MU-NLPC/Calc-aqua_rat huggingface dataset:
Valentine day 14 Feb. 2005 was celebrated by Anand and shilpa on Monday. They were very happy. What day of the week would come on 14 Feb. 2011? Choose the correct choice from the following answers:
A) monday
B) tuesday
C) sunday
D) wednesday
E) thursday

Solution: feb 14 2005 - monday   feb 14 2006 - tuesday   feb 14 2007 - wednesday   feb 14 2008 - thursday   feb 14 2009 - saturday [since 2008 is leap year , 2 days ll go forward]   feb 14 2010 - sunday   feb 14 2011 - monday   Feb 14 2012 - Tuesday   ANSWER:tuesday
Answer: B
A Fisher man can row 4 km against the stream in 30 minutes and returns in 20 minutes. What is the speed of the current?	Choose the correct option.
A) 1 km/hr  B) 2 km/hr  C) 3 km/hr  D) 4 km/hr  E) 5 km/hr

Solution: Explanation:   Speed up stream = (4/30) × 60 = 8 km/hr   Speed down stream = (4/20) × 60 = 12 km/hr   Speed of current = 1/2 (12 - 8) = 4/2= 
4/2 = 2
2 km/hr   Answer: Option 2 km/hr
Answer: B
An automobile financier claims to be lending money at simple interest, but he includesthe interest every six months for calculating the principal. If he is charging an interest of10%, the effective rate of interest becomes: Choose the correct choice from the following options.
A) 10%  B) 10.25%  C) 10.5%  D) none of these  E) Cannot be determined

Solution: Explanation:   Let the sum be Rs. 100. Then,   S.I. for first 6 months = Rs.[ (100 x 10 x 1)/(100 x 2) ]= Rs.5   S.I. for last 6 months =Rs.[(102 x 10 x 1)/(100 x 2) ] = Rs.5.25   So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25   Effective rate = (110.25 - 100)= 
(110.25 - 100) = 10.25
10.25%   Answer: 10.25%
Answer: B
The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?	Choose the correct choice:
A) 345  B) 340  C) 342  D) 346  E) 341

Solution: 400*(90/100)*(95/100)= 
400*(90/100)*(95/100) = 342
342   Answer:342
Answer: C
If 5 parallel lines in a plane is intersected by a family of another 8 parallel lines, how many parallelograms are there in the network thus formed?
Choose the correct choice from the following answers
A) 280  B) 63  C) 120  D) 160  E) 1260

Solution: parallelogram can formed by 2 horizontal and 2 vertical lines   for horizontal 5c2   for vertical 8c2   total parallelogram is 5 c2*8c2=10*28= 
10*28 = 280
280   280NSWER:280
Answer: A
A man invests Rs. 5,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum? Choose the correct choice from the following:
A) Rs. 1200 B) Rs. 1300 C) Rs. 2500 D) Rs. 2000 E) None of these

Solution: Explanation :   Interest on Rs.5000 at 5% per annum = ( 5000 × 5 × 1) / 100 = Rs. 250   Let his additional investment at 8% = x   Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25.   To earn 6% per annum for the total, interest = (5000 + x) × 6 × 1/100.   => 250 + 2x/25 = (5000 + x) × 6 × 1/100.   => 25000 + 8x = (5000 + x) × 6.   => 25000 + 8x = 30000 + 6x.   => 2x=5000.   => x=2500.   Answer : Rs. 2500
Answer: C
The probability that a number selected at random from the first 50 natural numbers is a composite number is ? Choose the correct option
A) 17/28 B) 17/25 C) 17/17 D) 17/19 E) 17/12

Solution: The number of exhaustive events = ⁵⁰C₁ = 50.   We have 15 primes from 1 to 50.   Number of favourable cases are 34.   Required probability = 34/50   = 17/25.   Answer:17/25
Answer: B
A train is 360 meter long is running at a speed of 47 km/hour. In what time will it pass a bridge of 140
meter length.  Pick one:
A) 28.3 seconds
B) 38.3 seconds
C) 48.3 seconds
D) 58.3 seconds
E) None of these

Solution: Explanation:   Speed = 47 Km/hr = 47*(5/18) m/sec   = 25/2 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= Distance/speed   =500/ 13 = 38.3 seconds   Answer: 38.3 seconds
Answer: B
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 3 kmph, what time will he take to cover 100 metres?	Select the correct option
A) 18  B) 17  C) 22  D) 20  E) 13

Solution: Speed of the boat downstream = 15 + 3= 
15 + 3 = 18
18 kmph= 18 * 5/18= 
18 * 5/18 = 5
5 m/s   Hence time taken to cover 100 m= 100/5= 
100/5 = 20
20 seconds.   Answer: 20
Answer: D
On dividing a certain number by 5, 7 and 8 successively, the remainders obtained are 2, 3 and 4 respectively. When the order of division is reversed and the number is successively divided by 8, 7 and 5, the respective remainders W will be:[/b]  Pick
A) 3, 3, 2
B) 3, 4, 2
C) 5, 4, 3
D) W=5, 5, 2
E) W=6, 4, 3

Solution: Let the original number be X. Then by the successive dividing we have followings :   X=5A+2   A=7B+3   B5 +2= 
5 +2 = 7
7B+3   B=8C+4.   So we have A=7*(8C+4)+3=7*8C+31, and X=5*(7*8C + 31)+2 = 5*7*8C + 157.   Now by dividing X by 8, 7, 5 successively we have followings :   X=8*(5*7C+19)+5   5*7C+19=7*(5C+2) + 5   5C+2=5C+2.   The remainders are, therefore, 5, 5, 2.   The answer is (W=5, 5, 2).
Answer: D
One boss decided to increase the salary of an employee by 5%. How much will he get if his salary was Rs.2000? Choose one:  A) 2200  B) 2000  C) 2100  D) 2300  E) None

Solution: Solution:   Actual salary is 2000 Rupees   5 % of 2000 = 2000 *5/100= 
2000 *5/100 = 100
100   So 100 Rupees increased=2000+100= 
2000+100 = 2_100
2100   He will get salary of 2100   Answer 2100
Answer: C
Sonika bought a V.C.R. at the list price of 18,800. If the rate of sales tax was 8%, find the amount she had to pay for purchasing the V.C.R.  Choose the most appropriate option.
A) 20,304
B) 19,780
C) 19,680
D) 19,380
E) None of these

Solution: Sol. List price of V.C.R. =18,800   Rate of sales tax = 8%   ∴ Sales tax = 8% of 18,800   = 8⁄100 × 18800 = 1504   So, total amount which Sonika had to pay for purchasing the V.C.R. = 18,800 + 1504   = 20,304. 20,304nswer 20,304
Answer: A
A certain quantity of 50% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?  Choose the correct choice from the following choices
A) 1/4  B) 1/3  C) 1/2  D) 2/3  E) 3/5

Solution: Let's say that the total original mixture A is 100 ml   The original mixture A thus has 50 ml of alcohol out of 100 ml of solution   You want to replace some of that original mixture A with another mixture B that contains 25 ml of alcohol per 100 ml. Thus, the difference between 50 ml and 25 ml is 25 ml per 100 ml of mixture. This means that every time you replace 100 ml of the original mixture A by 100 ml of mixture B, the original alcohol concentration will decrease by 25%. The question says that the new mixture, let's call it C, must be 35% alcohol, a decrease of only 15%. Therefore, 15 out of 25 is 3/5 and 3/5 is the answer.
Answer: E
The average age of a committee of 8 members is 52 years. A member aged 65 years retired and his place was taken by another member aged 42 years . The average age of
present committee is;  Choices
A) 39 years  B) 38 years  C) 36 years  D) 35 years  E) 49.1 years

Solution: Total age of the committee = 52*8= 
52*8 = 416
416,   Total age when a member is retired   and a new one was joined= 416-65 +42, =393   Average age of present committee = 393/8 = 49.1.   ANSW49.1 yearsR:49.1 years
Answer: E
The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?	Choose the correct option
A) 87 m	B) 17 m	C) 26 m	D) 28 m	E) 78 m

Solution: Let the breadth of the plot be b m.   Length of the plot = 3 b m   (3b)(b) = 867   3b2 = 867   b2 = 289 = 172 (b > 0)   b = 17 m.   Answer: 17 m
Answer: B
There are 25 balls which are red, blue or green. If 8 balls are blue and the sum of green balls and blue balls is less than 17, at most how many green balls are there? Choices:
A) 8  B) 5  C) 6  D) 7  E) 10

Solution: r+g+b=25   b=8   b + g < 17   => 8 + g < 17   => g < 9   => at most 8 green balls   8NSWER:8
Answer: A
An outlet pipe can empty 2/3 of a cistern in 20 minutes. In 8 minutes, what part of the cistern will be emptied?	Choose the correct choice from the following answers.
A) 1/2
B) 1/3
C) 2/9
D) 4/15
E) 9/20

Solution: 8/20 * 2/3 = 4/15   The answer is 4/15.
Answer: D
A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 45 times, A has killed:
Choose one:	A) 50 birds	B) 72 birds	C) 30 birds	D) 80 birds	E) 20 birds

Solution: Let the total number of shots be x. Then,   Shots fired by A =(5/8)x   Shots fired by B =(3/8)x   Killing shots by A =(1/3)of	(5/8)x=(5/24)x   Shots missed by B =(1/2) of (3/8)x	=(3/16)x   3x/16= 45 or x =(45 x 16)/3= 240.   Birds killed by A =(5x/24)	=(5/24*240)= 
(5/24*240) = 50
50.   50 birdsnswer is 50 birds
Answer: A
Each light bulb at a hotel is either incandescent or fluorescent. At a certain moment, thirty percent of the incandescent bulbs are switched on, and eighty percent of the fluorescent bulbs are switched on. If 40 percent of all the bulbs are switched on at this moment, what percent of the bulbs that are switched on are incandescent?	Choose one.
A) 20% B) 40% C) 50% D) 60% E) 80%

Solution: Let I be the number of incandescent bulbs.   Let F be the number of fluorescent bulbs.   0.3I + 0.8F = 0.4(I+F)   0.4F = 0.1I   F = 0.25I   This means that for every 4 incandescent bulbs, there is 1 fluorescent bulb.   The percent of bulbs that are switched on which are incandescent is:   0.3I / (0.3I + 0.8F) = 0.3I / (0.3I + 0.8*0.25I) = 0.3I / 0.5I = 3/5 = 60%.   The answer is 60%.
Answer: D
Three math classes: X, Y, and Z, take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score of all students in classes X and Y together is 79. The average score of all students in classes Y and Z together is 81. What is the average for all the three classes? Choose the correct choice from the following choices: A) 60.3 B) 70.3 C) 81.3 D) 85.3 E) 94.3

Solution: X = 83   Y =76   Z =85   so to find the average of x,y,z   (x+y+z)/3=244/3   ans is 81.33   ANSWRE:81.3
Answer: C
In a group of 70 people,60 like swimming,50 like wrestling. How many like both swimming and wrestling?  Pick: A) 30 B) 35 C) 40 D) 45 E) 50

Solution: Make a Venn diagram, and enter your data.   Let the number of people who like both swimming and wrestling be x   60-x+x+50-x = 70   x = 40   so number who like both swimming and wrestling = 40   Answer 40
Answer: C
Tough and Tricky questions: Coordinate Geometry.
Line L contains the points (2,3) and (e,q). If q = 2, which of the following could be the equation of line m, which is perpendicular to line L?
Select:
A) 2x + y = ex + 7	B) 2x + y = –ex	C) x + 2y = ex + 7	D) y – 7 = x ÷ (e – 2)	E) 2x + y = 7 – ex

Solution: we need m=e-2, so we should gety=mx+bform in answer choices   (A) 2x+y=ex+7 => y=ex-2x+7 => y=x(e-2)+7. It is what we need   (B) 2x + y = –ex => y=-ex-2x => y=x(-e-2). Wrong   (C) x + 2y = ex + 7 => y=x(e-1/2)+7/2. Wrong   (D) y – 7 = x ÷ (e – 2) => y=(1/e-2)x+7. Wrong   (E) 2x + y = 7 – ex => y=-ex-2x+7 => y=x(-e-2)+7. Wrong   2x + y = ex + 7
Answer: A
A group of hikers is planning a trip that will take them up a mountain using one route and back down using another route. They plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up, but the time each route will take is the same. If they will go up the mountain at a rate of 3 miles per day and it will take them two days, how many miles long is the route down the mountain?  Choose the correct choice from the following answers.
A) 7	B) 8	C) 9	D) 10	E) 11

Solution: On the way down, the rate is  1.5*3= 
 1.5*3 = 4.5
4.5 miles per day.   The distance of the route down the mountain is   2*4.5= 
  2*4.5 = 9
9 miles.   The answer is 9.
Answer: C
A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?  Choose the most appropriate option:
A) 2.91 m
B) 3 m
C) 5.82 m
D) 4.65 m
E) None of these

Solution: Area of the park = (60 x 40) m2 = 2400 m2.   Area of the lawn = 2109 m2.   Area of the crossroads = (2400 - 2109) m2 = 291 m2.   Let the width of the road be x metres. Then,   60x + 40x - x2 = 291   x2 - 100x + 291 = 0   (x - 97)(x - 3) = 0   Answer: Option 3 m   x = 3.
Answer: B
A man is facing west. He turns 45 degree in the clockwise direction and then another 180 degree in the same direction and then 270 degree in the anticlockwise direction. Find which direction he is facing now ?  Answers.
A) south-west B) west C) south D) east-south E) east

Solution: Please refer to the explanation image.   The man firstly faces the direction OA. On moving 45 degree clockwise[Please check carefully always if clockwise or anticlockwise], he faces the direction OB.   Now again he moved 180 degree clockwise, now he will be facing OC. From here he moved 270 degree anticlockwise, Finally he is facing OD, which is South west.   south-westNSWER south-west
Answer: A
It is required to seat 5 boys and 4 girls in a row so that the girls occupy the even places. How many such arrangements are possible?	Choose the correct choice from the following options.
A) 2880	B) 2148	C) 3680	D) 3280	E) 3680

Solution: Total number of candidates = 5 + 4= 
5 + 4 = 9
9. In the row of 9 positions, the even places are 2nd, 4th, 6th and 8th.   Now, number of even places= 4.   Number of girls to occupy the even places = 4.   Even places can be filled = P (4, 4) ways.   Number of boys = 5.   The remaining 5 places can be filled by 5 boys = P (5, 5) ways   By the fundamental principle of counting:   The required number of seating arrangements   P(4, 4) x P(5, 5) = 4! x 5! = 24 x 120 = 2,880   2880NSWER:2880
Answer: A
The polynomial P(x) = x4 + 4x3 + 8x2 + 8x + 4 is the square of another polynomial Q(x) =
ax2 + bx + c with positive coecients a, b, and c. Compute 4a + 2b + c.	Choose the correct answer:
A) 2  B) 4  C) 6  D) 8  E) 10

Solution: Note that Q(2) = 4a+2b+c and P(2) = [Q(2)]2 = 24+4*23+8 * 22+8* 2+4 = 100.   Since a, b, and c are positive, we have Q(2) > 0. Taking the positive square root, we get   Q(2) =√P(2) =√100 = 10 .   correct answer 10
Answer: E
96 +97+98+99=390. How many such 4 consecutive numbers are there less than 5000 when added gives a sum which is divisible by 10?  Options.
A) 100  B) 300  C) 500  D) 1000  E) 1500

Solution: since 1+2+3+4= 
1+2+3+4 = 10
10 & 6+7+8+9= 
6+7+8+9 = 30
30   any combination with these no be will give u desirable result...   so total no in 100 will be 20 & that's why in in 5000,it will be 1000   ANSWER:1000
Answer: D
The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is: Choices
A) 1500 B) 3900 C) 2600 D) 3100 E) 7400

Solution: Explanation:   Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.   Then, 10x =4y or y=5/2x.   15x + 2y = 4000   15x + 2 x	5/2x = 4000   20x = 4000   x = 200.   So, y =5/2x 200= 500.   Hence, the cost of 12 chairs and 3 tables = 12x + 3y   = Rs. (2400 + 1500)   = Rs. 3900.   Answer is 3900
Answer: B
Let q represent the integer length of a side of a triangle. If r represents the number of distinct values for q such that we can create a triangle with lengths q, 14, and 19, what is the value of r?	Choose one:
A) 20	B) 21	C) 26	D) 27	E) 33

Solution: From the triangle inequality rule, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, the three inequalities are:   1. q + 14 > 19   2. 14 + 19 > q   3. q + 19 > 14   Equation 3 is true for any positive value of q.   From equation 1, q > 5   From equation 2, 33 > q   Then 33 > q > 5 so q can be any value from 6 to 32 inclusive.   The number of possible values is 27.   The answer is 27.
Answer: D
If 6 persons can do 6 times of a particular work in 6 days, then, 7 persons can do 7 times of that work in? Choose the correct choice:
A) 3 days	B) 4 days	C) 6 days	D) 7 days	E) 8 days

Solution: That is, 1 person can do one time of the work in 6 days.   Therefore, 7 persons can do 7 times work in the same 6 days itself   6 days)
Answer: C
A baker filled with a measuring cup with 7/8 cup water. He poured 1/2 of the water into the batter, and then spilled 1/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?	Choose the correct choice from the following answers
A) 1/8 cup
B) 3/8 cup
C) 1/4 cup
D) 1/2 cup
E) 8/8 cup

Solution: 3/4 is the original water in cup .half in batter.So left is 3/8 out which 1/8 is spilled out.So again left with 2/8.   so 50% more than what he started was = 7/8+1/2*(3/4)=10/8   Amount of water needed to add = 10/8 - 2/8=8/8   ANSW8/8 cupR:8/8 cup
Answer: E
. By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?  Options.
A) 8
B) 7
C) 5
D) 3
E) 1

Solution: Explanation:   80% --- 12   120% --- ?     80/120 * 12= 
  80/120 * 12 = 8
8   8nswer:8
Answer: A
On an order of 5 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of:  Choose one.
A) 18 1/6%	B) 16 2/3%	C) 10 2/3%	D) 29 1/3%	E) 16 2/3%

Solution: E   Clearly, the retailer gets 1 dozen out of 6 dozens free.   16 2/3%quivalent discount = 1/6 * 100 = 16 2/3%.
Answer: E
What is the next number of the following sequence
12, 6, 24, 12, 48, 24, (...)
Choose the correct option:
A) 66  B) 72  C) 84  D) 96  E) 102

Solution: The series is   12/2= 
12/2 = 6
6   6*4= 
6*4 = 24
24   24/2= 
24/2 = 12
12   12*4= 
12*4 = 48
48   48/2= 
48/2 = 24
24   24*4= 
24*4 = 96
96   ANSWER: 96
Answer: D
Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 16. What is the value of x?	Select:
A) 20
B) 40
C) 80
D) 160
E) 320

Solution: y = 0.5*0.5*x = x/4   y%*x = 16   (y/100)*x = 16   (x/400)*x = 16   x^2 = 16*400   x = 80   The answer is 80.
Answer: C
Each week, Harry is paid X dollars per hour for the first 30 hours and 1.5X dollars for each additional hour worked that week. Each week, James is paid X dollars per hour for the first 40 hours and 2X dollars for each additional hour worked that week. Last week James worked a total of 56 hours. If Harry and James were paid the same amount last week, how many hours did Harry work last week?	Answers.
A) 35	B) 36	C) 37	D) 38	E) 58

Solution: Amount earned by James = 40*x + 16*2x = 72x   Therefore, Amount earned by Harry = 72x   But we know the amount Harry earned assuming working y hours (y>30) is 30*x + (y-30)*1.5x   [[We know y>30 because in 30h the most Harry could earn is 30x, but he has earned 72x]]   So x*(1.5y -45 +30) = 72x   Or x*(1.5y - 15) = 72x   So 1.5y - 15 = 72   So 1.5y = 87   So y = 58   Answer is 58
Answer: E
On average, activated yeast cells divide once every 120 minutes; that is, each individual cell divides into two individual cells over that time span. Given that a certain yeast colony consisted of 110,000 cells two hours ago, approximately how many cells will be populating the colony six hours from now? Choose the correct choice from the following choices
A) 77,500 B) 1,760,000 C) 2,480,000 D) 3,720,000 E) 4,960,000

Solution: 110,000 × 2 × 2×2×2 = 110,000 × 16 = 1,760,000
Answer: B
The area of a circular field is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 5 per metre approximately Choose the correct choice:	A) 4457	B) 4567	C) 4235	D) 4547	E) 7429

Solution: Explanation:   Area = (17.56 x 10000) m2= 175600 m2.   ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m.   Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m.   Cost of fencing = Rs. (1485.78 x 5) = Rs. 7429.   Answer: Option 7429
Answer: E
There are 3 identical pens and 5 identical books. In how many ways can a person select at least one object from this set?
Choose one
A) 23 B) 25 C) 31 D) 15 E) 45

Solution: total ways = 6*4=24..   But we are looking for ATLEAST 1, so subtract 1 way when both are 0..   ans 24-1=23..   23nswer is 23
Answer: A
Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 36 kilometers, Maxwell's walking speed is 2 km/h, and Brad's running speed is 4 km/h. What is the distance traveled by Maxwell when they meet in the middle?  Answers:
A) 10 B) 11 C) 12 D) 13 E) 9

Solution: Consider Max starts from Point A and Brad Starts from Point B and move towards each other.   Assume they shall meet at point O after Time 'T'. The question asks us to find OA.   From the question stem we can make out :- Distance OA = 50km - Distance OB   => 2xT = 36 - 4xT (i.e distance =Speed x Time)   => 6T = 36   Hence T = 6   OA = 2 x 6 = 12 Km   Answer : 12
Answer: C
The output of a factory was increased by 5% to keep up with rising demand. To handle the holiday rush, this new output was increased by 20%. By approximately what percent would the output now have to be decreased in order to restore the original output?
Choose the correct choice from the following answers:
A) 20%  B) 24%  C) 30%  D) 32%  E) 79%

Solution: The original output increases by 5% and then 20%.   Total % change = a + b + ab/100   Total % change = 5 + 20 + 5*20/100= 
5 + 20 + 5*20/100 = 26
26%   Now, you want to change it to 0, so,   0= 26 + x + 26x/100   x = -26(100)/126 = 20% approximately   20%nswer is 20%
Answer: A
Three grades of milk are 1 percent, 2.7 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2.7 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 2.5 percent grade, what is x in terms of y and z?	Choose the correct choice from the following answers:
A) y + 3z  B) (y +z) / 4  C) 2y + 5z  D) 3y + z  E) 3y + 4.5z

Solution: Based on the given information, the following equation could be dervied: 1% * x + 2.7% * y + 3% * z = 2.5% * (x+y+z) [equation*].   Then use algebra to figure out 1.5%*x = 0.2%*y + 0.5%*z. Thus, 15x = 2y + 5z.   2y + 5z
Answer: C
A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?	Choose the correct choice:
A) 87 liters
B) 17 liters
C) 10 liters
D) 17 liters
E) 16 liters

Solution: Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150= 
20/100 * 150 = 30
30 liters.   P liters of water added to the mixture to make water 25% of the new mixture.   Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).   (30 + P)= 25/100 * (150 + P)   120 + 4P = 150 + P => P = 10 liters.   Answer: 10 liters
Answer: C
The diagonal of a square is 4 ?2 cm. What will be the diameter of another square if their area is double that of the first square?  Select:
A) 8cm B) 9cm C) 10cm D) 11cm E) 12cm

Solution: d1=4 ? 2 => area = 1/2d12=1/2 * (4 ? 2)2 = 16cm2   8cmrea of new square = (2*16)cm2 = 32 cm2   Therefore 1/2*d22=32 =>d22=64 => d2=8cm   8cmnswer 8cm
Answer: A
A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance Q that he will have a matched pair?	Choose one:  A) Q=2/5  B) Q=3/5  C) Q=1/5  D) 1/2  E) 7/5

Solution: P(both doves) + P(both rabbits) = p(matched pair)   (3/5)*(2/4) + (2/5)*(1/4) = 2/5   Hi How did you get the probability 2/4 and 1/4???   You have 3 doves and 2 rabbits i.e. a total of 5 animals.   The probability that you pick a dove on your first pick is 3/5 (since there are 3 doves)   The probability that you pick a dove on your second pick too is 2/4 (because now only 2 doves are left after we picked a dove in the first pick. ALso only 4 animals are left to choose from)   Similarly,   The probability that you pick a rabbit on your first pick is 2/5 (since there are 2 rabbits)   The probability that you pick a rabbit on your second pick too is 1/4 (because now only 1 rabbit is left after we picked a rabbit in the first pick. Q=2/5lso only 4 animals are left to choose from)   Probability of picking a matched pair = 3/5 * 2/4 + 2/5 * 1/4 = 2/5
Answer: A