MU-NLPC/Calc-aqua_rat huggingface dataset:
A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?
Choose the correct answer:
A) 2.5π	B) 3π	C) 5π	D) 4π	E) 10π

Solution: If a rectangle is inscribed in a circle, then the diagonal of the rectangle = diameter of the circle.   In this case, diagonal = (9 + 16)^(1/2) = 5   Hence the radius = 2.5   5πircumference = 2πr = 2π*2.5 = 5π   5πorrect Option: 5π2 *2.5= 
2 *2.5 = 5
5π   5πorrect Option: 5π
Answer: C
A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet? Pick one.
A) 10.30 p.m B) 10.20 p.m C) 10.50 p.m D) 10.38 p.m E) 10.40 p.m

Solution: D = 70 * 1 ½ = 105 km   RS = 85 – 70 = 15   T = 105/15= 
105/15 = 7
7 h     3.30 + 7= 
  3.30 + 7 = 10.3
10.30 p.m.   Answer:10.50 p.m
Answer: C
189. The inside dimensions of a rectangular wooden box
are 2 inches by 4 inches by 6 inches. A cylindrical
canister is to be placed inside the box so that it stands
upright when the closed box rests on one of its six
faces. Of all such canisters that could be used, what is
the radius, in inches, of the one that has maximum
volume?  Pick one:
A) 2
B) 4
C) 5
D) 6
E) 8

Solution: Since the radius is squared, the biggest volume cylinder will have the biggest possible radius. To achieve that, let the smaller dimension of the rectangular box be the height. So, it will have 6x4 width x length. The biggest cylinder must fit both dimensions, so it must have at most a diameter of 4, so the radius will be 2.   2
Answer: A
A man can row upstream at 25 kmph and downstream at 55 kmph, and then find the speed of the man in still water? Choose the correct choice from the following:
A) 65
B) 40
C) 30
D) 78
E) 38

Solution: US = 25   DS = 55   M = (55 + 25)/2= 
(55 + 25)/2 = 40
40   Answer: 40
Answer: B
Several people are sitting around a round table playing a card game with a deck of 56 cards. Each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the first card of the deck and the last card of the deck, which of the following could be the total number of people sitting at the table?
Options.
A) 4 B) 6 C) 7 D) 11 E) 13

Solution: Let n be the number of people at the table.   If Martin gets the first and the last card, it means Martin got one more card than the others.   Thus 56/n has a remainder of 1 and so   56-1= 
  56-1 = 55
55 is a multiple of n.   The answer is 11.
Answer: D
8 points are marked on a straight line and another 7 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?  Choose the correct option:  A) 264  B) 91  C) 168  D) 196  E) 264

Solution: Solution: select 2 from 8 and one from 7 + select 2 from 7 and 1 from 8   8C2*7C1 + 7C2*8C1   = 196+ 168= 
196+ 168 = 364
364   264nswer : 264
Answer: A
In a partnership between A, B and C. A's capital is Rs.7000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?  Choices:
A) 23676
B) 19766
C) 29172
D) 16450
E) 11267

Solution: Explanation:   200 + 130= 
200 + 130 = 330
330   800 - 330= 
800 - 330 = 470
470   200 ---- 7000   470 ---- ?=> 16450   Answer:16450
Answer: D
A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 700 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?	Choose the most appropriate option:
A) 2880.	B) 4860.	C) 5780	D) 5040	E) 6380.

Solution: Normal 5040ay = 700 kw/h   Stormy 5040ay = 700*1.2= 
700*1.2 = 840
840 kw/h   3 windmills for 2 hours on stormy day     840*3*2= 
  840*3*2 = 5_040
5040   Answer: 5040
Answer: D
Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps, what is the least number of 4-cent stamps she could have bought ? Choose the correct answer.
A) 5
B) 10
C) 3.75
D) 20
E) 25

Solution: 2.65 = 0.05x + 0.25x + 2 * 0.10x + 0.04y   => 2.65 = 0.30x + 0.20x + 0.04y   => 265 = 50x + 4y   So Max value of 50x < 265 = 250   Hence y = 3.75   Answer - 3.75
Answer: C
A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 9 sec. What is the length of the platform?	Choose the correct choice from the following answers:
A) 389 m
B) 350 m
C) 289 m
D) 799 m
E) 1000 m

Solution: Speed = 300/9 = 100/3 m/sec.   Let the length of the platform be x meters.   Then, (x + 300)/39 = 100/3   => x = 1000 m.   Answer:1000 m
Answer: E
A certain club has 10 members, including Tarry. One of the 10 members is chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Tarry will be either the member chose to be secretary or the member chose to be treasurer? Choose the correct choice from the following.
A) 1/720  B) 1/80  C) 1/10  D) 1/9  E) 1/5

Solution: In order to become a secretary the person cannot be chosen as a president. This can be done in 9/10 ways. Then to become a secretary this person's probability is 1/9   Probability to become a secretary = (9/10 * 1/9) = 1/10   Similar concept for treasurer. Probability of not president = 9/10, Probability of not secretary = 8/9, probability of treasurer 1/8   probability to become a treasurer = (9/10 * 8/9 * 1/8) = 1/10   Since, the problem is saying Tarry secretary OR Treasurer it is addition: 1/10 + 1/10 = 1/5=1/5
Answer: E
At what time between 4 & 5 will the hands of a watch point in opposite directions?  Choose the correct choice from the following choices:
A) 50 min past 4	B) 42 5/11 min past 4	C) 43 min past 4	D) 40 min past 4	E) 50 4/11 min past 4

Solution: At 4 o'clock, the hands of the watch are 20 min. spaces apart.   To be in opposite directions, they must be 30min. spaces apart.   Minute hand will have to gain 5 min. spaces.   55min spaces are gained in 60 min.   5 min. spaces are gained in (60/55 * 50) min. or 54 6/11 min.   Required time = 54 6/11 min. past 4.   Answer is 50 4/11 min past 4
Answer: E
If the sum of two numbers is 22 and the sum of their squares is 386, then the product of the numbers is  Select.
A) 40  B) 49  C) 80  D) 88  E) 90

Solution: Sol.   Let the numbers be x and y.   Then, (x+y) = 22 and x2 + y2 = 386.   Now, 2xy = (x+y)2 - (x2 + y2)   = (22)2 - 386= 484 - 386= 
484 - 386 = 98
98   xy= 49.   Answer 49
Answer: B
What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?	Choose the correct choice from the following answers: A) Rs. 31 B) Rs. 32.10 C) Rs. 40.40 D) Rs. 64.10 E) Rs. 74.10

Solution: S.I. = (1000 * 10 * 4)/100 = Rs. 400   C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10   ANSWER:Rs. 64.10
Answer: D
Divide 71 into 2 parts such that 1 part exceeds the other by 8. What are the 2 no.'s in that part?  Choose the correct choice from the following options: A) 23 B) 14 C) 31 D) 35 E) 45

Solution: Let $let n$ be the smaller and 71 - n be the larger number. Now, since the larger number exceeds the smaller number by 7, we can form the equation   larger number – smaller number = 7   which is equivalent to   Simplifying, we have 71 - 2n = 7. This gives us 2n = 78 which implies that the larger number is . The smaller is 71-39=31.   31
Answer: C
The length of the side of a square is represented by x+2. The length of the side of an equilateral triangle is 2x. If the square and the equilateral triangle have equal perimeter,then the value of x is ?
Choose one.
A) 5 B) 7 C) 4 D) 8 E) 6

Solution: Since the side of the square is x + 2, its perimeter = 4 (x + 2) = 4x + 8   Since the side of the equilateral triangle is 2x, its perimeter = 3 * 2= 
3 * 2 = 6
6x   Also, the perimeters of both are equal.   (i.e.) 4x + 8= 6x   (i.e.) 2x = 8 è x = 4.   Answer:4
Answer: C
The 4 sticks in a complete bag of Pick-Up Sticks are all straight-line segments of negligible width, but each has a different length: 1 inch, 2 inches, 3 inches, and 4 inches, respectively. If Tommy picks a stick at random from each of 3 different complete bags of Pick-Up Sticks, what is the probability S that Tommy CANNOT form a triangle from the 3 sticks?	Answers.
A) 11/32  B) 13/32  C) 15/32  D) 17/32  E) 19/32

Solution: In order to form a triangle, the sum of two sides must be greater than the third side.   So we can choose the combination of numbers which will NOT result in a triangle.   Favorable outcomes:   1,1,4 (4>1+1): 3 ways of arriving at this (1,1,4), (1,4,1), (4,1,1) or   1,2,4 (4>1+2): 6 ways of arriving at this (1,2,4), (1,4,2), (2,1,4), (2,4,1), (4,1,2), (4,2,1) which is same as 3!   1,3,4 (4=1+3): 6 ways of arriving at this   2,2,4 (4=2+2): 3 ways of arriving at this   1,1,3 (3>1+1): 3 ways of arriving at this   1,2,3 (3=1+2): 6 ways of arriving at this   1,1,2 (2+1+1): 3 ways of arriving at this   Overall favourable outcomes: 30   Total outcomes:  4*4*4= 
 4*4*4 = 64
64 (4 ways of choosing a stick from each of the 3 bags)   Probability S that a triangle is not formed= 30/64 = 15/32   15/32 is the correct option here.
Answer: C
What is the sum of all 3 digit positive integers that can be formed using the digits 1, 5, and 8, if the digits are allowed to repeat within a number W?	Choose the correct choice from the following.
A) 126 B) 1386 C) 3108 D) 308 E) 13986

Solution: As we are using digits 1,5, 8 and digits are allowed to repeat. Each of the unit, tenth and hundredth digit can be used by each of three digits.   So,Total possible numbers with these digits=3 X 3 X 3 =27.   First, As we have 27 three digit number, Sum will be for sure more than 2700..Eliminate options A,B,D   Second, If you imagine numbers W with the given digits 1,5,8. We have numbers like 888,885,855,858,851. Sum is for sure more than 4000.Eliminate option C.   You are left withanswer 13986.
Answer: E
List I: 2, 6, 8, 19
List II: x, 2, 6, 8, 19	Choose the correct choice
A) 7
B) 8
C) 9
D) 10
E) 11

Solution: List I has even number of terms, thus its median is the average of two middle terms (when arranged in ascending/descending order), so median=(6+8)/2= 
(6+8)/2 = 7
7.   List II has odd number of terms, thus its median is the middle term (when arranged in ascending/descending order). As no other number in the list equal to 7, then x=7.   7nswer: 7.
Answer: A
David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?
Choose the correct choice from the following answers.
A) 19
B) 28
C) 30
D) 37
E) 47

Solution: Suppose their paths cross after x minutes. Then, 11 + 57x = 51 - 63x => 120x = 40   x=1/3   Number of floors covered by David in (1/3) min. = (1/3)*57= 
(1/3)*57 = 19
19   So, their paths cross at (11 +19) i.e., 30th floor.   ANSWER:30
Answer: C
By selling a book for 200, 20% profit was earned. What is the cost price of the book?	Choose the most appropriate option:
A) A)215  B) B)166  C) C)230  D) D)235  E) E)240

Solution: SP = 120% of CP; :. CP = 200 × 100/120 = 166   Option '166'
Answer: B
What will come in place of the x in the following Number series? 5,28,57 Choose the most appropriate option: A) 156 B) 159 C) 166 D) 170 E) 88

Solution: 28=23+5   57=29+28   88=31+57= 
31+57 = 88
88   88
Answer: E
What is the average of four tenths and six thousandths
Choose the correct choice:	A) 0.2022	B) 0.3325	C) 0.203	D) 0.2012	E) 0.2114

Solution: Explanation:   Four tenths = 0.4   Six thousandths = 0.006   The average is (0.4 + 0.006)/2= 
(0.4 + 0.006)/2 = 0.203
0.2030   Answer: 0.203
Answer: C
A Purse contains a total of 93 coins in the form of one rupee and 50 paise coins. If the total value of coins in the Purse is Rs.56, find the number of 50 paise coins in the Purse? Choose the correct choice: A) 59 B) 30 C) 60 D) 74 E) 80

Solution: D   74   Let the number of one rupee coins in the Purse be x.   Number of 50 paise coins in the Purse is 93 - x.   Total value of coins   [100x + 50(93 - x)]paise = 5600 paise   => x = 74
Answer: D
By selling a watch for Rs.400/-, a man loses 20% what is that watch cost price?
Choose the most appropriate option
A) s. 600/- B) s. 700/- C) s. 800/- D) s. 500/- E) s. 900/-

Solution: 80 % ------> 400 (80 * 5 = 400)   100 % ------>500 (100 * 5 = 500)   Cost price = Rs. 500/-   s. 500/-)
Answer: D
If the original mass of an element, in grams, is a whole number and the element has decayed by exactly 93 percent in some time period, which of the following could be the final mass of that element?
Answers:
A) 27 grams
B) 21 grams
C) 29 grams
D) 31 grams
E) 32 grams

Solution: Let original mass be 100   The final mass of that element will be 7   So whatever option we have it will be divisible by 7   Check for the options the one that doesn't produce non terminating decimal is our answer   A. 27 grams   27/7 = 3.857...   B. 21 grams   21/7= 
21/7 = 3
3   C. 29 grams   29/7= 4.142.......   D. 31 grams   31/7 = 4.428.....   E. 32 grams   32/7 = 4.571....   Hence our answer will be (21 grams)
Answer: B
At exactly what time past 5:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time?  Choose the correct choice.
A) 20 13/21 minutes past 7:00  B) 20 13/17 minutes past 7:00  C) 21 3/23 minutes past 7:00  D) 21 9/11 minutes past 7:00  E) 22 4/9 minutes past 5:00

Solution: A1 = hour angle   A2 = minute angle   A1-A2 = 90   Assume the minutes = M   A1 = (5*60+M)/12*60 )*360   A2 = M*360/60   Solving all three equation , results in the answer 22 4/9 minutes past 5:00
Answer: E
Which of the following is greatest? Pick
A) 1/10 B) 1/100 C) 1/1000 D) 1/10^9 E) 1/5

Solution: Simply we eliminate B,C,D. 1/5 > 1/10   Answer : 1/5
Answer: E
P, Q, R enter into a partnership. P initially invests 25 lakh & adds another 10 lakhs after one year. Q initially invests 35 lakh & withdrawal 10 lakh after 2 years and R invests Rs 30 Lakhs . In what ratio should the profit be divided at the end of 3 years?	Answers
A) 18:19:19  B) 18:18:19  C) 19:19:18  D) 18:19:19  E) None of these

Solution: Explanation :   P:Q:R = (25*1+35*2) : (35*2 : 25*1) : (30*3)   = 95 : 95 : 90   = 19 : 19: 18. Answer : Option 19:19:18
Answer: C
The admission charge in a water park is $1 by adult and $0.75 by child accompanying an adult.
How much was there of child with an adult who paid in quite $3.25 to have access to the water park?	Choose the correct choice from the following answers.
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: a = # of adults Price for on adult = $1.00   e = # of kids Price for on kid (accompanying an adult) = $0.75   t = total ($) $3.25   t = Price for an adult*a + Price for on kid * e   3.25 = $1*a + $0.75*e   3.25 = a + $0.75*e   Because the kids have to be accompanying by an adult, a = 1   $3.25 = 1 + $0.75*e   $3.25 - 1 = 1 - 1 + $0.75*e   $2.25 = $0.75*e   $2.25 / $0.75 = ($0.75*e) / $0.75   3 = e = number of kids accompanying an adult.   3orrect option: 3) 3 kids
Answer: C
A five digit number is to be formed using each of the digits 1, 2, 3, 4 ONLY ONCE. How many numbers can be formed when 1 and 2 are not together ?	Choose the correct option:
A) 12
B) 36
C) 72
D) 60
E) 120

Solution: Reqd ways = (Total No. of ways - cases when both 1 and 2 are together)   4 numbers can be arranged in 4 places in 4! ways. Now tie 1 and 2 together so effectively there are 4 nos. they can be arranged in 3! ways. 1 and 2 can be arranged within themselves in 2!ways.   Reqd. 12nswer = 4! - 3!2! = 24 - (6*2)= 
24 - (6*2) = 12
12   12nswer: 12
Answer: A
In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together. Choose the most appropriate option.
A) 680 B) 700 C) 720 D) 740 E) 760

Solution: 720   720
Answer: C
5 and 20 are the first two terms in a geometric sequence. What is the arithmetic difference between the 10th term and the 12th term? Choose the correct choice from the following choices.
A) 3*5^2  B) 5* 3^13 - 5 * 3^11  C) 75*4^10  D) 40 * 3^10  E) 3^12 - 3^10

Solution: Common ratio = 20/5= 
20/5 = 4
4   12th term= 5*4^12   10th term = 5*4^10   5 * (4^12 - 4^10) = 5 * 4^10*(4^2 - 1)   = 5 * 4^10 * 15   = 75 * 4^10....   75*4^10
Answer: C
Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next? Choose the correct choice from the following answers:
A) 4.2 B) 4.4 C) 4.7 D) 5.1 E) 1.2

Solution: Answer: Option 4.7   In this simple addition series, each number increases by 0.8.
Answer: C
David obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, mathematics, physics, chemistry and biology. What are his average marks?  Choose the correct choice from the following options.
A) 65 B) 69 C) 75 D) None of these E) Cannot be determined

Solution: Solution:   Average= (76+65+82+67+85)/5 =375/5= 
375/5 = 75
75.   Hence, average=75.   Answer: Option 75
Answer: C
A certain class of students is being divided into teams. The class can either be divided into 12 teams with an equal number of players on each team or 24 teams with an equal number of players on each team. What is the lowest possible number of students in the class? Answers:
A) 24	B) 36	C) 48	D) 60	E) 72

Solution: Let total no of students in the class be N   So, we are told that N is divisible by both 12 24   So, Lets find the least common multiple of 12 24 , ie 24   So our answer is (24) 24
Answer: A
Find all rational zeros of P(x) = x3 - 7x + 6.  Pick one:
A) x=1,2,-3 B) x=2,2,-5 C) x=7,4,-8 D) x=6,6,-9 E) x=2,1,-3

Solution: P(x) = x3 - 7x + 6 : given   leading coefficient 1 and its factors are : +1,-1   constant term is 6 and its factors are : +1,-1,+2,-2,+3,-3,+6,-6   possible rational zeros : +1,-1,+2,-2,+3,-3,+6,-6   test : P(1) = 0, P(2) = 0 and P(-3) = 0   x = 1, x = 2 and x = -3 are the zeros of P(x).   correct answer x=1,2,-3
Answer: A
What is the remainder when 3^29 is divided by 5?
Choose one
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: The units digit of powers of 3 follow a repeating cycle of four: {3, 9, 7, 1}   29 has the form 4k+1, so the units digit of 3^29 is 3.   The remainder when dividing by 5 is 3.   The answer is 3.
Answer: D
Find out the square of a number which when doubled exceeds its one nineth by 17 ? Choose the correct choice from the following:  A) 16  B) 25  C) 81  D) 26  E) 17

Solution: Let the number be p, then the square will be p^2   According to question:   2p = (p/9) + 17   => 18p = p + 153   => p = 9   p^2 =9^2 = 81   Answer : 81
Answer: C
The probability of Sam passing the exam is 1/2. The probability of Sam passing the exam and Michael passing the driving test is 1/6. What is the probability of Michael passing his driving test?	Select:
A) 1/24.
B) 1/2.
C) 1/3.
D) 2/3.
E) 2/5

Solution: 1/2 *1/m= 1/6 , 1/m = 1/3   Answer 1/3.
Answer: C
Mr. Wayne bungee jumps from the top of a building straight to the ground at a constant speed. 3 seconds after he starts plummeting he passes the 20th floor. 15 seconds after he starts plummeting he passes the 5th floor. Each floor is 3.8 meters high. What is Mr. Wayne's speed in meters per second?	Pick one:	A) 3	B) 4.75	C) 4	D) 4.25	E) 5

Solution: IMO: 4.75   15 Floors * 3.8 Meter/Floor = 57 Meters   Time= 12 sec   Rate * 12 = 57   Rate= 57/12= 
57/12 = 19/4 = around 4.75
4.75   Answer 4.75
Answer: B
Manie spent 2⁄5 of her money on new clothes and then deposited 1⁄2 of what remained into her savings account. If she then had $21 left, how much did she have at the start?	Choose the most appropriate option
A) $30  B) $35  C) $70  D) $105  E) $210

Solution: Manie spent 2⁄5 of her money on new clothes but if you see 21 is half of 3/5 money so 210 is too huge to be correct..   solution..   let the money be x..   2/5 is used...   1/2 of remaining 3/5 is put in savings account and remaining half is 21..   so 1/2 * 3/5 *x=21..   x=21*2*5/3=70..   $70
Answer: C
If John takes 5 minutes to eat x raisins, how many seconds will it take him to eat z raisins, assuming he continues to eat at the same rate?	Answers
A) 5z/x B) 300z/x C) 300xz D) 300x/z E) 5x/z

Solution: It will take (z/x)(5) minutes which is (z/x)(5)(60) seconds = 300z/x seconds.   The answer is 300z/x.
Answer: B
If there are 35 red and blue marbles in a jar, and the ratio of red to blue marbles is 3:4, what is the probability that, drawing twice, you will select two red marbles if you return the marbles after each draw?	Select the correct option: A) 1/25 B) 2/25 C) 3/25 D) 4/25 E) 6/49

Solution: 35 red and blue marbles in a jar, and the ratio of red to blue marbles is 3:4   So, 7x=35 ---> x=5   Red marbles = 3*x = 3*5= 
3*5 = 15
15   Blue marbles= 4*x = 4*5= 
4*5 = 20
20   Prob to select a red marble= 15/35 = 3/7   Prob to select 2 red marbles with replacement = 3/7*2*7= 
3/7*2*7 = 6
6/49   Hence, answer will be 6/49.
Answer: E
A firm has 5 senior partners and 7 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Note that two groups are considered different if at least one group member is different.)
Answers
A) 145 B) 155 C) 165 D) 175 E) 185

Solution: The number of ways to form a group of 3 is 12C3 = 220   The number of groups with no senior partner is 7C3 = 35   The number of groups with at least one senior partner is 220-35= 
220-35 = 185
185   The answer is 185.
Answer: E
If the sum of two numbers is 45 and the H.C.F and L.C.M of these numbers are 3 and 100 respectively, then the sum of the reciprocal of the numbers is equal to:  Choices:
A) 103/300  B) 103/200  C) 112/300  D) 154/140  E) 100/300

Solution: Let the numbers be a and b.   Then, a + b = 45 and ab = 3*100= 
3*100 = 300
300.   Required sum= 1/a + 1/b = (a + b)/ab = 103/300   103/300NSWER:103/300
Answer: A
Which of the following lines is perpendicular to y = − 2x + 3 and has the same y-intercept as y = 2x − 6?	Select the correct option:
A) y = -1/2*x + 3	B) y = 1/2*x - 6	C) y = 1/2*x + 3	D) y = 2x + 3	E) y = 2x − 3

Solution: Since our line has to perpendicular to y = − 2x + 3   Slope of this line , m = -2   Slope will be required line L = 1/2 ( Product of slope of perpendicular lines = -1)   y-intercept of line L is same as y intercept of line y = 2x − 6   y - intercept of line L = -6   Required line = 1/2* x - 6   Answer y = 1/2*x - 6
Answer: B
Which of the following could be the value of x, if |4x – 2| = 10?	Options:
A) –3
B) –2
C) 1
D) 2
E) 4

Solution: |4x – 2| = 10   => 4x - 2 = 10   or 4x - 2 = -10   => 4x = 12 or 4x = -8   => x = 3 or x = -2   Answer –2
Answer: B
In a hotel we can order two types of varieties, but we can make 4 more varieties in home. One can choose the four varieties with two from hotel as must. Find how many ways one can order.
Choose the correct choice from the following answers.
A) 4	B) 5	C) 6	D) 8	E) 9

Solution: 2c2*4c2=6ways   ANSWER:6
Answer: C
Calculate the fourth proportional to 5.2, 6.6 and 9.1?  Options.
A) 19.55 B) 10.55 C) 11.55 D) 10.2 E) 12.5

Solution: Explanation:   Formula = Fourth propotional = (b × c)/a   A = 5.2 , B = 6.6 and 11.55 = 9.1   (6.6 × 9.1)/5.2 = 11.55   Answer: Option 11.55
Answer: C
A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If four, rather than seven people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month? Select the correct option.
A) x/4	B) x/7	C) x/11	D) x/28	E) 3x/28

Solution: If 7 people share the rent, each person would pay x/7.   If 4 people share the rent, each person will pay x/4.   The extra amount each person pays is x/4 - x/7 = 7x/28 - 4x/28 = 3x/28   The answer is 3x/28.
Answer: E