MU-NLPC/Calc-aqua_rat huggingface dataset:
If the reciprocals of two consecutive positive integers are added together, what is the sum in terms of the greater integer x?
Pick.
A) x/3
B) x^2 - x
C) 2x - 1
D) (2x - 1)/(x^2 + x)
E) (2x - 1)/(x^2 - x)

Solution: Let two consecutive positive integers be x and x-1 (Greater integer is x)   So,   (1/x) + [1/(x-1)]   = (2x-1)/x(x-1)   =(2x-1)/(x^2- x)   Answer (2x - 1)/(x^2 - x)
Answer: E
A person starting with Rs.64 & making 6 bets, wins three times and loses 3times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If eachwager is for half the money remaining at thetime of the bet, then the final result is?  Choose the most appropriate option:
A) Rs.37 B) Rs.57 C) Rs.60 D) Rs.64 E) Rs.68

Solution: As the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5, we will multiply initial amount by 1.5 thrice and by 0.5 thrice (in any order).   The overall resultant will remain same.   So final amount with the person will be (in all cases):   =64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)==64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)= Rs 2727   Hence the final result is:   64−27=3764−27=37:   Rs.37 loss of Rs.37   Rs.37
Answer: A
The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 22nd of September 1990? Pick one:	A) Monday	B) Tuesday	C) Wednesday	D) Friday	E) Saturday

Solution: 19th September   1987: Saturday   1988: Monday (due to leap year)   1989: Tuesday   1990: Wednesday   Hence 22nd September was a Saturday.   The answer is Saturday.
Answer: E
When 100 is divided by positive integer x, the remainder is 4. What is the remainder when 196 is divided by x?
Pick:
A) 2  B) 3  C) 4  D) 6  E) 8

Solution: f100/x leaves a reminder 4 then (100-4) i.e. 96 is divisible by x   So (100+96)/x leaves a reminder rem(100/x)+rem(96/x)=> 4+0= 
4+0 = 4
4   Answer :4
Answer: C
An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq. m ? Answers:  A) Rs. 4082.40  B) Rs. 1024.21  C) Rs. 2810.6  D) Rs. 3214  E) Rs. 2140

Solution: Explanation:   Length of the first carpet = (1.44)(6) = 8.64 cm   Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)   = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m   Cost of the second carpet = (45)(12.96 x 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40   Rs. 4082.40NSWER IS Rs. 4082.40
Answer: A
If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in?  Answers.
A) 2 days  B) 3 days  C) 5 days  D) 7 days  E) 9 days

Solution: That is, 1 person can do one time of the work in 3 days.   Therefore, 7 persons can do 7 times work in the same 3 days itself.   3 days)
Answer: B
Nicky and Cristina are running a race. Since Cristina is faster than Nicky, she gives him a 48 meter head start. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him? Choose the correct choice:
A) 15 seconds
B) 18 seconds
C) 24 seconds
D) 30 seconds
E) 45 seconds

Solution: used pluging in method   say t is the time for cristina to catch up with Nicky, the equation will be as under:   for Nicky=N=3*t+48   for 24 secondsristina=24 seconds=5*t   @t=24, N=120 24 seconds=120 right answer   ans:24 seconds
Answer: C
Submarine P and Submarine Q are equipped with sonar devices that can operate within a 2,000 yard range. Submarine P remains in place while Submarine Q moves 1,700 yards south from Submarine P. Submarine Q then changes course and moves due east, stopping at the maximum range of the sonar devices. In which of the following directions can Submarine Q continue to move and still be within the sonar range of Submarine P? I. North II. South III. West Choose the correct answer
A) III only B) I,II only C) II only D) I only E) I and III only

Solution: It's evident if we make a diagram for the Movement of Q respect to P.   From its South position to the east position, it has covered the maximum radius for the south direction. Similarly, it's east movement further will also make it out of range.   Thus it can only move north or west or anything in that curve.   Answer : I and III only
Answer: E
Number of divisors of 22050 except 1 and itself is.	Select the correct option:
A) 22 B) 52 C) 87 D) 26 E) 19

Solution: Explanation: 2 22050 3 11025 3 3675 5 1225 5 245 7 49 7 ⇒ 22050 = 21 × 32 × 52 × 72 Using the formula discussed earlier, ∴ Number of divisors = (1+1) (2+1) (2+1) (2+1) = 54 ∴ Number of divisors except 1 and itself = 54 –2 = 52   Answer:52
Answer: B
Paul completes a piece of work in 80 days, Rose completes the same work in 120 days. If both of them work together, then the number of days required to complete the work is?  Choose the correct choice from the following options
A) 42 B) 44 C) 46 D) 48 E) 50

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days.   That is, the required No. of days = 80 × 120/200 = 48 days   Answer is 48
Answer: D
If log303 = a, log305 = b, then log308 =?	Choose the correct choice from the following:
A) 3(1 - a - b) B) (a - b + 1) C) (1 - a - b) D) (a - b + 1) E) none of these

Solution: a + b = log3015 = log30(30/2) = 1- log302   => log302 = (1 - a - b)   Therefore, log308 = 3(1 - a - b).   3(1 - a - b)NSWER:3(1 - a - b)
Answer: A
If the height of an equilateral triangle QBC is equal in length to the hypotenuse of an isosceles right triangle DEF, a side of ΔQBC is how many times as long as a leg of the right triangle DEF? Choose the correct answer:
A) (√2)/(√3)
B) (√3)/(√2)
C) √2
D) (2√2)/(√3)
E) 2/(√3)

Solution: Side of the equilateral triangle QBC = 2m ----> height = m * sqtr(2)   Hipotenuse of the right triangle QBC = m * sqrt(3) ----> side = m * sqtr(3) / sqtr(2)   Question is 2m/m * sqtr(3) / sqtr(2) = 2*sqrt(2)/sqrt(3)=(2√2)/(√3)
Answer: D
If a-b= 6 and a^2+b^2=100, find the value of ab	Choose the correct choice from the following choices
A) 10  B) 32  C) 15  D) 18  E) 19

Solution: 2ab = (a^2 + b^2) - (a - b)^2   = 100 - 36= 
100 - 36 = 64
64=> ab = 32   ANSWER:32
Answer: B
Find the area of a parallelogram with base 24 cm and height 16 cm.	Pick one:
A) 384 cm^2  B) 200 cm^2  C) 250 cm^2  D) 350 cm^2  E) 400 cm^2

Solution: 384 cm^2rea of a parallelogram = base * height = 24 * 16= 
24 * 16 = 384
384 cm2   384 cm^2NSWER 384 cm^2
Answer: A
If Q is an odd number and the median of Q consecutive integers is 110, what is the largest of these integers?  Choose the most appropriate option
A) (Q - 1)/2 + 110	B) Q/2 + 109	C) Q/2 + 110	D) (Q + 109)/2	E) (Q + 110)/2

Solution: Consider the easiest case, say Q=3, then;   Set = {109, 110, 111};   The largest integer = 111.   Now, plug Q=3 into the answers to see which yields 111.   (Q - 1)/2 + 110nswer: (Q - 1)/2 + 110.
Answer: A
The area of one square is x^2 + 10x + 25 and the area of another square is x^2 − 6x + 9. If the sum of the perimeters of both squares is 32, what is the value of x? Answers:
A) 3
B) 2
C) 2.5
D) 4.67
E) 10

Solution: spotting the pattern of equations both are in form of (X+C)^2 so   31= (x+5)^232= (x-3)^2   L1= x+5L2= -3   P1 = 4( x+5)P2=4(x-3)   P1+P2=32   4( x+5) +4(x-3)=32.....3   3ns :3
Answer: A
What is the value of 3x^2 − 2x + 0.3 for x = 0.5?	Choices:
A) −0.3	B) 0	C) 0.05	D) 1.08	E) 2.46

Solution: 3x^2-2x+0.3 for x=0.6   =3(0.5*0.5)-4*0.5*(0.5)+0.3   =-0.5*0.5+0.3   =-0.25+0.3= 
-0.25+0.3 = 0.05
0.05   0.05orrect Option : 0.05
Answer: C
A certain manufacturer of cake, muffin, and bread mixes has 90 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
Select: A) a. 1/10 B) b. 3/10 C) c. 1/3 D) d. 7/10 E) e. 9/10

Solution: C+M+B-CM-MB-CB-2CMB = 90   C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.   the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.   50 + 40 + B-CB-MB-20-2CMB = 90   B-CB-MB-2CMB = 30   hence the probability = 30/90 = 30/90=1/3.   c. 1/3
Answer: C
The avg. age of a group of 32 students is 20 years.If 4 more students join the group,the avg age increases by 1 year.The avg age of the new student is?  Select:
A) 22 years  B) 23 years  C) 24 years  D) 25 years  E) 29 years

Solution: Total age of 32 students=32*20= 
32*20 = 640
640   If total age of 4 students=x   Then, (640+x)/(32+4) =(20+1), x=116   So average age of new students=116/4= 
116/4 = 29
29 years   ANSW29 yearsR:29 years
Answer: E
Find the C.I. on Rs. 15,625 for 9 months at 16% per annum compounded quarterly?	Choose the correct choice from the following answers.
A) 2776  B) 2777  C) 1951  D) 2966  E) 1971

Solution: Explanation:   P = Rs. 15625, n = 9 months = 3 quarters, R = 16% p.a. per quarter.   Amount = [15625 * (1 + 4/100)3]   = (15625 * 26/25 * 26/25 * 26/25) = Rs. 17576 C.I. = 17576 - 15625 = Rs. 1951.   Answer: 1951
Answer: C
In my core I have 5 But 500 stand in the beginning and the end of mine. I also include the first letter and the first number to make me complete. I am the name of a King.
Who am I?  Choose the correct choice:
A) Johny B) Jacky C) Ricky D) David E) Alex

Solution: D   I am DAVID.   At the core I have 5   If we talk in roman numeric system, 5 = V   Similarly, 500 stands in the beginning and end   500 = D   I also include the first letter i.e. A and the first number i.e. I (in roman numeric system)   All of them combine to form DavidAVIDavid.
Answer: D
A train 120 m long passed a pole in 20 sec. How long will it take to pass a platform 780 m long?
Choose the correct option.
A) 150	B) 170	C) 160	D) 100	E) 120

Solution: Speed = 120/20= 
120/20 = 6
6 m/sec.   Required time= (120 + 780)/6= 
(120 + 780)/6 = 150
150 sec.   150nswer: Option 150
Answer: A
Raju age after 9 years will be 5 times his age 3 years back, What is the present age of Raju Choose the correct answer:
A) 8 years
B) 7 years
C) 6 years
D) 5 years
E) 4 years

Solution: Explanation:   6 yearslearly,   x+9 = 5(x-3)   <=> 4x = 24 => x = 6   Option 6 years
Answer: C
The perimeter of a rhombus is 120 feet and one of its diagonal has a length of 40 feet. Find the area of the rhombus.
Choose the correct choice from the following:
A) 100 sqrt(5) ft.sq	B) 400 sqrt(5) ft.sq	C) 500 sqrt(5) ft.sq	D) 200 sqrt(5) ft.sq	E) 150 sqrt(5) ft.sq

Solution: A perimeter of 120 when divided by 4 gives the side of the rhombus 30 feet. The length of the side OC of the right triangle is equal to half the diagonal: 20 feet. Let us now consider the right triangle BOC and apply Pythagora's theorem to find the length of side BO.   30^2 = BO^2 + 20^2   BO = 10 sqrt(5) feet   We now calculate the area of the right triangle BOC and multiply it by 4 to obtain the area of the rhombus.   area = 4 ( 1/2) 400 sqrt(5) ft.sqO * OC = 4 (1/2)10 sqrt (5) * 20   = 400 sqrt(5) ft.sq   Answer is 400 sqrt(5) ft.sq
Answer: B
How many positive integers less than 24 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?
Choose the most appropriate option:  A) 19  B) 25  C) 24  D) 22  E) 20

Solution: 9 prime numbers less than 28: {2, 3, 5, 7, 11, 13, 17, 19, 23}   2 odd multiples of 5: {5, 15}   9 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4: {6, 8, 10, 12, 14, 16, 18, 20, 22}   Notice, that 5 is in two sets, thus total # of integers satisfying the given conditions is  9+2+9-1= 
 9+2+9-1 = 19
19.   19nswer: 19.
Answer: A
A newly-wed couple is using a website to design an eBook Wedding Album to distribute to their friends and families. The template they have chosen has places for 3 large photos and 19 smaller photos. The couple has 6 large photos they could use for those three slots, and 21 smaller photos they could use for those 19 slots. Given these choices, how many different possible albums could they create? Options:
A) 3,150 B) 4,200 C) 5,040 D) 20,520 E) 84,000

Solution: For the big album they have to choose 3 out of their 6 photos, and leave out 3:   6! / 3!3! = 20   For the small album they have to choose 19 out of their 21 photos and leave out 2:   21! / 19!2! = 210   All combinations together: 210*20= 
210*20 = 4_200
4200, ANS 4,200
Answer: B
Find the average of the series : 235,222,125,135,123  Choose the correct choice:
A) 168  B) 308  C) 267  D) 207  E) 174

Solution: 168verage = (235+222+125+135+123)/5   = 840/5= 
840/5 = 168
168   168nswer: 168
Answer: A
At a certain ice cream parlor, customers can choose among five different ice cream flavors and can choose either a sugar cone or a waffle cone. Considering both ice cream flavor and cone type, how many distinct triple-scoop cones with three different ice cream flavors are available?
Choose the correct answer
A) 12 B) 16 C) 20 D) 24 E) 30

Solution: Customer can choose 3 out of 5 flavors 5C3=10;   Customer can choose 1 out of 2 cone type 2C1=2;   Total # of combinations possible  10*2= 
 10*2 = 20
20.   ANS:20
Answer: C
Set K contains every multiple of 6 from 18 to 306 inclusive. If w is the median of set K, and x is the average (arithmetic mean) of set K, what is the value of w-x?	Choose one
A) -6
B) -3
C) 0
D) 3
E) 6

Solution: Set K ={18,24,30,....306}   Let the no. of terms be n.   so we know the AP formulae to calculate the the tn term:   tn= a+(n-1)*d where d = common difference of the terms.   306= 18 +(n-1)*6   n=49.   So the set K consist of n terms.   The median of the set having odd nos of elements is (n+1)/2., which in this case is 25.   Let's find the 25th term using the same formulae again:   t25= 18+(25-1)*6   t25= 162   So , the median of the set K is 162 i.e. w=162.   Now. lets find the average (arithmetic mean) of the set. For that we need to find the sum of all the elements first, lets call it S.   Since, set k is nothing but a Arithmetic Progression series having first element(a) as 18, common difference (d) as 6 and no. of terms(n) as 49.   Using the formulae to calculate sum of an AP series, which is   S= n/2[2a + (n-1)*d], we will calculate the sum.   so, S= 49/2 [2*18 + (49-1)*6]   This gives us S= 7938.   Now Arithmetic mean of Set K = 7938/no. of terms= 7938/49= 
7938/49 = 162
162.   So x= 162.   Now, (w-x) = (162-162)= 
(162-162) = 0
0.   Therefore 0orrect Answer= 0
Answer: C
In a 300 member association consisting of men and women, exactly 20% of men and exactly 25 % women are homeowners. What is the least number of members who are homeowners? Choices:
A) 79	B) 77	C) 85	D) 83	E) 61

Solution: Solution simple   Out of 300 20% are male i.e 60 and 25% are female i.e 75 , so total homeowner is 135.   Now min number homeowner is 60 and max is 135 so question ask us to find least and 61 has least value among all option.   So ans is 61.   Answer : 61
Answer: E
If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in? Choose the correct choice from the following answers:	A) days	B) days	C) days	D) days	E) days

Solution: That is, 1 person can do one time of the work in 3 days.   Therefore, 7 persons can do 7 times work in the same 3 days itself.   days)
Answer: B
The labeled price of a table is Rs. 7,500. The shopkeeper sold it by giving 5% discount on the labeled price and earned a profit of 15%. What approximately is the cost price of the table?  Choose the correct choice from the following answers:
A) Rs. 6195 B) Rs. 6199 C) Rs. 6192 D) Rs. 6191 E) Rs. 6194

Solution: Explanation:   Labeled price = Rs. 7,500   By giving 5% discount on labeled price, the selling price is   = 95 / 100 * 7500 = Rs. 7125   By earning 15% profit on the selling of price Rs. 7125 the cost price is   = 100 / 115 * 7125 = Rs. 6195.65   Therefore, approximate cost is 6195.65   Rs. 6195NSWER: Rs. 6195
Answer: A
From the set of numbers {t, u, v, w, x, y, z}, how many different combinations can we have without the t in them? Ex:. (x,y), (x), (w,z,y,x), etc... and note that (x,y)=(y,x) Select the correct option.
A) 16
B) 31
C) 32
D) 63
E) 64

Solution: Any letter (u, v, w, x, y, z) can be included or not.   Thus there are 2^6 combinations - 1 empty combination = 63 combinations   The answer is 63.
Answer: D
Find out the C.I on Rs.3000 at 4% p.a. compound half-yearly for 1 1/2 years.	Choose one
A) A)Rs.181.62 B) B)Rs.182.62 C) C)Rs.183.62 D) D)Rs.184.62 E) E)Rs.185.62

Solution: A = 3000(51/50)3   = 3183.62   3000   -----------   183.62   ANSWER:Rs.183.62
Answer: C
If a man can cover 20 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?  Choose the correct choice from the following answers:
A) 288	B) 162	C) 220	D) 270	E) 122

Solution: 20 m/s = 20 * 18/5 kmph   3 hours 45 minutes = 3 3/4 hours = 15/4 hours   Distance = speed * time = 20 * 18/5 * 15/4= 
20 * 18/5 * 15/4 = 270
270 km.   Answer: 270
Answer: D
The area of a square field is 7201 sq m. How long will a lady take to cross the field diagonally at the rate of 2.4 km/hr?  Choices.
A) 1 min 15 sec	B) 1.5 min	C) 1 min	D) 2.5 min	E) 2 min

Solution: Area of a square field = 7201 sq m   Let the side of square = a   a^2 = 7201   => a = 84.86   Diagonal = (2)^(1/2) * a   = 1.414 * 84.86   =120   Speed of lady = 2.4 km / hour   = 2400 m / hour   = 60 m / min   Time taken by lady to cross the field diagonally = 120/60= 
120/60 = 2
2 min   Answer 2 min
Answer: E
What is the rate percent when the simple interest on Rs.5000 amount to Rs.2500 in 5 Years?  Pick one:
A) 9% B) 8% C) 10% D) 10.5% E) 7.5%

Solution: Interest for 1 year = 2500/5= 
2500/5 = 500
500   Interest on Rs 5000 p/a= 500   interest rate = 500/5000*100= 
500/5000*100 = 10
10%   Answer : 10%
Answer: C
The speed of light is approximately 1,86 * 10^6 miles per second. This approximate speed is how many miles per hour?  Choose the correct choice from the following answers.
A) 1,11 * 10^7	B) 6,70 * 10^7	C) 1,11 * 10^8	D) 6,,70 * 10^9	E) 6,70 * 10^8

Solution: The easiest way to answer this question is by POE, it does not require any calculation (answered in 30seconds). In one hour there are 3600 seconds, therefore speed in miles/hour will be.   (1.86*10^6)*3600 = (1.86*10^6)*(3.6*10^3) = some number*10^9..   The key is realizing that thesome numberhas to be bigger thatn 1.86 (because 1.86*3.6), and the only answer that fits that is 6,,70 * 10^9
Answer: D
If y > 0, (8y)/20 + (3y)/10 is what percent of y?
Choose the most appropriate option
A) 40%
B) 50%
C) 60%
D) 70%
E) 80%

Solution: can be reduced to 4y/10+3y/10 =7y/10=70%   Answer 70%
Answer: D
If p, q and r are positive integers and satisfy x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p, then the value of x is?	Select:
A) -1
B) 1
C) 2
D) -2
E) -3

Solution: When two or more ratios are equal, each of the ratios are equal to sum of the numerators divided by the sum of the denominators, provided sum of the denominators is non-zero.   Hence, x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p   => x = (p + q - r + p - q + r + q + r - p) / (r + q + p)   => x = (r + q + p) / (r + q + p) = 1   p + q + r is non-zero.   Answer: 1
Answer: B
A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?  Select:	A) 999	B) 279	C) 120metre	D) 99	E) 21

Solution: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.   Length of the train = 20 * 6= 
20 * 6 = 120
120 m.   Answer: 120metre
Answer: C
Ravi purchased a refrigerator and a mobile phone for Rs. 15000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent. Overall he make a.?
Choose the correct choice from the following answers.
A) 277
B) 209
C) 121
D) 200
E) 128

Solution: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.   r = 15000(1 - 4/100) = 15000 - 600   m = 8000(1 + 10/100) = 8000 + 800   Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200   As this is positive, an overall profit of Rs. 200 was made.   Answer: 200
Answer: D
A diagonal is a line segment that connects non-adjacent vertices in a polygon. How many diagonals does an octagon have?	Choices
A) 20 B) 40 C) 60 D) 90 E) 80

Solution: Select one vertex and you can draw 5 diagonals.   If you draw 5 such diagonals for each of the 8 vertices, you will draw a total of 5 × 8 = 40 diagonals. But you actually draw each diagonal twice, once from each of its ends. Therefore, there are a total of 40 ÷ 2 = 20 different diagonals   correct answer 20
Answer: A
The slant height of a cone is 18 cm and radius of the base is 8cm, find the curved surface of the cone?
Choose the correct choice
A) 26 B) 452 C) 450 D) 440 E) 28

Solution: π * 18 * 8   = 452   Answer:452
Answer: B
A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
Choose the correct answer
A) 1000	B) 2287	C) 2677	D) 2887	E) 2688

Solution: 90%   104%   --------   14% ---- 140   100% ---- ? => Rs.1000   1000nswer: 1000
Answer: A
What least value must be assigned to * so that the number 197*5462 is divisible by 9	Choose one
A) 0
B) 2
C) 4
D) 9
E) 8

Solution: Let the missing digit be x.   Sum of digits = (1 + 9 + 7 + x + 5 + 4 + 6 +»2) = (34 + x).   For (34 + x) to be divisible by 9, x must be replaced by 2 .   Hence, the digit in place of * must be 2.   ANSWER 2 2
Answer: B
A bowl was filled with 120 ounces of milk, and 0.01 ounce of the milk evaporated each day during a 60-day period. What percent of the original amount of milk evaporated during this period?  Choices
A) A)0.005%  B) B)0.05%  C) C)5%  D) D)0.50%  E) E)4.2%

Solution: Total amount of milk evaporated each day during a 60-day period = .01 * 60= 
.01 * 60 = 0.6
0.6   percent of the original amount of milk evaporated during this period= (.6/120) * 100= 
(.6/120) * 100 = 0.5
0.5 %   Answer 0.50%
Answer: D
In how many ways Chief Minister and Minister be elected from a team of 12 members?
Choose the correct choice from the following
A) 125 B) 131 C) 132 D) 145 E) 147

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
Positive Integer A gives the remainder of 18 when divided by another positive Integer B. If A/B = 147.24, what is the value of B?
Choose the correct answer:
A) 96 B) 75 C) 48 D) 25 E) 12

Solution: .24 of B = Remainder   .24 of B = 18   B = (18*100) / 24= 
(18*100) / 24 = 75
75.   75
Answer: B
The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 77 on the exam is in what percentile of the school?
Choices Choose the correct choice from the following options.
A) 63rd percentile  B) 68th percentile  C) 84th percentile  D) 96th percentile  E) 98th percentile

Solution: (78-65)/6.5= 
(78-65)/6.5 = 2
2 sigmas or 95.5th percentile for +-2 sigma but in our case we need only upper tail, so it's 100 - (100 - 95.5)/2= 96th percentile   96th percentile
Answer: D
A cistern which could be filled in 9 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?
Pick
A) 22  B) 27  C) 29  D) 90  E) 12

Solution: 1/9 - 1/x = 1/10   => 90 hrs   Answer: 90
Answer: D
The two lines y=x and x=-8 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x-axis?  Select:
A) 28
B) 32
C) 36
D) 40
E) 44

Solution: The point of intersection is (-8,-8).   The triangle has a base of length 8 and a height of 8.   area = (1/2)*base*height = (1/2)*8*8= 
(1/2)*8*8 = 32
32   The answer is 32.
Answer: B