MU-NLPC/Calc-aqua_rat huggingface dataset:
A credit card number has 6 digits (between 1 to 9 inclusive). The first two digits are 12 in that order, the third digit is bigger than 6, the fourth digit is divisible by 3, and the fifth digit is 4 times the sixth. How many different credit card numbers are possible?
Choices.
A) 12
B) 15
C) 18
D) 24
E) 36

Solution: The first two digits are fixed.   The third digit can be 7, 8, or 9 so there are 3 choices.   The fourth digit can be 3, 6, or 9 so there are 3 choices.   The fifth digit depends entirely on the sixth digit.   The sixth digit can be 1 or 2 so there are 2 choices.   The number of possibilities is  3*3*2= 
 3*3*2 = 18
18   The answer is 18.
Answer: C
The breath of a rectangle is three- seventh of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the length is 10 units?  Choose the correct choice: A) 310 sq.units B) 110 sq.units C) 210 sq.units D) 105 sq.units E) 205 sq.units

Solution: Given that the area of the square = 4900 sq.units   => Side of square = √4900 = 70units   The radius of the circle = side of the square = 49 units breath of the rectangle = 3/7 * 49= 
3/7 * 49 = 21
21units   Given that length= 10 units   Area of the rectangle = lb = 21 * 10= 
21 * 10 = 210
210 sq.units   Answer:210 sq.units
Answer: C
Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 12?
Choose the correct answer.
A) 8
B) 4
C) 5
D) 6
E) 7

Solution: i'm not sure i got the question right, if it is what i think it is, then 8 should be the right answer   0,1,2,3,4,5, will not have 2 slip sum of 10, add another (either 6,7,8 or 9) and we'll have a pair with sum 12   8ns:8
Answer: A
Out of the fractions 4/7, 5/13, 6/11, 3/5 and 2/3 which is the second smallest fraction ?	Choose the correct option.
A) 4/7  B) 5/13  C) 6/11  D) 3/5  E) None

Solution: Answer   4/7 = 0.57,   5/13 = 0.38,   6/11 = 0.54,   3/5= 
3/5 = 3/5 = around 0.6
0.6 and   2/3= 0.67   6/11learly, the second smallest fraction is 6/11   6/11orrect Option: 6/11
Answer: C
Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%? Choices.
A) 2978 B) 2681 C) 2689 D) 1000 E) 2760

Solution: (x*5*1)/100 + [(2500 - x)*6*1]/100   = 140   X = 1000   Answer: 1000
Answer: D
The difference between a number and its two-fifth is 510. What is 10% of that number?  Choose the correct choice from the following choices.
A) 12.75	B) 85	C) 204	D) 224	E) 95

Solution: Let the number be x. Then,   x - 2/5 x = 510   x = (510 * 5)/3= 
(510 * 5)/3 = 850
850   10% of 850= 85.   ANSWER:85
Answer: B
A train of 40 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?  Choices
A) 6  B) 3  C) 4  D) 3.9  E) 3.6

Solution: 3.9 = 40 * 60 + 1500= 
40 * 60 + 1500 = 3_900
3900 m   T= 3900/60 * 18/5= 
3900/60 * 18/5 = 234
234 sec= 3.9 mins   Answer:3.9
Answer: D
Two mixtures A and B contain milk and water in the ratios 2:5 and 5:4 respectively. How many gallons of A must be mixed with 90 gallons of B so that the resultant mixture contains 40% milk? Choose the correct choice from the following answers:	A) 144	B) 122.5	C) 105.1	D) 72	E) 134

Solution: Mixture A: 2:5 ratio of Milk:Water   Mixture B: 5:4 ratio of Milk:water   90 gallons mixture B with a ratio of 5:4 = 50 gallons of milk and 40 gallons of water 90/(5+4)= 
90/(5+4) = 10
10. 10*5= 50 and   10*4= 
  10*4 = 40
40.   (50+(2/7x))/(90+x)= .40   50+(2/7x)=.4(90+x)   50+(2/7x)=(2/5x)+36   50+(10/35x)=(14/35x) +36   4/35x=14   4x=14*35   4x=490   x=122.5 gallons   ANSWER:122.5
Answer: B
0.1 decates ago, Vijaya was quadrice as old as her daughter Simran. 0.6 decades hence, Vijaya’s age will beat her daughter’s age by 0.9 decades. The proportion of the current ages of Vijaya and Simran is : [ 0.1 Decates =1 Year; quadrice = 4 times]	Choose one:  A) 8:1  B) 10:2  C) 11:4  D) 13:4  E) None of these

Solution: Explanation:   Let, Ages of Vijaya and Simran – 1 year ago was 4A and A years correspondingly.   Then, [(4A + 1) + 6] – [(A + 1) + 6] = 9   3A = 9 A = 3   Needed Ratio = (4A + 1) : (A + 1) = 13 : 4.. Answer: 13:4
Answer: D
The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red
Answers:	A) 5.456%	B) 6.124%	C) 6.125%	D) 7.256%	E) 8.234%

Solution: Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W   Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125%   6.125%
Answer: C
Points M(9,4) and N(5,8) lie on the xy - plane. What is the midpoint of line segment MN? Choose the most appropriate option.
A) (7,6)  B) (0,5)  C) (0, (136^(1/2))/2)  D) (3/2,0)  E) (1,5)

Solution: The midpoint of a segment is exactly halfway between its endpoints and it's location can be found using the Midpoint Theorem, which states:   • The x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints.   • Likewise, the y-coordinate is the average of the y-coordinates of the endpoints.   So, x=(9+5)/2= 
(9+5)/2 = 7
7 and y=(4+8)/2= 
(4+8)/2 = 6
6 --> coordinates of the midpoint are (7, 6).   (7,6)nswer: (7,6).
Answer: A
A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
Choices:
A) 2:6
B) 2:6
C) 2:3
D) 2:4
E) 2:9

Solution: Let the principal be P and rate of interest be R%.   Required ratio = [(P * R * 6)/100] / [(P * R * 9)/100]   = 6PR/9PR = 6/9   = 2:3   Answer: 2:3
Answer: C
The ratio between a two-digit number and the sum of the digits of that
number is 4 : 1.If the digit in the unit's place is 3 more than the digit in the ten’s place, what is the number?
Choose the correct option
A) 47
B) 36
C) 58
D) 25
E) 14

Solution: Let the ten's digit be x. Then, unit's digit = (x + 3).   Sum of the digits = x + (x + 3) = 2x + 3. Number = l0x + (x + 3) = llx + 3.   11x+3 / 2x + 3 = 4 / 1 => 11x + 3 = 4 (2x + 3) => 3x = 9 => x = 3.   Hence, required number = 11x + 3 = 36.   Answer is 36.
Answer: B
The ratio of number of ladies to gents at a party was 1 : 2, but when 2 ladies and 2 gents left, the ratio became 1 : 3. How many people were originally present at the party? Choose the correct choice from the following answers
A) 6  B) 9  C) 12  D) 10  E) 11

Solution: Let number of ladies = x   then, number of gents = 2x   Now, x−2/2x−2=1/3⇒ 3x - 6 = 2x - 2   ⇒ x = 4   ∴ Total number of people originally present = 4 + 8= 
4 + 8 = 12
12   Answer 12
Answer: C
15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men? Choose the correct choice from the following answers:	A) 16	B) 30	C) 86	D) 27	E) 82

Solution: 3W = 2M   15M ------ 21 * 8 hours   21 W ------ x * 6 hours   14 M ------ x * 6   15 * 21 * 8 = 14 * x * 6   x = 30   Answer: 86
Answer: C
A student traveled 30 percent of the distance of the trip alone, continued another 20 miles with a friend, and then finished the last half of the trip alone. How many miles long was the trip?
Select.
A) 240	B) 200	C) 160	D) 100	E) 50

Solution: Let x be the total length of the trip.   0.3x + 20 miles + 0.5x = x   20 miles = 0.2x   x = 100 miles   The answer is 100.
Answer: D
A and B enter into a partnership with respective capitals of Rs. 20,000 and Rs. 40,000. At the end of the year, the total profit is Rs. 27,000. If A receives Rs. 15,000 as both his salary and profit, then what is his salary?	Choose the correct choice:  A) Rs. 2000  B) Rs. 4000  C) Rs. 6000  D) Rs. 3000  E) None of these

Solution: Explanation:   A's capital : B 's capital   20000 : 40000 = 1 : 2   Since, the time period is fixed, the profit is distributed in the ratio of capital 1 : 2   Profit of A = (1/3) * 27,000 = Rs. 9,000   Salary of A = Rs. (15000 – 9000) = Rs. 6000   ANSWER: Rs. 6000
Answer: C
On dividing $200 between A and B such that twice of A's share is less than 2 times the total share of A and B by 100. Find B's share.	Choose the correct answer
A) 100  B) 120  C) 70  D) 90  E) 50

Solution: Let A's share be X and B's share be Y.   =>2*X=2*(X+Y)-100   =>2Y=100   =>Y=50   Option 50
Answer: E
If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 217, what is the common ratio of the G.P?  Choose the correct option.
A) 3
B) 1/3
C) 2
D) 6
E) 1/6

Solution: 217=(a1+a2+a3+a4+a5+a6)/(a1+a2+a3)   Factorize the same terms   217=1+(a4+a5+a6)/(a1+a2+a3)   Write every term with respect to r   a1=a1   a2=a1*r^1   a3=a1*r^2   .........   217=1+(a1(r^3+r^4+r^5))/(a1(1+r^1+r^2))   216=(r^3 (1+r^1+r^2))/((1+r^1+r^2))   216=r^3   r=6   6
Answer: D
Find the sum of all 3 digit natural numbers, which are divisible by 8	Select the correct option
A) 61376	B) 54411	C) 612314	D) 64170	E) 64171

Solution: The three digit natural numbers divisible by 8 are   104, 112, 120, …. 992.   Let Sndenote their sum. That is, Sn = 104 112 120 128 , 992 g + + + + + .   Now, the sequence 104, 112, 120, g, 992 forms an A.P.   a=104, d=8, l=992   n=l-a/d   n=112   S112=n/2(a+l)=61376   61376NSWER 61376 61376
Answer: A
If x=3y=4z, what is z+y, in terms of x?	Choose the correct option.
A) 3x/5 B) 4x/9 C) 11x/13 D) 7x/12 E) 5x/11

Solution: x=3y=4z   x/4 = z   and y = x/3   z+y = x/4 + x/3 = 7x/12   Answer is 7x/12
Answer: D
What amount does Kiran get if he invests Rs.6450 at 15% p.a. compound interest for two years, compounding done annually?
Options
A) 8400	B) 8900	C) 4560	D) 8530	E) 9890

Solution: A= P{1 + R/100}n   => 6450{1 + 15/100}2   = Rs.8530   Answer: 8530
Answer: D
On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 18 more transactions than Cal. How much transactions did Jade handled? Answers:
A) 80  B) 81  C) 82  D) 83  E) 84

Solution: Solution:   Mabel handled 90 transactions   Anthony handled 10% more transactions than Mabel   Anthony = 90 + 90 × 10%   = 90 + 90 × 0.10   = 90 + 9= 
90 + 9 = 99
99   Cal handled 2/3rds of the transactions than Anthony handled   Cal= 2/3 × 99   = 66   Jade handled 18 more transactions than Cal.   Jade = 66 + 18= 
66 + 18 = 84
84   Jade handled= 84 transactions.   Answer: 84
Answer: E
Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?  Choose the most appropriate option.
A) 125
B) 879
C) 476
D) 255
E) 789

Solution: Explanation:   3 1/2 * 8 1/2 = 1/4 * 1/4 * x => x = 476   Answer : 476
Answer: C
Find large number from below question The difference of two numbers is 1375. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder Choose the correct choice
A) 1245  B) 1345  C) 1455  D) 1577  E) 1647

Solution: Let the smaller number be x. Then larger number = (x + 1375).   x + 1375 = 6x + 15   5x = 1360   x = 272   Large number = 272+1375= 
272+1375 = 1_647
1647   1647
Answer: E
The average weight of 10 persons increases by 3.2 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?  Choose the correct choice from the following choices:
A) 76 kg
B) 80 kg
C) 85 kg
D) 97 kg
E) None

Solution: Solution   Total weight increased	= (10 x 3.2)kg   = 32 kg.   Weight of new person	= (65 + 32)= 
(65 + 32) = 97
97 kg.   Answer 97 kg
Answer: D
What no. should be subtracted from x^3+4x^2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3?	Pick:
A) 40	B) 42	C) 44	D) 48	E) 52

Solution: According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(−a)f(−a).   In this case, as x+3x+3 divides x3+4x2−7x+12–kx3+4x2−7x+12–k perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.   i.e., (−3)3+4(−3)2−7(−3)+12−k=0(−3)3+4(−3)2−7(−3)+12−k=0   or −27+36+21+12=k−27+36+21+12=k   or k=k= 42   42
Answer: B
If tomorrow will be a Sunday, what day was the day before yesterday?	Choose the correct choice:	A) Monday	B) Tuesday	C) Wednesday	D) Thursday	E) Friday

Solution: Explanation:   Tomorrow will be a Sunday   =>Today is a Saturday   => Yesterday was a Friday   => The day before yesterday was Thursday   Answer: Option Thursday
Answer: D
There are b cities. What is the number of airlines that connected 2 different cities (airline from city A to city B is different with airline from city B to city A)?  Select
A) n(n-1)
B) n(n+1)
C) n(n-1)/2
D) n(n+1)/2
E) b(b-1)

Solution: First of all, the possible number of airlines is b. Then, the possible number of airlines departing from one city to another becomes (b-1). Hence, the answer is b(b-1), which makes b(b-1)
Answer: E
What approximate value should come in place of the question mark (?) in each of the following equations ?
52.861 + 0.2563 + 8.1 + 57.35 + 0.0087 = ? Select the correct option:  A) 119  B) 116  C) 121  D) 115  E) 120

Solution: Explanation :   52.8 + 3 + 8 + 57.4 + 0087 = 118.5 + 0.0087 = 119   119nswer : Option 119
Answer: A
If 1/4 of the passengers on a ship are from North America, 1/8 are Europeans, 1/12 are from Africa, 1/6 are from Asia and the remaining 36 people are citizens of other continents, then how many passengers are on board the ship?  Choose one
A) 92 B) 96 C) 100 D) 104 E) 108

Solution: 1/4 + 1/8 + 1/12 + 1/6 = (6+3+2+4)/24 = 15/24   Let x be the number of passengers on the ship.   36 = (9/24)x = 3x/8   x = 96   The answer is 96.
Answer: B
Two ants, Arthur and Amy, have discovered a picnic and are bringing crumbs back to the anthill. Amy makes twice as many trips and carries one and a half times as many crumbs per trip as Arthur. If Arthur carries a total of z crumbs to the anthill, how many crumbs will Amy bring to the anthill, in terms of z?	Choose the correct answer
A) z/2  B) z  C) 3z/2  D) 2z  E) 3z

Solution: Lets do it by picking up numbers. Let Arthur carry 2 crumbs per trip, this means Amy carries 3 crumbs per trip. Also let Arthur make 2 trips and so Amy makes 4 trips.   Thus total crumbs carried by Arthur (z) = 2 x 2 = 4, total crumbs carried by Amy = 3 x 4 = 12. 12 is 3 times 4, so 3z
Answer: E
A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work? Choose the correct choice from the following answers:  A) 8 days  B) 5 days  C) 2 days  D) 9 days  E) 1 days

Solution: 3/12 + (3 + x)/16 = 1   x = 9 days   Answer: 9 days
Answer: D
A book is bought for $60 and sold for $63. What is the profit in percentage?  Choose the correct choice from the following answers:
A) 3  B) 5  C) 7  D) 9  E) 11

Solution: 63/60= 
63/60 = 21/20 = around 1.05
1.05   The answer is 5.
Answer: B
In how many ways a hockey team of eleven can be elected from 16 players?  Choose the most appropriate option:  A) 4368  B) 4267  C) 5368  D) 4166  E) None of these

Solution: Solution   The required number of selections   = 3C1 × 4C1 × 2C1 (6C3 + 6C2 + 6C0) = 42 × 4!. 4368nswer 4368
Answer: A
Iron company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks?
Options
A) 16	B) 64	C) 256	D) 576	E) 4096

Solution: MAGOOSHOFFICIAL SOLUTION:   Iron company has four empty trucks that will head out in the morning, all four to the same destination.Where we put one box has absolutely no bearing on where we put any of the other boxes. The placement of the four boxes is completely independent of one another. For each box, we have four choices.   N = 4*4*4*4 = 16*16= 
16*16 = 256
256   Answer= (256)
Answer: C
In an increasing sequence of 8 consecutive integers, the sum of the first 4 integers is 570. What is the sum of the last 4 integers in the sequence?
Answers:
A) 585
B) 580
C) 586
D) 587
E) 589

Solution: Solution:   In solving this problem we must first remember that when we have 8 consecutive integers we can display them in terms of just 1 variable. Thus, we have the following:   Integer 1: x   Integer 2: x + 1   Integer 3: x + 2   Integer 4: x + 3   Integer 5: x + 4   Integer 6: x + 5   Integer 7: x + 6   Integer 8: x + 7   We are given that the sum of the first 4 integers is 570. This means that:   x + x+1 + x+2 + x+3 = 570   4x + 6 = 570   4x = 564   x = 141   The sum of the last 4 integers can be expressed and simplified as:   x+4 + x+5 + x+6+ x+7 = 4x + 22   Substituting 141 for x yields:   (4)(141) + 22 = 586   Answer: 586
Answer: C
How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 7?  Choose the correct choice from the following answers:	A) 4	B) 5	C) 6	D) 7	E) 8

Solution: 6   Highest two digit number divisible by 7 is 63, so we count down the correct answers from there and see if they are feasible.   63 -yes   56 -yes   49 -no   42 - yes   35 - yes   28 - no   21 - yes   14- yes   6orrect answer is 6.
Answer: C
Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 12 days. How many additional pipes, each draining water at the same constant rate, will be needed to drain the pool in 3 days?	Pick one
A) 6	B) 9	C) 10	D) 12	E) 15

Solution: This is an inverse proportional problem......   5 pipes in 12 days; So for 3 days, it will be = 12 x 5 / 3 = 20   So, 20-5 = 15   Answer 15
Answer: E
Two circles with centres P and Q cut each other at two distinct points A and B. The circles have the same radii and neither P nor Q falls within the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees?  Choose the correct choice from the following answers
A) Between 0 and 90  B) Between 0 and 30  C) Between 0 and 60  D) Between 0 and 75  E) Between 0 and 45

Solution: Explanation :   It says P&Q falls outside the intersection area of the circle.   The maximum point where P&Q can be in the circle is represented by the 2 small dashes P1 and Q1, when they can be on the circumference of the other circle.   Suppose P & Q are on the circumference of the other circle. (Represented by P1 and Q1)   Then AP1 = r1 (Radius of 1st circle)   AQ1 = r2 (Radius of 2nd circle)   Also P1Q1 = r1 = r2 (As radius of both the circles are same)   So AP1 = AQ1 = P1Q1. Hence ∆AP1Q1 is equilateral, and ∠AQ1P1 = 600.   Suppose P1 and Q1 drift away from the circle, and are at the points P&Q represented in the diagram. Then the value is definitely less than 600.   If P and Q are collinear with A, then the angle is 0(0).   So, the maximum value is 600, and minimum 0(0)   Answer : Between 0 and 60
Answer: C
Divide $2000 among B,C in the ratio 4:16. How many $ that C get?
Choose the correct choice
A) $1200 B) $1400 C) $1600 D) $1800 E) $2000

Solution: Sum of ratio terms = 4+16= 
4+16 = 20
20   $1600= 2000*16/20= 
2000*16/20 = 1_600
$1600   Answer is $1600
Answer: C
A container has 3L of pure wine. 1L from the container is taken out and 2L water is added.The process is repeated several times. After 19 such operations, qty of wine in mixture is	Choose one
A) 2/7 L
B) 3/7 L
C) 6/19L
D) 7/23L
E) 8/25L

Solution: First operation: 3L-1L=23 -1= 
3 -1 = 2
2=6/3L of wine left, total 4L;   #2: 6/3L-(6/3)/4=6/3-6/12=18/12=6/4L of wine left, total 5L;   #3: 6/4L-(6/4)/5=6/4-6/20=24/20=6/5L, total 6L;   #4: 6/5L-(6/5)/6=6/5-6/30=30/30=6/6L, total 7L;   ....   2/7 Lt this point it's already possible to see the pattern: x=6/(n+2)   n=19 --> x=6/(19+2)=6/21=2/7L   2/7 Lnswer: 2/7 L.
Answer: A
A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 1/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?	Choose the correct choice:  A) 7/16  B) 7/15  C) 10/21  D) 17/35  E) 1/10

Solution: Let the total # of cups be 10.   # of small cups sold 3/5*10= 
3/5*10 = 6
6;   # of large cups sold  10-6= 
 10-6 = 4
4;   Let the price of small cup be $6, then the price of larges cup would be 1/6*6= 
1/6*6 = 1
$1;   Revenue from small cups: 6*$6=$36;   Revenue from large cups cups: 4*$1  6* 6= 
  6* 6 = 36
$36;   Revenue from large cups cups: 4*$1=$4;   Fraction of total revenue from large cups: 4/(36+4) 4* 1= 
 4* 1 = 4
$4;   Fraction of total revenue from large cups: 4/(36+4)=1/10.   Answer: 1/10.
Answer: E
If it would take one machine 6 minutes to fill a large production order and another machine 8 minutes to fill the same order, how many minutes would it take both machines working together, at their respective rates, to fill the order?	Pick one.
A) 2 1/60
B) 3 3/7
C) 5 5/11
D) 5 1/2
E) 11

Solution: Since , Machine 1-M1 take 6 mins to fill the order   The work done by M1 in a min = 1/6   Machine 2- M2 take 8 mins to fill the same order   and work done by M2 in a min = 1/8   Total work done by M1 and M2 in a min = 1/6 + 1/8 = 7/24   Time needed for M1 and M2 to complete the order = 24/7 = 3 3/7   Answer 3 3/7
Answer: B
Mona and Donald fly to Rome for the weekend. They take cash only in notes of $10 and notes of €10. Mona carries three times the amount of euros Donald carries. She also carries as many dollars as Donald carries. The number of €10 notes they take is double the number of $10 notes they take. If Donald carries a total of 45 notes (of either $10 or €10,) then what is the total number of notes (of either $10 or €10,) they take?	Choose the correct choice from the following options:
A) 70 B) 80 C) 150 D) 120 E) 140

Solution: .let e10 =x no. d10 =y no. donald is having x+y notes mona carries 3x+y again x =2y or donald x+y =45   or 3y =45 y =15 ;x =30 , total notes they carry = 4x+2y = 120+30= 
120+30 = 150
150   150
Answer: C
A frog can climb up a well at 3 ft per min but due to slipperiness of the well, frog slips down 2 ft before it starts climbing the next minute. If the depth of the well is 57 ft, how much time will the frog take to reach the top?
Options.
A) 29
B) 27
C) 55
D) 17
E) 10

Solution: Explanation:   As per given, in 1 min,frog climbs up 3 ft and slips down by 2 ft.   So the frog climbs only 1 ft in 1 min   So after 54 mins,it would have climbed 54ft.   At the end of 55 mins it climbs up 3 ft to make it 57 ft and come out of the well.   Once it had reached the destination,it will not slip.   So the frog will take only 55 minutes to climb up the well.   Answer: 55
Answer: C
If xy = 5 and x^2 + y^2 = 20, then x/y + y/x =  Choose the correct choice from the following choices.
A) 2 2/5
B) 3 1/7
C) 5 1/3
D) 4
E) 60

Solution: x/y+y/x=(x^2+y^2)/xy =substitute given we get 20/5= 
20/5 = 4
4 answer 4
Answer: D
If 20 men can build a wall 66 metres long in 6 days, what length of a similar can be built by 86 men in 8 days?  Choose the correct choice from the following.
A) 49.5m
B) 46 m
C) 49 m
D) 46.5m
E) 45 m

Solution: Let the required length be x metres   More men, More length built (Direct Proportion)   Less days, Less length built (Direct Proportion)   Men 20: 35   Days 6: 3 : : 56 : x   Therefore (20 x 6 x x)=(35 x 3 x 56)<=>x=(35 x 3 x 56)/120=49   Hence, the required length is 49 m.   Answer is 49 m.
Answer: C
The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 300 m, its area is?	Pick one:
A) 150	B) 882	C) 277	D) 261	E) 281

Solution: 5x + 12x + 13x = 300 => x = 10   a = 50, b = 120, c = 130   S = (50 + 120 + 130)/2= 
(50 + 120 + 130)/2 = 150
150   150nswer: 150
Answer: A