' not 'and', so it could be any of the three possibilities. Thus I and III are not necessarily true.   The answer is II only.
Answer: B
A palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 100 that is both a prime and a palindrome. What is the sum of the digits of p? Choose the most appropriate option:	A) 3	B) 4	C) 5	D) 6	E) 7

Solution: Given that p is smallest integer greater than 200 - assume there is a 3-digit that satisfies the above conditions. Let the number be xyx ; question asks us the values of 2x+y   We can straight away cross out options A) and D) - sum of digits 3 or 6 implies it is divisible by 3 ---> we know that p is a prime number   5oming to option B) 2x + y = 4 --> only x = 2 and y = 0 satisfy this equation ( x> 2 will never give sum of digits = 4) ; but 202 is divisible by 2 ; we know that p is a prime number   Similarly option 5) 2x+y = 5 --> only x = 2 and y = 1 satisfy this equation ( x> 2 will never give sum of digits = 5) ; but 212 is divisible by 2 ; we know that p is a prime number   Therefore answer option should be E ---> can be verified by taking 2x+y = 7 ---> x = 3 and y = 1 ; gives 313   5
Answer: C
A monkey start climbing up a tree 19 ft tall.Each hour it hops 3 ft and slips back 2 ft. How much time would it take the monkey to reach the top.
Pick:
A) 15 hrs	B) 18 hrs	C) 19 hrs	D) 17 hrs	E) 16 hrs

Solution: if monkey hops 3ft and slips back 2ft in a hour, it means the monkey hops (3ft-2ft)= 1ft/hr.   similarly in 16hrs it wil be 16ft.   Bt since the height of the tree is 19ft, so if the monkey hops up the tree in the next hr i.e 17th hr then it reaches at the top of the tree.   hence it takes 17 hrs for monkey to reach at the top   ANSWER:17 hrs  (3  -2  )= 
  (3  -2  ) = 1
1ft/hr.   similarly in 16hrs it wil be 16ft.   Bt since the height of the tree is 19ft, so if the monkey hops up the tree in the next hr i.e 17th hr then it reaches at the top of the tree.   hence it takes 17 hrs for monkey to reach at the top   ANSWER:17 hrs
Answer: D
In a boat there are 8 men whose average weight is increased by 1 kg when 1 man of 60 kg is replaced by a new man. What is weight of new comer?  Choices
A) 70	B) 66	C) 68	D) 69	E) 72

Solution: Solution: Member in group * age increased = difference of replacement   Or, 8*1 = new comer - man going out   Or, new comer = 8+60;   Or, new comer = 68 years.   Answer: Option 68
Answer: C
If there are 10 apples and 20 oranges, what is the ratio of apples to oranges?
Choose the correct choice from the following options:
A) 10:20	B) 2:4	C) 1:2	D) 4:8	E) It cannot be determined from the information given

Solution: A ratio should be reduced to the lowest common denominator.   10:20 means 10x:20x which can be written as 1(10):2(10)...   ANSWER:1:2
Answer: C
The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 5 kmph, what time will he take to cover 60 metres? Choose the correct option:  A) 16 seconds  B) 76 seconds  C) 10.8 seconds  D) 12 seconds  E) 18 seconds

Solution: Speed of the boat downstream = 15 + 5= 
15 + 5 = 20
20 kmph= 20 * 5/18 = 50/9 m/s   Hence time taken to cover 60 m   = 60*9/50= 
60*9/50 = 54/5 = around 10.8
10.8 seconds.   Answer: 10.8 seconds
Answer: C
Find the first term and the common ratio of a G.P whose fourth term is 250 and seventh term is 31,250  Choose the correct choice from the following answers
A) 2/5,25
B) 4,5/2
C) 1,16
D) 2,5
E) 1,5

Solution: a*r ^3 = 250, a *r ^6 =31,250, r ^3 =31,250/250 = 125   r = 5, a* 125 = 250, a = 2   ANSWER:2,5
Answer: D
Juan is a gold medalist in athletics. In the month of May, if Juan takes 13 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
Choices.
A) 10x/y B) 11x/y C) 9x/y D) 12x/y E) 13x/y

Solution: velocity=distance/time;   since he ran at same rate both d tyms,   y/13=x/t   so t=13x/y   ANSW13x/yR:13x/y
Answer: E
A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?	Choices
A) 4 min	B) 5 min	C) 3 min 4 sec	D) 4 min 5 sec	E) Data inadequate

Solution: Explanation:   S = 600/40= 
600/40 = 15
15 mps   S= 3600/15= 
3600/15 = 240
240 sec= 4 min   4 minNSWER IS 4 min
Answer: A
Calculate the HCF of 64, 592, 960	Pick
A) 15 B) 16 C) 13 D) 14 E) 12

Solution: Explanation:   Lets solve this question by factorization method.   The factors of 64 are: 1, 2, 4, 8, 16, 32, 64   The factors of 592 are: 1, 2, 4, 8, 16, 37, 74, 148, 296, 592   The factors of 960 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960   Then the greatest common factor is 16.   Answer: Option 16
Answer: B
What is the next number in the series?
1,5,9,13... Pick one:
A) 19	B) 17	C) 24	D) 25	E) 28

Solution: Adding (0,2,4,6,8,10) to the odd numbers    1+0= 
 1+0 = 1
1   3+2= 
3+2 = 5
5   5+4= 
5+4 = 9
9   7+6= 
7+6 = 13
13   9+8= 
9+8 = 17
17   answer 17
Answer: B
A train takes 9 hrs to cover distance with the speed 85kmph. Find distance the train travelled. Choose the correct choice from the following options:  A) 750  B) 850  C) 725  D) 765  E) 675

Solution: Length = Speed * time   Length =85kmph * 9 hrs   Length =765km   Ans : (765)
Answer: D
A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is?  Choose the correct option:
A) 16%	B) 15%	C) 12%	D) 22%	E) 19%

Solution: S.I. for 3 years = (12005 - 9800) = Rs. 2205   S.I. for 5 years = Rs. 2205/3 * 5 = Rs. 3675.   Principal = (9800 - 3675) = Rs. 6125   Hence, rate = (100 * 3675) / (6125 * 5)= 
(100 * 3675) / (6125 * 5) = 12
12%   Answer: 12%
Answer: C
Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 16% if no discount was offered?	Choose the correct choice:
A) 17608 B) 17606 C) 17604 D) 17600 E) 18560

Solution: Price at which the TV set is bought = Rs. 12,500   Discount offered = 20%   Marked Price = 12500 * 100/80 = Rs. 15625   The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000   The price at which the TV should be sold to get a profit of 16% if no discount was offered = 16000 * 116/100 = Rs. 18560.Answer: 18560
Answer: E
There is enough provisions for 600 men in an army camp for 25 days. If there were 100 men less, how long will the provision last?
Pick one:	A) 10days	B) 50days	C) 100days	D) 150days	E) 200days

Solution: Exp: We have, M1D1 = M2D2   600*25= 100* D2   D2 = 600*25/100= 
600*25/100 = 150
150 days.   Answer: 150days
Answer: D
A cheese factory sells its cheese in rectangular blocks. A normal block has a volume of 5 cubic feet. If a large block has twice the width, twice the depth, and the same length of a normal block, what is the volume of cheese in a large block in cubic feet?
Choose the correct choice.
A) 15	B) 30	C) 20	D) 18	E) 25

Solution: Volume of cube=lbh=5   New cube l ,b, h are increases of l, 2b,2h   New volume of cube =l*2b*2h=4*lbh   =4*5= 
4*5 = 20
20   Answer: 20
Answer: C
If the sides of a triangle are 65 cm, 60 cm and 25 cm, what is its area?  Choose the correct answer
A) 120 cm2
B) 750 cm2
C) 216 cm2
D) 197 cm2
E) 275 cm2

Solution: The triangle with sides 65 cm, 60 cm and 25 cm is right angled, where the hypotenuse is 65 cm.   Area of the triangle   = 1/2 * 60 * 25= 
1/2 * 60 * 25 = 750
750 cm2   Answer:750 cm2
Answer: B
The ratio of two quantities is 3 to 4. If each of the quantities is increased 4 and 3 respectively, what is the ratio of these two new quantities?
Choose the correct choice from the following answers
A) 3/4 B) 8/9 C) 18/19 D) 23/24 E) It cannot be determined from the information given

Solution: 3/4 = 3x/4x   we need to find out (3x+4)/(4x+3) off course we cannot solve this to arrive at any rational number hence It cannot be determined from the information given.
Answer: E
Let S1 be a square of side a. Another square S2 is formed by joining the mid-points of the sides of S1. The same process is applied to S2 to form yet another square S3, and so on. If A1, A2, A3 .. be the areas and P1, P2, P3,…….. be the perimeters of S1, S2, S3,..., respectively, then the ratio (P1 + P2 +P3+ ......) / (A1 + A2 + A3 +.......) equals :-	Select:
A) 2(1+√2)/a
B) 2(2+√2)/a
C) 2(2+√2)/a
D) 2(1+2√2)/a
E) None of these

Solution: Explanation :   side of S1= a, perimeter of S1= 4a, area of S1 = a2   side of S2= a/√2 , perimeter of S2= 2√2a , area of S2 = a2/2   side of S3= a/2 , perimeter of S3= 2a , area of S3= a2/4   So, for P1 + P2 + P3 .... we will have a GP as below   4a + 2√2a + 2a + .....   First term =4a, common ratio = 1/√2, Sum = 4a/( 1-1/√2) = 4√2a/(√2 - 1)   For A1 + A2 + A3....we will have another GP   a2 + a2/2 + a2/4 .....   First term = a2 , common ratio = 1/2 , Sum = 2a2.   Hence, the required ratio :-   i.e (P1 + P2 + P3....) / (A1+ A2+A3....).   => 4√2a / (√2 - 1) / 2a2.   => 2√2(√2 + 1)/a.   => 2(2 +√2)/a .   Answer : 2(2+√2)/a
Answer: B
A survey reveals that the average income of a company’s customers is $45,000 per year. If 40 customers respond to the survey and the average income of the wealthiest 10 of those customers is $75,000, what is the average income of the other 30 customers?
Is there a way to solve this using weighted average concept instead of doing tedious calculations?  Choose the most appropriate option:
A) $27,500  B) $35,000  C) $37,500  D) $42,500  E) $50,000

Solution: let x be the average of 30 customers   30*x + 10* 75000 = 40*45000   solving this we have x= 35000   Answer is $35,000.
Answer: B
A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?	Choices:
A) 780m
B) 180m
C) 170m
D) 140m
E) 186m

Solution: Length of the train be ‘X’   X + 120/15 = X + 180/18   6X + 720 = 5X + 900   X = 180m   Answer:180m
Answer: B
In a box, there are 7 red, 3 blue and 5 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green? Pick.
A) 2/3	B) 8/21	C) 3/7	D) 7/15	E) 10/21

Solution: Explanation:   Total number of balls = (7 + 3 + 5)= 
(7 + 3 + 5) = 15
15.   Let E= event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.   Therefore, n(E) = 7.   P(E) = 7/15.   Answer: Option 7/15
Answer: D
The average weight of 20 persons sitting in a boat had some value. A new person added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 20 persons?  Choose the most appropriate option
A) 55
B) 56
C) 57
D) 58
E) 59

Solution: 20x + 46 = 21(x – 5)   X=59   ANSW59R:59
Answer: E
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 10 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is :
Choose one:
A) 22	B) 21	C) 88	D) 30	E) 29

Solution: Explanation:   Lot the total number of workers be v Then,   8OOOv = (12000 * 10) + 6000 (v - 10) <=> 2000v = 60000 <=> v = 30   Answer: 30) 30
Answer: D
A 4-letter code word consists of letters D, E, and G. If the code includes all the three letters, how many such codes are possible? Choose the most appropriate option.
A) 72
B) 48
C) 36
D) 24
E) 18

Solution: Note that the correct answer to this question is 36, not 72.   D-DEG can be arranged in 4!/2!=12 ways;   E-DEG can be arranged in 4!/2!=12 ways;   G-DEG can be arranged in 4!/2!=12 ways;   Total:  12+12+12= 
 12+12+12 = 36
36.   Answer: 36.
Answer: C
If x+y=3 and x2y3 + y2x3=27, what is the value of xy? Choose the correct option:
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: xy=3   As x+y=3   x2y3+y2x3=27   x2y2(y+x)=27   Substituting x+y   x2y2=9   xy=3   ANSWER:3
Answer: C
Without stoppages, a train travels certain distance with an average speed of 250 km/h, and with stoppages, it covers the same distance with an average speed of 125 km/h. How many minutes per hour the train stops ?  Choose the correct choice from the following answers.
A) 25 B) 30 C) 35 D) 40 E) 45

Solution: Due to stoppages, it covers 125 km less .   Time taken to cover 125 km = 125â„250h = 1â„2h   = 1â„2 Ã— 60 min = 30 min   Answer 30
Answer: B
A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 14% while buying and by 20% while selling. What is his percentage profit?
Choices:  A) 10.22%  B) 20.22%  C) 21.22%  D) 42.5%  E) Can't be calculated

Solution: The owner buys 100 kg but actually gets 114kg;   The owner sells 100 kg but actually gives 80kg;   Profit:   (114-80)/80*100= 
  (114-80)/80*100 = 85/2 = around 42.5
~42.5%   Answer: 42.5%.
Answer: D
Three numbers are in the ratio 3:4:5 and their L.C.M. is 600. Their H.C.F is?	Choose the correct choice:
A) 10
B) 30
C) 40
D) 50
E) 60

Solution: Let the numbers be 3x,4x and 5x   their L.C.M. = 60x   60x =600   x = 10   The numbers are 3*10 , 4*10 , 5*10   Hence required H.C.F. = 10   10nswer is 10
Answer: A