MU-NLPC/Calc-aqua_rat huggingface dataset:
The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?  Choose the correct choice from the following.
A) 757 B) 758 C) 718 D) 750 E) 738

Solution: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.   Let the length of the train and that of the platform be x meters.   Then, 2x/60 = 25 è x = 25 * 60 / 2= 
25 * 60 / 2 = 750
750   Answer:750
Answer: D
Two trains are traveling on a collision course. If train A is traveling at a speed of 350 mph and train B is traveling 28% slower, how much time will it take the trains to collide if the initial distance between the two is 1655.5 miles?	Answers:  A) Two hours and 30 minutes.  B) One hour and 10 minutes.  C) Two hours and 45 minutes.  D) Three hours and 15 minutes.  E) Four hours and 20 minutes.

Solution: Answer is C. Two hours and 45 minutes.   Since they are racing towards each other, the speed is accumulative, ie. 350 mph + 350*0.72 = 602 (0.72 because the second train is 28% slower)   So time before collision is total distance / total speed = 1655.5/602 = 2 hours and 45 mins
Answer: C
The regular price per can of a certain brand of soda is $0.55. If the regular price per can is discounted 25 percent when the soda is purchased in 24-can cases, what is the price of 70 cans of this brand of soda purchased in 24-can cases?	Pick.
A) $16.32 B) $18.00 C) $21.60 D) $24.48 E) $28.87

Solution: The discounted price of one can of soda is (0.75)($0.55), or $0.4125   Therefore, the price of 70 cans of soda at the discounted price would be (70)($0.4125) = 28.875   Answer: $28.87
Answer: E
A certain article of clothing was discounted during a special sale to 3/4 of its original retail price. When the clothing didn't sell, it was discounted even further to 2/5 of its original retail price during a second sale. By what percent did the price of this article of clothing decrease from the first sale to the second sale?
Choose the correct choice from the following answers.
A) 50%
B) 33.33%
C) 25%
D) 46.66%
E) 12.5%

Solution: Say the original retail price of the item was $200.   The price after the first sale = 3/4 * $200 = $150.   The price after the second sale 3/4 *  200= 
3/4 *  200 = 150
$150.   The price after the second sale= 2/5 * $200 = $80.   The percent change from the first sale to the second 2/5 *  200= 
2/5 *  200 = 80
$80.   The percent change from the first sale to the second= (150 -80) / 150 = 1/3 = 46.66%.   Answer: 46.66%.
Answer: D
Mike invested Rs. 3750 in a scheme for 3 years at compound interest rate 6.5% p.a. How much amount will Mike get on maturity of the fixed deposit?
Options
A) s.4581.29 B) s.4450 C) s.4500 D) s.4500.25 E) s.4529.81

Solution: Amount = [3750 * (1 + 6.5/100)3]   = 3750 *106.5/100 * 106.5/100 *106.5/100   = Rs.4529.81   Answer:s.4529.81
Answer: E
A part-time employee’s hourly wage was increased by 20%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased?
Select the correct option.
A) 9%
B) 17%
C) 25%
D) 50%
E) 100%

Solution: Let's plug in somenicenumbers and see what's needed.   Let's say the employee used to make $1/hour and worked 100 hours/week   So, the TOTAL weekly income was $100/week   After the 20% wage increase, the employee makes $1.20/hour   We want the employee's income to remain at $100/week.   So, we want ($1.20/hour)(new # of hours) = $100   Divide both sides by 1.20 to get:   new # of hours = 100/1.20   ≈ 83 hours   So, the number of hours decreases from 100 hours to (approximately) 83 hours.   This represents a 17% decrease (approximately) .   Answer : 17%
Answer: B
The average of 13 numbers is 60. Average of the first 7 of them is 55 and that of the last 7 is 61. Find the 8th number?  Select
A) 32	B) 83	C) 45	D) 53	E) 64

Solution: Sum of all the 13 numbers = 13 * 60= 
13 * 60 = 780
780   Sum of the first 7 of them= 7 * 55= 
7 * 55 = 385
385   Sum of the last 7 of them= 7 * 61= 
7 * 61 = 427
427   So, the 8th number= 427 + 385 - 780= 
427 + 385 - 780 = 32
32.   32nswer:32
Answer: A
If 60% of of a number is 36, then the number is  Choose the correct choice from the following
A) 223
B) 378
C) 100
D) 298
E) 2778

Solution: Explanation:   Let the number be x.Then   60% of {\color{Black} \frac{3}{5}}of x=36.   {\color{Black} \Rightarrow }{\color{Black} \frac{60}{100}\times \frac{3}{5}\times x=36}   {\color{Black} \Rightarrow x=100}   Required number is 100.   Answer: 100) 100
Answer: C
We invested a total of $1,000. We invested one part of the money at 3% and the rest of the money at 4%. The total investment with interest at the end of the year was $1,036.70. How much money did we invest at 3%?  Choose the correct choice from the following answers.
A) $300 B) $330 C) $360 D) $390 E) $420

Solution: Let x be the money invested at 3%.   1.03x+1.04(1000-x)=1036.70.   0.01x=1040-1036.70.   0.01x=3.30.   x=330.   The answer is $330.
Answer: B
In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.150, what is B's capital?
Pick one:
A) 19878
B) 12798
C) 26908
D) 11250
E) 22073

Solution: 200 + 150= 
200 + 150 = 350
350   800 - 350= 
800 - 350 = 450
450   200 ---- 5000   450 ---- ?=> 11250   Answer: 11250
Answer: D
P is three times as fast as Q and working together, they can complete a work in 12 days. In how many days can Q alone complete the work?	Choose one:
A) 16
B) 77
C) 88
D) 55
E) 778

Solution: P = 3Q   P + Q = 3Q + Q = 4Q   These 4Q people can do the work in 12 days, which means Q can do the work in 48 days.   Hence, P can do the work in 16 days.   16nswer:16
Answer: A
A manufacturer produces a certain men's athletic shoe in integer sizes from 8 to 17. For this particular shoe, each unit increase in size corresponds to a 1/5-inch increase in the length of the shoe. If the largest size of this shoe is 40% longer than the smallest size, how long, in inches, is the shoe in size 15?  Choose the correct choice from the following answers.
A) 5.4 B) 5.9 C) 6.3 D) 6.7 E) 7.5

Solution: Let x be the length of the size 8 shoe.   Then 0.4x = 9/5   x = 4.5 inches   The size 15 shoe has a length of  4.5 + 7/5= 
 4.5 + 7/5 = 5.9
5.9 inches   The answer is 5.9.
Answer: B
A train 100 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train? Choose the correct choice from the following choices:
A) 6 sec  B) 9 sec  C) 12 sec  D) 15 sec  E) 18 sec

Solution: Speed of the train relative to man = (68 - 8) kmph   = (60* 5/18) m/sec = (50/3)m/sec   Time taken by the train to cross the man   = Time taken by It to cover 100 m at 50/3 m / sec   = 100 *3/ 50= 
100 *3/ 50 = 6
6sec   6 secnswer : 6 sec
Answer: A
What is the probability of getting sum 10 with the help of three dice?
Choose the correct answer.
A) 1/4 B) 1/8 C) 1/16 D) 1/24 E) 1/32

Solution: (1,3,6) 3!=6 (2,2,6) =3!/2=3   (1,4,5) 3!=6 (2,4,4)=3   (2,3,5) 3!=6 (3,3,4)=3   prob. of getting sum 10 =(6+6+6+3+3+3)/216 =1/8 Ans   ANSWER:1/8
Answer: B
On a certain transatlantic crossing, 15 percent of a ship's passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship's passengers held round-trip tickets?  Choose the correct choice
A) 37.5%	B) 40%	C) 50%	D) 60%	E) 66.6%

Solution: 0.15P = RT + C   0.6(RT) = no C   => 0.40(RT) had C   0.15P = 0.40(RT)   RT/P = 37.5%   37.5%nswer - 37.5%
Answer: A
A bus started its journey from Mumbai and reached Pune in 54min with its average speed of 55km/hr. If the average speed of the bus is increased by 6km/hr, how much time will it take to cover the same distance? Pick:
A) 45 min. 30sec B) 43min. C) 45min. D) 44 min. 30sec E) 46min.

Solution: Sol. Distance between Mumbai and Pune=(55*54)/60=99/2   Average speed of the bus is increased by 6 km/hr then the   speed of the bus = 60 km/hr   Required time = 99/2*60/60 = 44 min. 30sec   44 min. 30sec
Answer: D
A number is selected at random from the first 30 natural numbers. What is the probability that the number is a multiple of either 3 or 17? Pick one
A) 17/30
B) 2/5
C) 7/15
D) 4/15
E) 11/30

Solution: Number of Multiples of 3 from 1 through 30 = 30/3= 
30/3 = 10
10   Number of Multiples of 17 from 1 through 30= 30/17 = 1   Number of Multiples of 3 and 17 both from 1 through 30 = Number of Multiples of 17*3(=51) = 0   Total favourable cases = 10 + 1 - 0= 
10 + 1 - 0 = 11
11   Probability= 11 / 30   Answer: option 11/30
Answer: E
Average between two sets of numbers is closer to the set withmore numbers?  Choose the correct choice from the following:
A) 75
B) 80
C) 85
D) 90
E) 96

Solution: If on a test three people answered 90% of the questions correctly and two people answered 80% correctly, then the average for the group is not 85% but rather 3×90+2×805=4305=86.3×90+2×805=4305=86.   Here, 90 has a weight of 3 => it occurs 3 times.   Whereas 80 has a weight of 2 => it occurs 2 times.   So the average is closer to 90 than to 80 as we have just calculated.   80
Answer: B
In how many ways can a group of 12 friends be seated round 2 tables if one of the tables can seat 8 and the other can seat 4 people?
Choose the correct answer:
A) 15C5 * 9! *4!
B) 15C3 * 8! *3!
C) 15C4 * 9! *3!
D) 15C2 * 10! *3!
E) 12C4 * 7! * 3!

Solution: 8 people can be selected from 12 people in 12C8 ways.   Remaining 4 people can be selected from 4 people in 4C4 ways.   Now, arranging 8 people on a round table = (8-1)= 
(8-1) = 7
7!   Arranging 4 people on a round table= (4-1)= 
(4-1) = 3
3!   Hence, total number of ways= 12C8 * 7! * 4C4 * 3!   = 12C4 * 7! * 3!   12C4 * 7! * 3!
Answer: E
What are the last two digits of 63*35*37*82*71*41*53? Select the correct option:  A) 10  B) 30  C) 40  D) 70  E) 80

Solution: We know that to find the last two digits, we need to find the remainder we get when we divide the product by 100.   Remainder of (63*35*37*82*71*41)/ 100   Note that we can simplify this expression by canceling out the 5 and 2 in the numerator and denominator. But before we do that, here is an important note:   Note: We cannot just cancel off the common terms in the numerator and denominator to get the remainder. But, if we want to cancel off to simplify the question, we can do it, provided we remember to multiply it back again.   So say, we want to find the remainder when 14 is divided by 10 i.e. 14/10 (remainder 4). But we cancel off the common 2 to get 7/5. The remainder here will be 2 which is not the same as the remainder obtained by dividing 14 by 10. But if we multiply 2 back by 2 (the number we canceled off), the remainder will become 2*2= 
2*2 = 4
4 which is correct.   Take another example to reinforce this – what is the remainder when 85 is divided by 20? It is 5.   We might rephrase it as – what is the remainder when 17 is divided by 4 (cancel off 5 from the numerator and the denominator). The remainder in this case is 1. We multiply the 5 back to 1 to get the remainder as 5 which is correct.   So keeping this very important point in mind, let’s go ahead and cancel the common 5 and 2.   We need the   Remainder of (63*7*37*41*71*41*5*2)/10*5*2   Remainder of (63*7*37*41*71*41)/10   Now using concept 2, let’s write the numbers in form of multiples of 10   Remainder of (60+3)*7*(30+7)*(40+1)*(70+1)*(40+1)/10   Remainder of 3*7*7*1*1*1/10   Remainder of 147/10= 7   Now remember, we had canceled off 10 so to get the actual remainder so we need to multiply by 10: 7*10 = 70.   When 63*35*37*82*71*41 is divided by 100, the remainder is 70. So the last two digits of 63*35*37*82*71*41 must be 80.   Answer (80)
Answer: E
What is the are of an equilateral triangle of side 4 cm?  Choose the correct choice from the following answers:	A) 64√5	B) 4√3	C) 64√4	D) 64√3	E) 64√2

Solution: Area of an equilateral triangle = √3/4 S2   If S = 4, Area of triangle = √3/4 * 4 * 4 = 4√3 cm2;   Answer: 4√3
Answer: B
If "PLANT" is given a code of 63, then what is the sum of "SOIL" and "STEM"?  Choose the correct answer:	A) 112	B) 100	C) -2	D) 2	E) 120

Solution: Case – Codes : 112 - 1, B - 2, C - 3, D - 4, E - 5, F - 6, G - 7, H - 8, I - 9, J - 10, K - 11, L - 12, M - 13, N - 14, O - 15, P - 16, Q - 17, R - 18, S - 19, T - 20, U - 21, V - 22, W - 23, X - 24, Y - 25, Z - 26   SOIL-55   STEM-57   112nswer: 112
Answer: A
Set J consists of the terms {a, b, c, d, e}, where e > d > c > b > a >0.1. Which of the following operations would decrease the standard deviation of Set J?	Choose the correct choice from the following:  A) Multiply each term by e/d  B) Divide each term by e/c  C) Multiply each term by −1  D) Divide each term by d/e  E) Multiply each term by 1

Solution: CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.   1) It depends on the separation between the successive terms of the set   2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant   3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number   Divide each term by e/c
Answer: B
A can contains a mixture of liquids A and B is the ratio 7:5. When 6 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many liter of liquid A was contained by the can initially?
Select
A) 12  B) 18  C) 14  D) 20  E) 22

Solution: Ci*Vi = Cf*Vf   (7/12)*(V1 - 6) = (7/16)*V1   (V1 - 6)/V1 = 3/4   6 accounts for the difference of 1 on ratio scale so Initial volume = V1 = 4*6= 
4*6 = 24
24 litres.   7/12 of the initial mixture was liquid A so liquid A was   (7/12)*24= 
  (7/12)*24 = 14
14 litres.   Answer : 14
Answer: C
According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 15 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice? Options:
A) 25
B) 34
C) 50
D) 20
E) 100

Solution: Orange juice concentrate: water::1:3   total quantity of orange juice = 200*6= 
200*6 = 1_200
1200 oz   so Orange juice concentrate: water :: 300 oz:900 oz   no. of 15 oz can= 300 oz/15 oz = 20   Answer 20, 20 cans
Answer: D
Out of 40 applicants to a law school, 15 majored in political science, 20 had a grade point average higher than 3.0, and 10 did not major in political science and had a GPA equal to or lower than 3.0. How many R applicants majored in political science and had a GPA higher than 3.0?	Select the correct option.
A) 5  B) 10  C) 15  D) 25  E) 35

Solution: Total applicants = 40   Political science = 15 and Non political science = 40 - 15= 
40 - 15 = 25
25   GP5 > 3.0= 20 and GP5 <= 3.0 = 20   10 Non political science students had GP5 <= 3.0 --> 15 Non political science students had GP5 > 3.0   GP5 > 3.0 in political science = Total - (GP5 > 3.0 in non political science) R= 20 - 15= 
20 - 15 = 5
5   5nswer: 5
Answer: A
What is the perimeter, in meters, of a rectangular garden 24 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide? Choose the correct choice from the following answers.
A) 48	B) 56	C) 64	D) 76	E) 192

Solution: Say Length of garden is L meters.   Then (L*24) = 16 * 12 [Given area is same. Area= L * B]   Therefore L works out to 8 meters.   Perimeter of Garden = 2* (8+24)= 
2* (8+24) = 64
64 meter.   Answer is 64
Answer: C
In a fuel station the service costs $2.10 per vehicle and every liter of fuel costs $0.70. Assuming that you fill up 3 mini-vans and 2 trucks, what will be the total cost, if a mini-van's tank is 65 liters and a truck's tank is 120% bigger and they are all empty?
Choose one:
A) $338.50	B) $341.40	C) $344.30	D) $347.20	E) $350.10

Solution: The service cost of 3 vans and 2 trucks is 5*2.10 $10.50   The fuel in 3 vans is 3*65= 
3*65 = 195
195 liters   The fuel in 2 trucks is   2*65*2.2= 
  2*65*2.2 = 286
286 liters   The total fuel (vans + trucks)= 481 liters   The total fuel cost is 481*0.7= 
481*0.7 = 336.7
$336.70   The total cost is $336.70 + $10.50 = $347.20   The answer is $347.20. 336.70 +  10.50= 
 336.70 +  10.50 = 347.2
$347.20   The answer is $347.20.
Answer: D
The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).  Choose the correct answer:
A) 8, 20, 28
B) 16, 28, 36
C) 20, 35, 45
D) 18, 24, 32
E) None of these

Solution: Explanation:   Let their present ages be 4x, 7x and 9x years respectively.   Then, (4x - 8) + (7x - 8) + (9x - 8) = 56   20x = 80   x = 4.   Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.   Answer: 16, 28, 36
Answer: B
The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?  Choose the correct choice from the following answers
A) 5  B) 6  C) 8  D) 9  E) 1

Solution: S = 4   M = x   DS = x + 4   US = x - 4   6/(x + 4) + 6/(x - 4) = 2   x = 8.Answer:8
Answer: C
A number when divided by 128 gives a remainder 34, what remainder will be obtained by dividing the same number 19?  Choose the correct choice from the following choices:
A) 7
B) 6
C) 9
D) 10
E) 3

Solution: Explanation:   128 + 34= 
128 + 34 = 162
162/19= 10 (Remainder)   Answer: 10
Answer: D
If $ 5,000 is invested in an account that earns 8% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest? Select the correct option: A) $ 4 B) $ 8 C) $ 12 D) $ 16 E) $ 432

Solution: Solution   Amount (CI) = P+(1+r/n)^nt = 5000+(1+0.08/2)^2= 5408   Amount (SI) = P+PTR/100 = 5000+(5000*1*8/100)= 
5000+(5000*1*8/100) = 5_400
5400   Difference= 5408-5400= 
5408-5400 = 8
8 $   ANSWER:$ 8
Answer: B
Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
Select the correct option
A) 11  B) 10  C) 17  D) 16  E) 18

Solution: 4/12 + x/15 = 1   x = 10   Answer:10
Answer: B
The average weight of 10 bags of sand is 20 pounds. Another bag of sand is added to the group and decreases the average weight by 1 pound. How much does the new bag of sand weigh? Select the correct option.
A) 7	B) 21	C) 29	D) 9	E) 19

Solution: Total weight of 10 bags of sand = 10*20= 
10*20 = 200
200   Total weight of 11 bags of sand= 11*19= 
11*19 = 209
209   Weight of new bag= 209-200= 
209-200 = 9
9 pounds   Answer is 9
Answer: D
A, B and C rents a pasture for Rs.435. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should B pay?  Select:
A) 180  B) 227  C) 268  D) 198  E) 176

Solution: 12*8 :16*9 = 18*6   8: 12: 9   12/29 * 435= 
12/29 * 435 = 180
180   180nswer:180
Answer: A
30 carrots on a scale weigh 5.94 kg. When 3 carrots are removed from the scale, the average weight of the 27 carrots is 200 grams. What is the average weight (in grams) of the 3 carrots which were removed?
Choose the correct choice from the following
A) 165  B) 170  C) 175  D) 180  E) 185

Solution: 27*200= 
27*200 = 5_400
5400.   The other 3 carrots weigh a total of 540 grams.   The average weight is  540/3= 
 540/3 = 180
180 grams.   The answer is 180.
Answer: D
A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age nine years back was?  Select:
A) 10yr  B) 15yr  C) 20yr  D) 25yr  E) 30yr

Solution: Let the son's present age be x years   Then, 38-x = x   x = 19   Son's age 9 years back = 19-9= 
19-9 = 10
10 years   10yrnswer is 10yr
Answer: A
Find the probability that a number selected from numbers 1, 2, 3,..., 50 is a prime number, when each of the given numbers is equally likely to be selected? Choose one:
A) 10/50	B) 15/50	C) 8/50	D) 3/50	E) 7/50

Solution: Let X be the event of selecting a prime number.   X = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47}   n(X) = 15,   n(S) = 50   Hence, the required probability is 15/50.   ANSWER:15/50
Answer: B
The fourth proportional to 12, 18 and 26 is?
Choose the correct answer.
A) 21
B) 66
C) 39
D) 88
E) 61

Solution: (18*26)/12= 
(18*26)/12 = 39
39   Answer:39
Answer: C
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 2x units of product P in 6 days?	Pick.
A) 24
B) 18
C) 16
D) 12
E) 8

Solution: 4 machines do x units in 6 days   we have x/6 => rate of the 4 machines   we know that we need to have 2x units in 4 days   therefore, we need to get to 2x/4 rate of the machines.   rate of one machine is x/6*1/4 = x/24.   now, we need to know how many machines need to work simultaneously, to get 2x done in 6 days.   2x/6 work needs to be done by machines that work at x/24 rate.   let's assign a constant Y for the number of machines:   (x/24)*y = 2x/6   y = 2x/6 * 24/x   cancel 6 with 24, and x with x and get -> 8. Answer choice 8
Answer: E
For every $20 that a billionaire spends, a millionaire spends the equivalent of 20 cents. For every $2 that a millionaire spends, a yuppie spends the equivalent of $1. The ratio of money spent by a yuppie, millionaire, and billionaire can be expressed as  Choose one:
A) 1 : 4 : 400
B) 1 : 4 : 100
C) 20 : 4 : 1
D) 100 : 4 : 1
E) 400 : 4 : 1

Solution: millionaire 20 cents = 1/5 dollar ..therefore 1 dollar M = 100 dollar of B   therefore 2 dollar M = 200 dollar of B also 1 dollar Y   Y:M:B = 1:2:200   = 1:2:200   400 : 4 : 1
Answer: E
How many 1 1/2 foot pieces of cable can be cut out of a piece that is 30 feet long?  Pick one:
A) a.10
B) b.16
C) c.17
D) d.18
E) e. 20

Solution: Pretty Simple..the answer is choice (E) 20.   All that one has to do is :   1: Convert 1 1/2 into an improper fraction (3/2) or a decimal (1.5)   2: Divide 30 by 3/2 (or 1.5)   Answer =20 (e. 20)
Answer: E
T(x, y) is the intersection point between the circle (x^2 + y^2 = 4) and the line (y = x +2). Which of the following can be the point T?
Pick:
A) (1, 2).
B) (2, 0).
C) (0, -2).
D) (-2, 0).
E) (2, 2).

Solution: A quick glance at the options, T(x, y) and we can see that A and E do not satisfy the circle equation. Now we are left with B, C and D. Now B and C do not satisfy the line equation. So we are just left with D. And thats the answer=(-2, 0).
Answer: D
Three times the first of three consecutive odd integers is 5 more than twice the third. The third integer is:
Pick
A) 9	B) 11	C) 13	D) 15	E) 17

Solution: Let the three integers be x, x + 2 and x+ 4.   Then,   3x = 2(x + 4) + 5   x = 12   Third integer = x + 4 = 17.   ANSW17R:17
Answer: E
A can do a work in 9 days and B can do the same work in 27 days. If they work together, in how many days will they complete the work?  Choose the correct option
A) 6 3/4 days B) 7 3/4 days C) 5 3/4 days D) 6 1/4 days E) 6 2/4 days

Solution: One day's work of A and B = 1/9 + 1/27 = (3+1)/27 = 4/27 So, the time taken to complete the work is 6 3/4 days.   6 3/4 daysNSWER:6 3/4 days
Answer: A
Bhajan Singh purchased 120 reams of paper at Rs 80 per ream. He spent Rs 280 on transportation, paid octroi at the rate of 40 paise per ream and paid Rs 72 to the coolie. If he wants to have a gain of 8 %, what must be the selling price per ream?	Pick:
A) 90  B) 22  C) 28  D) 27  E) 92

Solution: Explanation:   Total investment = Rs. (120 * 80 + 280 + (40/100) * 120 + 72).   = Rs. (9600 + 280+48 + 72) = Rs, 10000.   Sell price of 120 reams = 108% of Rs. 10000 = Rs. 10800.   Sell Price per ream = Rs. [10800/120] = Rs. 90.   90nswer: 90) 90
Answer: A