MU-NLPC/Calc-aqua_rat huggingface dataset:
If a real number x is chosen at random in the interval [0,4] and a real number y is chosen at random in the interval [0,6], what is the probability that x < y?  Choose the correct choice from the following answers:  A) 2/5  B) 3/5  C) 2/3  D) 3/10  E) 7/10

Solution: Since x is in [0,4] and y is in [0,6] we can draw a rectangle in the coordinate plane with vertices (0, 0), (4, 0), (0, 6), and (4, 6).   The points above the line y=x satisfy x < y.   The part of the rectangle below y=x has an area of 8.   The whole rectangle has an area of 24.   P(x < y) = (24-8)/24 = 16/24 = 2/3   The answer is 2/3.
Answer: C
Mike, Jim and Bob are all professional fisherman. Mike can catch 30 fish in one hour, Jim can catch twice as much and Bob can catch 50% more than Jim. If the three started to fish together and after 40 minutes Mike and Bob left, how many fish did the three fishermen catch in one hour?  Choose the correct choice from the following answers.
A) 110	B) 120	C) 140	D) 130	E) 112

Solution: All of them catch fishes in relation to number 30....   2/3*30+2*30+2*1.5*30*2/3= 
2/3*30+2*30+2*1.5*30*2/3 = 140
140   Answer is 140
Answer: C
A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 135 km downstream Choose the correct option
A) 5 hours
B) 4 hours
C) 3 hours
D) 2 hours
E) None of these

Solution: Explanation :   Speed of the boat in still water = 22 km/hr   speed of the stream = 5 km/hr   Speed downstream = (22+5)= 
(22+5) = 27
27 km/hr   Distance travelled downstream= 135 km   Time taken = distance/speed = 135/27= 
135/27 = 5
5 hours. 5 hoursnswer : Option 5 hours
Answer: A
A tradesman by means of his false balance defrauds to the extent of 26%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?	Pick.
A) 58.76% B) 49.89% C) 84.67% D) 24.65% E) 45%

Solution: g% = 26 + 26 + (26*26)/100= 
26 + 26 + (26*26)/100 = 1_469/25 = around 58.76
58.76%   58.76%nswer: 58.76%
Answer: A
At a conference table, 5 employees gather around a table. One of the employees is the manager and he sits at the head of the table. Two of the employees sit on either side of the table. How many different seating arrangements can be made with these five employees?  Choose the correct choice from the following options:  A) 5  B) 10  C) 24  D) 32  E) 120

Solution: Head's sit is fixed. Now 4 people is left with 4 seats.   4 people can sit on 4 seats in 4! ways or 24 ways.   Ans is 24
Answer: C
How many positive four-digit integers do not contain any digits other than 1 or 0 and are such that the sum of the first two digits equals the sum of the last two digits?	Choose the correct choice from the following answers:  A) 3  B) 4  C) 8  D) 10  E) 12

Solution: The sum of the first two (last two) digits cannot be 0 because 0000 is not a four-digit integer. If the sum of the first two digits is 1, two variants are possible: 1001 and 1010 (we have to remember that 0 cannot be the first digit). If the sum of the first two digits is 2, one variant is possible: 1111. In all, there are three numbers that satisfy the given conditions: 1001, 1010, and 1111.   3nswer: 3
Answer: A
Find the area of region enclosed by | x | + | y | = 3  Choose the correct choice.
A) 18 B) 11 C) 28 D) 26 E) 91

Solution: We have to consider separately the form of the function w.r.t to where x, y lies.   x >0, y >0, x + y = 3   x > 0, y < 0, x - y = 3   x < 0, y >0, x - y = - 3   x < 0, y < 0, x + y = - 3   After having drawn the above 4 lines on the graph, the graph looks like aboe   Now the area of the graph = 4 right angle triangles.   18rea of the right angle triangle = 12×3×3=9212×3×3=92   18rea of the entire region = 92×492×4 = 18 units   18nswer:18
Answer: A
The mean of four integers W will not change if all the integers are multiplied by any constant. What is always true about this set of numbers?
I. The mean of the set is 0
II. The sum of the largest member and the smallest member of the set is 0
III. The set contains both positive and negative integers
Choose the correct choice from the following choices:	A) I only	B) II only	C) III only	D) I and II only	E) I, II, and III

Solution: If we consider a set {1,2,3,4}, when multiplied with a constant we take that constant as 1 and multiply resulting set will contain the same numbers as the original. so how can the answer be I only.....I only
Answer: A
Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?
Choose the correct choice:	A) 1/3	B) 1/9	C) 1/4	D) 1/2	E) 1/6

Solution: 1/10 + 1/15 = 1/6 * 4 = 2/3   1 - 2/3 = 1/3   1/10 + 1/15 - 1/x = 1/3   x = 8.1/3nswer: 1/3
Answer: A
All the faces of cubes are painted with red colour.It is then cut into 64 equal small cubes.Find How many small cubes have no faces coloured ?  Answers.
A) 24
B) 8
C) 16
D) 0
E) 4

Solution: There are 64 small cubes,Hence one side side of the big cube is 3√64=4 cm   Number of small cubes having only one faces coloured = (x - 2)^3   Here, x = side of big cube / side of small cube   x = 4 /1= 
4 /1 = 4
4   Required number= (4 -2)^3   = 8   Answer :8
Answer: B
In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs.157300 was their profit, how much amount did B receive? Choose the correct choice.
A) 48400
B) 48000
C) 48100
D) 48500
E) 48600

Solution: 48400ssume that investment of C =x   Then, investment of 48400 =2x   Investment of B =4x/3   48400:B:C =2x:(4x)/3:x   =2:4/3:1=6:4:3   B's share =157300×4/(6+4+3)   =157300×4/13=12100×4=48400   48400nswer is 48400.
Answer: A
The profits of QRS company rose 10% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June? Choose the correct choice from the following choices.
A) 15% B) 32% C) 40% D) 62% E) 80%

Solution: We need multipliers.   multiplier for a 10% increases = 1 + 0.10= 
1 + 0.10 = 1.1
1.1   multiplier for a 20% decreases= 1 – 0.20 = 0.8   multiplier for a 50% increases = 1 + 0.50= 
1 + 0.50 = 1.5
1.5   Now, multiply these. First, multiply (0.8) and (1.5), using the doubling & halving trick. Half of 0.80 is 0.40, and twice 1.5 is 3   (0.8)*(1.5)= (0.4)*(3)= 
(0.4)*(3) = 1.2
1.2   Now, multiply this by 1.1   1.2*1.1= 
1.2*1.1 = 1.32
1.32   Thus, the three percent changes combined produce a 32% increase. Answer= (32%).
Answer: B
For what values of 'k' will the pair of equations 3x + 4y = 12 and kx + 12y = 30 NOT have a unique solution?  Choose the most appropriate option.
A) 12	B) 9	C) 3	D) 7.5	E) 2.5

Solution: Explanatory Answer   Condition for Unique Solution to Linear Equations   A system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a unique solution if the two lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at a point.   i.e., if the two lines are neither parallel nor coincident.   Essentially, the slopes of the two lines should be different.   What does that translate into?   ax + by + c = 0 and dx + ey + g = 0 will intersect at one point if their slopes are different.   Express both the equations in the standardized y = mx + c format, where 'm' is the slope of the line and 'c' is the y-intercept.   ax + by + c = 0 can be written as y = −abx−ca−abx−ca   And dx + ey + g = 0 can be written as y = −dex−ge−dex−ge   Slope of the first line is −ab−ab and that of the second line is −de−de   For a unique solution, the slopes of the lines should be different.   ∴ −ab≠−de−ab≠−de   Or ad≠bead≠be   Condition for the equations to NOT have a unique solution   The slopes should be equal   Or ad=bead=be   Apply the condition in the given equations to find k   In the question given above, a = 3, b = 4, d = k and e = 12.   Therefore, 3k=4123k=412   Or 'k' should be equal to 9 for the pair of equations to NOT have a unique solution.   When k = 9, the system of equations will represent a pair of parallel lines (their y-intercepts are different). So, there will be NO solution.   Answer 9
Answer: B
If two positive numbers are in the ratio 1/6 : 1/5, then by what percent is the second number more than the first?
Answers: A) 70% B) 90% C) 60% D) 50% E) 20%

Solution: Given ratio = 1/6 : 1/5 = 5 : 6   Let first number be 5x and the second number be 9x.   The second number is more than first number by 1x.   Required percentage = x/5x * 100 = 20%.   Answer:20%
Answer: E
Two trains of length 100 m and 200 m are 90 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
Choose the correct choice from the following options:  A) 21/9 sec  B) 32/3 sec  C) 18/7 sec  D) 32/3 sec  E) 53/2 sec

Solution: They are moving in opposite directions, relative speed is equal to the sum of their speeds.   Relative speed = (54 + 72)*5/18 = 7*5= 
7*5 = 35
35 mps.   The time required= d/s = 90/35 = 18/7 sec.   Answer:18/7 sec
Answer: C
If the annual increase in the population of a town is 10% and the present number of people is 14000, what will the population be in 2 years?
Choose the correct answer:
A) 12100
B) 15240
C) 12456
D) 16940
E) 10002

Solution: The required population is = 14000 (1 + 10/100)^2   = 14000 * 11/10 * 11/10= 
14000 * 11/10 * 11/10 = 16_940
16940   Answer is 16940
Answer: D
A reduction of 30% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?  Pick:
A) s.42	B) s.46	C) s.48	D) s.41	E) s.34

Solution: 800*(25/100) = 240 ---- 5   ? ---- 1 => Rs.48   Answer: s.48
Answer: C
If a /2= b/3 = c/5, then the value of (a + b + c)/c is :	Pick one: A) 1/√5 B) √2 C) 2 D) 5 E) 6

Solution: a/2= b/3 = c/5 = k (say).   Then, a = 2k, b = 3k, c = 5k.   (a + b + c)/c = (2k + 3k + 5k)/5k   = 10k/5k   = 2.   ANSWER:210 /5= 
10 /5 = 2
2.   ANSWER:2
Answer: C
In how many of ways can 4 balls be placed in 5 tins if any number of balls can be placed in any tin? Choose the most appropriate option:  A) 5C4  B) 5P4  C) 54  D) 4^5  E) 5^4

Solution: Now, each of the 4 different balls has 5 choices (5 tins to go to), so total # of distribution is 5*5*5*5=5^4.   Answer: 5^4.
Answer: E
In how many ways Chief Minister and Minister be elected from a team of 12 members?  Choose the correct option:
A) 124  B) 131  C) 132  D) 145  E) 165

Solution: To do this, if captain is elected first, then we have 12 ways of doing this.   For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)   So, the ans is 12*11= 
12*11 = 132
132 ways.   132
Answer: C
When positive integer N is divided by positive integer J, the remainder is 26. If N/J = 150.40, what is value of J? Choices.
A) 75	B) 65	C) 60	D) 130	E) 30

Solution: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder   So, Dividend/Divisor = Quotient + Remainder/Divisor   Given that N/J = 150.40   Here 150 the quotient.   Given that Remainder = 26   So, 150.40 = 150 + 26/J   So, J = 65   Answer: 65
Answer: B
The ratio between the radii of two spheres is 1:3. Find the ratio between their volumes? Answers
A) 1:28  B) 1:27  C) 1:22  D) 1:21  E) 1:29

Solution: r1 : r2 = 1:3   r13 : r23 = 1:27   Answer: 1:27
Answer: B
The speed of a boat in still water is 20 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 21 minutes is:  Answers:
A) 9.75  B) 5.75  C) 8.75  D) 6.75  E) 5.15

Solution: Explanation:   Speed downstream = (20+5)= 
(20+5) = 25
25 kmph   Distance travelled= (25*(21/60))= 
(25*(21/60)) = 35/4 = around 8.75
8.75 km.   ANSWER:8.75
Answer: C
The simple form of the ratio 4/3:2/5 is?	Options:
A) 10:6
B) 10:3
C) 15:3
D) 25:3
E) 30:3

Solution: 4/3 : 2/5 = 20:6 = 10:3   ANSWER:10:3
Answer: B
During a sale, the price of a pair of shoes is marked down 15% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?	Choose the most appropriate option: A) 9% B) 10% C) 11% D) 18% E) 90%

Solution: Assume the price = 100   Price during sale = 85   Price after sale = 100   Percent increase = 15/85*100 = 18% approx.   Correct Option: 18%
Answer: D
The train 160 m long is running with a speed of 80 km/hr. In what time will it pass a man running in same direction with the speed of 8 km/hr. Choose the correct choice from the following answers: A) 16 seconds B) 8 seconds C) 15 seconds D) 6 seconds E) 28 seconds

Solution: Man and train are running in same direction,   Relative Speed = 80 - 8= 
80 - 8 = 72
72 kmph.= (72 * 5)/18= 
(72 * 5)/18 = 20
20 m/sec   Length of the train= 160 m.   Time taken to pass the man = 160/20= 
160/20 = 8
8 seconds.   Answer: Option 8 seconds
Answer: B
In a college, 70 percent of students study math, 75 percent of students study English, 85 percent study French and 80 percent study German.
Can you find out the percentage of students who study all 4 subjects ?
Select
A) 12%	B) 10%	C) 16%	D) 18%	E) 19%

Solution: 10%   10% of student study all four subjects.
Answer: B
If the perimeter of a rectangular garden is 950 m, its length when its breadth is 100 m is? Choose one:
A) 338 m
B) 778 m
C) 375 m
D) 276 m
E) 971 m

Solution: 2(l + 100)   = 950 => l   = 375 m   Answer:375 m
Answer: C
A man is walking at a speed of 10 km per hour. After every kilometre, he takes rest for 5 minutes. How much time will be take to cover a distance of 5 kilometres?  Pick one
A) 48 min.  B) 50 min.  C) 45 min.  D) 55 min  E) None of these

Solution: explanation   Rest time = Number of rest × Time for each rest   = 4 × 5 = 20 minutes   Total time to cover 5km   = (5⁄10 × 60)minutes + 20 minutes = 50 minutes   Answer 50 min.
Answer: B
A caterer ordered 200 ice-cream bars and 200 sundaes. If the total price was $200.00 and the price of each ice-cream bar was $0.40, what was the price of each sundae?
Choose the most appropriate option:
A) $0.60  B) $0.80  C) $1.00  D) $1.20  E) $1.60

Solution: Let price of a sundae = S   Price of ice cream bar = .4 $   200 * .4 + 200*S = 200   => 200*S = 200   => S =0.6   $0.60nswer $0.60
Answer: A
A card is drawn from a pack of 52 cards.The probability of getting a queen club or a king of heart?	Choices
A) 3/26 B) 1/26 C) 4/26 D) 6/26 E) 10/26

Solution: n(s)=52   Let e=event of getting a queen of club or a king of heart.   n(e)=2   P(e)=n(e)/n(s)   =2/52   =1/26   Option:1/26
Answer: B
Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety of tea in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, what is the price of the third variety per kg ?  Choose the correct choice: A) Rs.182.50 B) Rs.170.5 C) Rs.175.50 D) Rs.180 E) Rs.190

Solution: Explanation:   Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed in the ratio 1 : 1   So their average price   =(126 + 135)/2= 
(126 + 135)/2 = 261/2 = around 130.5
130.5   Hence let's consider that the mixture is formed by mixing two varieties of tea, one at Rs. 130.50 per kg and the other at Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. Now let's find out x   By rule of alligation,   (xâˆ’153):22.5=1:1   â‡’xâˆ’153=22.50   â‡’x=153+22.5= 
153+22.5 = 175.5
175.5   Answer IS Rs.175.50
Answer: C
M is a certain set of numbers with an average (arithmetic mean) of 10 and a standard deviation of 3. Q is a subset of M consisting of 5 terms. Exactly 80% of the numbers in Q are located within 2 standard deviations from the average of M. Which of the following could Q be?	Choose one
A) {3, 4, 5, 10, 14}
B) {4, 6, 7, 10, 12}
C) {3, 5, 5, 10, 17}
D) {1, 5, 7, 10, 18}
E) {5, 6, 7, 10, 12}

Solution: Exactly 80% of the numbers in Q, so 4 out of 5 numbers are from 10 - 2*{SD} = 4 to 10 + 2*{SD} = 16.   A. {3, 4,5, 10, 14} --> 4 numbers are in this range. Ok   B. {4,6, 7, 10, 12} --> all 5 numbers are in this range. Discard.   C. {3,5, 5, 10, 17} --> only 3 numbers are in this range. Discard.   D. {1,5, 7, 10, 18} --> only 3 numbers are in this range. Discard.   E. {5, 6, 7, 10, 12} --> all 5 numbers are in this range. Discard.   {3, 4, 5, 10, 14}nswer: {3, 4, 5, 10, 14}.
Answer: A
At a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint.Verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 35 liters of forest green to change it to Verdant green?	Pick one
A) 1/3
B) 2/3
C) 4/3
D) 35/3
E) 10/3

Solution: 35 liter of Forset green have 20 liter of blue and 15 liter of yellow   Suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is   Blue/yellow =20/(15+x) = ¾   45+3x=80 => x =35/3   Answer : 35/3
Answer: D
Which of these numbers is not divisible by 3? Choices.
A) 339 B) 342 C) 552 D) 1111 E) 672

Solution: One may answer this question using a calculator and test for divisibility by 3. However we can also test for divisibilty by adding the digits and if the result is divisible by3 then the number is divisible by 3.   3 + 3 + 9= 
3 + 3 + 9 = 15
15 , divisible by 3.   3 + 4 + 2= 
3 + 4 + 2 = 9
9 , divisible by 3.   5 + 5 + 2= 
5 + 5 + 2 = 12
12 , divisible by 3.   1 + 1 + 1 + 1= 
1 + 1 + 1 + 1 = 4
4 , not divisible by 3.   The number 1111 is not divisible by 3 the answer is 1111.
Answer: D
If (t-8) is a factor of t^2-kt-40, then k=
Choose the correct choice:
A) 16 B) 1 C) 2 D) 6 E) 14

Solution: t^2-kt-48 = (t-8)(t+m) where m is any positive integer.   if 48/8= 
48/8 = 6
6, then we know as a matter of fact that:   m= +6   and thus k = 8-6 = 1   t^2-kt-m = (t-a)(t+m) where a>m   t^2+kt-m = (t-a)(t+m) where a<m   t^2-kt+m = (t-a)(t-m)   t^2+kt+m = (t+a)(t+m)   1
Answer: B
A man buys a cycle for Rs. 1750 and sells it at a loss of 8%. What is the selling price of the cycle?	Select the correct option
A) s. 1090	B) s. 1610	C) s. 1190	D) s. 1202	E) s. 1092

Solution: S.P. = 92% of Rs. 1750 = Rs.	92	x 1750/100 = Rs. 1610   Answer: Option s. 1610
Answer: B
A train passes a station platform in 42 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? Choices:  A) 123  B) 166  C) 240  D) 157  E) 330

Solution: Speed = [54 * 5/18] m/sec = 15 m/sec.   Length of the train = (15 * 20)= 
(15 * 20) = 300
300 m.   Let the length of the platform be x meters.   Then, (x + 300) / 42= 15   x + 300 = 630   x = 330 m.   Answer: 330
Answer: E
The value of Underrot 72pi/9 + Underrot 4 is most nearly equal to which of the following integers? (Please refer to the picture below for the exact version of the question)	Pick one:
A) 27
B) 14
C) 18
D) 19
E) 21

Solution: Under root (72pi/9) ~ 25   Under root (4) = 2   Hence, 9+1 = 10 is the approx answer. 27 is the correct answer.
Answer: A
A boy swims downstream 91 km and upstream 21 km taking 7 hours each time, what is the speed of the boy in still water?
Choose the correct choice from the following answers.
A) 6 B) 7 C) 8 D) 9 E) 10

Solution: 91 --- 7 DS = 13   ? ---- 1   21 ---- 7 US = 3   ? ---- 1 M = ?   M = (13 + 3)/2= 
(13 + 3)/2 = 8
8   Answer:8
Answer: C
Pipes A and B can fill a tank in 5 hours and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in. Choices:	A) 3 9/5	B) 3 9/17	C) 3 7/5	D) 3 7/17	E) None of these

Solution: Explanation:   Net part filled in 1 hour =(1/5 + 1/6 - 1/12)   =17/60hrs   =3 9/17   Answer is 3 9/17
Answer: B
How many 7-letter words can be formed using the letters of the English alphabet that contain 2 different vowels and 5 different consonants?	Answers:
A) 4!*5c2 *21c2
B) 4!*5c3 *21c2
C) 5!*5c2 *21c2
D) 7!*5c2 *21c5
E) 6!*5c2 *21c2

Solution: combination for 2 vowels out of 5 = 5c2 ways   combination for 5 consonants of 21 = 21c5 ways   Additionally the arrangement can be = 7!   total arrangements =7!*5c2 *21c5   7!*5c2 *21c5
Answer: D
A box contains 90 nuts each of 100 gms and 100 bolts each of 150 gms. If the entire box weighs 35.5 kg., then the weight of the empty box is Choose the correct choice from the following answers:
A) 8
B) 9.5
C) 10
D) 11.5
E) 12

Solution: Let w(e) be weight of empty box.   Total weight = 35.5 Kg   Weight of nuts, w(n) = 90 * 100= 
90 * 100 = 9_000
9000gms= 9 kg   Weight of bolts, w(b) = 100 * 150= 
100 * 150 = 15_000
15000gms= 15 kg   Total weight = w(n)+w(b)+w(e)   w(e) = Total weight-w(n)-w(b)   => w(e) = 35.5-15-9= 
35.5-15-9 = 11.5
11.5 Answer : 11.5
Answer: D
January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008 ? Choose the correct choice from the following choices
A) Monday  B) Tuesday  C) wednesday  D) Sunday  E) None of these

Solution: Solution   The year 2007 is an ordinary year. So, it has 1 odd day.   1st day of the year 2007 was Monday.   1st day of the year 2008 will be 1 day beyond Monday.   Hence, it will be Tuesday. Answer Tuesday
Answer: B
a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. 4a = 2b = c, and a > 0.
What is the difference between the two greatest possible values of x?
Tip: Dont stop till you have exhausted all answer choices to arrive at the correct one.  Choices.
A) 124  B) 297  C) 394  D) 421  E) 842

Solution: Ratio of a:b:c= 1:2:4   Two possible greatest single digit values for c are 8 and 4   if c is 8, then x= 248   if c is 4, then x= 124   difference= 248-124= 
248-124 = 124
124   124 is the answer
Answer: A
If (c - a)/(c - b) = 1, then (5b - 2a)/(c - a) =  Choose one:	A) 0.5	B) 1	C) 1.5	D) 2	E) 6

Solution: Let's say c=3, b=2, a=2 so that our 1st expression holds true. Now, ibsert those numbers in the second expression and we'll get 6   Answer 6 (hopefully )))
Answer: E
Michael cashed a check for $1,300 and received only $10 and $50 bills in return. During the course of a day, he used 15 bills and then lost the rest of the money. If the number of $10 bills used was either one more or one less than the number of $50 bills used, what is the minimum possible amount of money that was lost?	Pick:
A) $830
B) $800
C) $770
D) $730
E) $700

Solution: 1. 15 bills spent   2. Number of $10 bills is one more or one less than number of $50 bills.   So, 2 choices   1. 7*10 + 8*50 = $470   2. 8*10 + 7*50 = $430   Least money lost implies most money spent. i.e $470   Therefore, lost money = 1300 - 470= 
1300 - 470 = 830
830.   $830nswer $830
Answer: A
A baseball team won 55 percent of the first 80 games it played. How many of the remaining 82 games will the team have to win in order to have won exactly 50 percent of all the games it played? Pick one: A) 36 B) 45 C) 50 D) 55 E) 37

Solution: Games won out of first 80 questions = (55/100)*80= 
(55/100)*80 = 44
44   Total Games= 80+82= 
80+82 = 162
162   Games to be won= (50/100)*162= 
(50/100)*162 = 81
81   Remaining games to be won= 81-44= 
81-44 = 37
37   Answer: Option 37
Answer: E
If there are 9 horizontal lines and 9 vertical lines in a chess board, how many rectangles can be formed in the chess board? Pick.
A) 1452  B) 1243  C) 1564  D) 1296  E) 1234

Solution: Number of rectangles that can be formed by using m horizontal lines and n vertical lines   = mC2 × nC2   Here m = 9, n = 9   Hence, number of rectangles that can be formed   = mC2 × nC2   = 9C2 × 9C2 = (9C2)2   =(9×82×1)2=362=1296=(9×82×1)2=362=1296   Ans: 1296
Answer: D
In the coordinate plane, Line A has a slope of -2 and an x-intercept of 2. Line B has a slope of 5 and a y-intercept of -10. If the two lines intersect at the point (a,b), what is the sum a+b?  Choose the correct choice from the following:	A) 0	B) 1	C) 2	D) 3	E) 4

Solution: The equation of Line A is y = -2x + 4   The equation of Line B is y = 5x - 10   5x - 10 = -2x + 4   x = 2   y -2  + 4= 
-2  + 4 = 2
2   y= 0   The point of intersection is (2,0) and then a+b = 2.   The answer is 2.
Answer: C