MU-NLPC/Calc-aqua_rat huggingface dataset:
How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 24 percent alcohol?
Choose the correct answer.
A) 7/2	B) 5	C) 20/3	D) 100/19	E) 39/4

Solution: 20% Alcohol solution means; in the 100 liter solution, 20 liters of solution is alcohol and 80 liters other solvents.   If we addxliters of alcohol to the solution, the solution becomes100+xliters and alcohol, which was 20 liters, becomes 20+x liters.   According to the statement;   20+x = 24% of (100+x)   OR   20+x=(100+x)6/25   500+25x=600+6x   19x=100   x=100/19   Ans:100/19
Answer: D
Area of four walls of a room is 99 m2. The length and breadth of the room are 7.5 m and 3.5m respectively. The height of the room is:
Select:
A) 2.5m B) 3.5m C) 1.5m D) 4.5m E) 5.5m

Solution: 2(7.5+3.5)×h = 99   2(11)h = 99   22h = 99   h = 99/22 = 9/2= 
9/2 = 9/2 = around 4.5
4.5 m   Answer is 4.5m.
Answer: D
3 OUT OF 2500 PARTS OF EARTH IS SULPHUR. WHAT IS THE PERCENTAGE OF SULPHUR IN EARTH Choose the correct choice from the following choices
A) 11/50	B) 1/8	C) 1/45	D) 2/45	E) NONE OF THESE

Solution: REQUIRED PERCENTAGE=(3/2500*100)%=1/8%   CORRECT OPTIONS: 1/8
Answer: B
How many multiples of 5 are there between 1 and 100 (both are inclusive)?	Choose the correct choice from the following answers:	A) 1.2	B) 20.8	C) 2.3	D) 6.7	E) 8.2

Solution: the answer is (100-1)/5+1= 
(100-1)/5+1 = 104/5 = around 20.8
20.8   Answer is 20.8
Answer: B
A truck covers the distance of 550 meters in 1 minute where as a bus covers a distance of 33kms in 45 minutes.Find the ratio of their speed?	Answers.
A) 3:1
B) 4:3
C) 5:2
D) 3:4
E) 2:2

Solution: Formula: d=s*t   Ratio of speed=[(550/50)*(18/5)]:[33*(45*60)](1 minute=60 sec)   =(11*3):(11*4)   =33:44   =3:4   Ratio of speed in car and bus is 3:4   Answer: option 3:4
Answer: D
The area of a circular place is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 3/meter approximately. Pick one.
A) Rs. 4233  B) Rs. 4350  C) Rs. 4457  D) Rs. 4670  E) Rs. 4756

Solution: 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 3) = Rs. 4457.   Rs. 4457
Answer: C
A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?  Choose the correct choice:
A) 9179  B) 3000  C) 2997  D) 2678  E) 2682

Solution: 60*5:36*6:75*3   100: 72: 75   100/247 * 7410= 
100/247 * 7410 = 3_000
3000   Answer: 3000
Answer: B
As x increases from 111 to 112, which of the following increases? I) x−1/x II) 17−1/x III) (17+x)/x  Choose the correct answer:
A) II only B) I,II only C) III only D) I only E) I,III only

Solution: On Increasing the value of x from 111 to 112   I) x−1/x will increase as 1/x will be very small and x will increase by 1 unit   II) 17−1/x Will Increase as the value of 1/x will decrease thereby increasing the value of 17-(1/x)   III) (17+x)/x = (17/x)+1 will Decrease as 1/x will decrease thereby decreasing the value of (17/x)   Answer: I,II only
Answer: B
If the probability T of rain on any given day in city x is 50% what is the probability it with rain on exactly 3 days in a five day period? Choices
A) 8/125  B) 2/25  C) 5/16  D) 8/25  E) 3/4

Solution: 55/163 (1/2)^3(1/2)^2   = (5 * 4 * 3!)/2!3! * 1/32   T= 5/16   Answer - 5/16
Answer: C
a father said to his son ,i was as old as your are at the present at the time of your birth. if the father's age is 38 years now. the son's age five years back was: Choose one.
A) 14	B) 19	C) 33	D) 38	E) 12

Solution: son's age x years, then (38-x) = x   2x=38, x=19, therefore = son's age 5 years back (19-5)= 
(19-5) = 14
14 years   correct answer(14)
Answer: A
On his drive to work, Leo listens to one of three radio stations A, B or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.15 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?  Answers.
A) 0.027	B) 0.386	C) 0.417	D) 0.657	E) 0.9

Solution: Probability he hears a song is like:   Tune to A and likes what he is hearing = 0.15   Tune to A, don't find he like what they are airing, then tune to 0.386 and likes what he finds there = 0.85 * 0.15= 
0.85 * 0.15 = 0.1275
0.1275   Tune to A, finds crap there, Tune to 0.386, hears a similar crap, Tune to C and finally falls in love with the program= 0.85^2 * 0.15 = 0.1084   Total = 0.386   Ans 0.386
Answer: B
Three students appear at an examination of Mathematics. The probability of their success are 2/3, 1/4, 1/5 respectively. Find the probability of success of at least two.
Choose the correct choice from the following:	A) 17/60	B) 2/50	C) 3/40	D) 13/50	E) 14/60

Solution: The probability of success of at least two students will involve the following possibilities.   The first two students are successful, the last two students are successful, the first and third students are successful and all the three students are successful.   Therefore, the required probability = 2/3 x 1/4 x 4/5 + 1/4 x 1/5 x 1/3 + 2/3 x 1/5 x 3/4 + 2/3 x 1/4 x 1/5 = 17/60   17/60NSWER:17/60
Answer: A
A train crosses a platform of 130 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Pick.
A) 150 B) 230 C) 77 D) 62 E) 52

Solution: Length of the train be â€˜Xâ€™   X + 130/15 = X + 250/20   4X + 520 = 3X + 750   X = 230m   Answer: 230
Answer: B
The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?  Choices.
A) 1:96 B) 2:96 C) 1:86 D) 1:94 E) 2:96

Solution: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.   (4x)(3x) = 6912   12x2 = 6912   x2 = 576 = 4 * 144 = 22 * 122 (x > 0)   => x = 2 * 12= 
2 * 12 = 24
24   Ratio of the breadth and the areas= 3x : 12x2 = 1 : 4x = 1: 96.   1:96nswer:1:96
Answer: A
Two persons starting from the same place walk at a rate of 4kmph and 5.5kmph respectively. What time will they take to be 9km apart, if they walk in the same direction? Choose the correct choice from the following:
A) 6 hrs	B) 22 hrs	C) 25 hrs	D) 12 hrs	E) 14 hrs

Solution: The relative speed of the boys = 5.5kmph â€“ 4kmph   = 1.5 kmph   Distance between them is 9 km   Time= 9km / 1.5 kmph = 6 hrs   6 hrsnswer : 6 hrs.
Answer: A
If 4a^4 − 41a^2 + 100 = 0, then what is the sum of the two greatest possible values of a ? Pick.
A) 4  B) 9/2  C) 7  D) 41/4  E) 25

Solution: just forget about the value of a^4 for the moment and let a^2= X. (its better to work with power of 2 than 4)   now we have equation as 4x^2 -41x +100 =0, factoring them gives us 4X^2 -16x -25x +100 =0. which can be solved as (4x-25)(x-4) , so x= 4 and 25/4.   so a^2 = 4 and 25/4   so a= +2 and minus 2 and +5/2 and minus 5/2   The two greatest values are +2 and +5/2. so their sum 2+5/2 =9/2 = 9/2
Answer: B
Only a single rail track exists between stations A and B on a railway line. One hour after the north bound super fast train N leaves station A for station B, a south-bound passenger train S reaches
station A from station B. The speed of the super fast train is twice that of a normal express train E, while the speed of a passenger train S is half that of E. On a particular day, N leaves for B from A, 20 min behind the normal schedule. In order to maintain the schedule, both N and S increased their speeds. If the super fast train doubles its speed, what should be the ratio (approximately) of the speeds of passenger train to that of the super fast train so that the passenger train S reaches exactly at the scheduled time at A on that day?
Choose the correct option.
A) 1 : 3  B) 1 : 4  C) 1 : 5  D) 1 : 6  E) None of these

Solution: Explanation :   If speed of N = 4, speed of S = 1.   => Average speed = (2 X 4 x 1) / ( 4 + 1) = 1.6.   Because time available is 2/3, speed = 3/2.   Now Average speed = 2.4   Now speed of N = 8.   Speed of S = y.   => (2 x 8 x y) / (8+y) = 2.4   => y = 1.3   The required ratio is 1.3 : 8 i.e 1 : 6.   Answer : 1 : 6
Answer: D
In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 52, the dividend is:
Answers:  A) 5324  B) 5334  C) 6812  D) 7356  E) 7400

Solution: Divisor = (5 * 52)= 
(5 * 52) = 260
260= 10 * Quotient = Divisor   => Quotient = 260/10= 
260/10 = 26
26   Dividend= (Divisor * Quotient) + Remainder   Dividend = (260 * 26) + 52= 
(260 * 26) + 52 = 6_812
6812   6812
Answer: C
P, Q, R subscribe Rs. 50,000 for a business. P subscribes Rs. 4000 more than Q and Q Rs. 5000 more than R. Out of a total profit of Rs. 25,000, what will be P's share?
Select
A) 10,509 B) 10,502 C) 10,500 D) 10,501 E) 10,506

Solution: Explanation:   Let amount subscribed for R be x.   Therefore, Q = x + 5000 and P = x + 5000 + 4000 = x + 9000   So, x + x + 5000 + x + 9000 = 50000   3x = 36000   x = 12000   P : Q : R = 21000 : 17000 : 12000 = 21 : 17 : 12   ANSWER: Rs. 10,500   P’s share = 25000 X (21/50) = Rs. 10,500   ANSWER:10,500
Answer: C
Sravan and Bhavan began business with Rs.16000 and Rs.20000 after 8 months, Sravan advances Rs.4000 more and Bhavan withdraws Rs.4000. At the end of two years, their profits amounted to Rs.5535 find the share of Sravan.
Choose the correct choice.
A) 2850
B) 2870
C) 3000
D) 2800
E) 2825

Solution: (16*8 + 20*16):(20*8 + 16*16)   14:13   14/27 * 5535= 
14/27 * 5535 = 2_870
2870. Answer: 2870
Answer: B
In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?
Choose one:
A) 10.6
B) 11.6
C) 12.6
D) 13.6
E) 14.6

Solution: Explanation:   Total age of 50 students   (30X 13+20 X 12) = 630   Average = 630/50= 
630/50 = 63/5 = around 12.6
12.6 Years   Answer 12.6
Answer: C
A certain school supplies store arranges pencils on display such that each of the six different colors of pencils, yellow, orange, green, red, blue, and purple are consecutive in a repeating pattern. If seven consecutively displayed pencils are purchased, what is the probability that two of the pencils
are purple?
Choose the correct option
A) 1/6 B) 1/36 C) 1/20 D) 2/3 E) 2/5

Solution: After yellow, orange, green, red, blue, and purple, the next pencil can be of any given six colours, therefore we have total six possibilites, out of which we need purple i.e. 1 therefore prob is 1/6.
Answer: A
From the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 20 percent. What percent of the stock’s 2007 starting price was the price of the stock at the end of 2009?	Choose one.
A) 80  B) 90  C) 95  D) 100  E) 108

Solution: Assume a value at the beginning of 2007. As this is a % question, assume P=100.   At the end of 2007 it becmae = 1.2*100= 
1.2*100 = 120
120   At the end of 2008 it decreased by 25%= 120*.75= 
120*.75 = 90
90   At the end of 2009 it increased by 20%= 90*1.2= 
90*1.2 = 108
108   Thus ratio= 108/100= 
108/100 = 27/25 = around 1.08
1.08 (in % terms= 108%). Thus 108 is the correct answer.
Answer: E
At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 250-pack for $20.95. What is the greatest number of hot dogs you can buy at this store with $300?  Pick one
A) 3,108	B) 3,100	C) 3,108	D) 3,540	E) 3,256

Solution: To maximize number of hot dogs with 300$   Total number of hot dogs bought in 250-pack = 20.95*14= 
20.95*14 = 293.3
293.30$   Amount remaining= 300 - 293.30= 
300 - 293.30 = 6.7
6.7$   Total number of hot dogs bought in 20-pack= 3.05*2= 
3.05*2 = 6.1
6.10$   Amount remaining= 6.70 - 6.10= 
6.70 - 6.10 = 0.6
0.6$   This amount is too less to buy any 8- pack .   Greatest number of hot dogs one can buy with 300 $= 250*14+20*2 = 3,540   Answer 3,540
Answer: D
if A and B both work for 6 hrs,B and C work for 7.5 hrs,C and A work for 10 hrs .
i dont remember but ......its arrange in increasing order by their work Choose one:
A) cab
B) cba
C) abc
D) bac
E) none of these

Solution: A and B both can finish the work in 6 days means   1/A+1/B=1/6 ................(i)   B and C both can finish the work in 7.5 days means   1/B+1/C=1/7.5 ...................(ii)   C and A both can finish the work in 10 days means   1/A+1/B=1/10 ........................(iii)   Adding (i),(ii) and (iii), we get   2(1/A+1/B+1/C)=2/5 ......................(iv)   from (i) we have 1/A+1/B=1/6 put in (iv) ,we wiil get   1/6+1/C=1/5   C=30   Similarly, we will get A=15 and B=10   so in increasing order it will be BAC   ANSWER:bac
Answer: D
A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.25000, find their shares?
Choose the correct choice from the following answers:	A) Rs.1300	B) Rs.1599	C) Rs.7290	D) Rs.15000	E) Rs.72821

Solution: The ratio of their profits A:B = 8:12 = 2:3   Share of A in the total profit = 2/5 * 25000 = Rs.10000 Share of A in the total profit = 3/5 * 25000 = Rs.15000   Answer:Rs.15000
Answer: D
If x is a positive integer with fewer than 3 digits, what is the probability Q that x*(x + 1) is a multiple of either 4 or 5?  Pick one.
A) 4/99
B) 2/25
C) 8/99
D) 49/100
E) 86/99

Solution: Interesting question! Also one that we should be able to answer very quickly be keeping an eye on our best friends, the answer choices.   We know that x belongs to the set {1, 2, 3, ... , 99}. We want to know the probability Q that x(x+1) is a multiple of either 4 or 5.   When will this happen? If either x OR (x+1) is a multiple of 4 or 5.   Since 4*5 is 20, let's look at the first 20 numbers to get a rough idea of how often this happens.   Out of the numbers from 1 to 20:   4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 20   So, 14 out of the first 20 numbers match our criteria. Since:   probability = (# of desired outcomes)/(total # of possibilities), we guesstimate the answer to be 14/20. Since (86/99) is the only answer greater than 1/2, we go with (86/99).
Answer: E
A can do piece of work in 15 days and B in 20 days they finished the work with the assistance of c in 5 days and got Rs.45 as their wages find the share for each in wages?
Select.
A) 11,12,13  B) 15,11,13  C) 15,11.25,18.75  D) 11,15.25,18.75  E) None of these

Solution: Explanation:   A’s 1 day work =1/3   B’s 1 day work =1/4   15,11.25,18.75’s 1 day work =1-1/4-1/3 =5/12   A’s share =45 *1/3= 
45 *1/3 = 15
15   B’s share= 45*1/4= 
45*1/4 = 45/4 = around 11.25
11.25   15,11.25,18.75’s share=45*5/12= 
45*5/12 = 75/4 = around 18.75
18.75   Answer: Option 15,11.25,18.75
Answer: C
The rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started. If after a minute and a half the gyroscope reached a speed of 6400 meters per second, what was the speed, in meters per second, when the stopwatch was started?
Choose the correct choice from the following answers
A) 25/2 B) 25/4 C) 25/8 D) 25/16 E) 25/32

Solution: Let x be the original speed when the stopwatch was started.   In 90 seconds, the speed doubled 9 times.   2^9 * x = 6400   x = (2^8 * 25) / 2^9 = 25/2   The answer is 25/2.
Answer: A
If v and t are integers and v^2 – t^2 is an odd integer, which of the following must be an even integer?
I. v + t + 2
II. v^2 + 2vt + t^2
III. v^2 + t^2 Choose the correct choice from the following choices
A) None
B) I only
C) II only
D) III only
E) I, II, and III

Solution: v^2–t^2 is an odd integer means that either v is even and t is odd or v is odd and t is even.   Check all options:   I. v + t + 2 --> even+odd+even=odd or odd+even+even=odd. Discard;   II. v^2 + 2vt + t^2 --> even+even+odd=odd or odd+even+even=odd. Discard;   III. v^2 + t^2 --> even+odd=odd or odd+even=odd. Discard.   Nonenswer: None.
Answer: A
If Jesse flips a coin seven times in a row, what is the probability that the result will be heads at all the times?  Choose the correct option:	A) 1/128	B) 29/128	C) 35/128	D) 1/16	E) 1/4

Solution: In a flip of a coin seven times in a row, heads at all times means,   Heads = at least 7 heads   Atleast 7 heads in 7 flip.   The total outcome of flip is = 2^7 = 128   For any Coins problem write the ask in the shown format.   HHHHHHH   Once you have written in the above mentioned format the answer is pretty straight.   HHHHHHH = [7!]/[7!] = 1   Sum 7  / 7= 
7  / 7 = 1
1   Sum= 1 =   1/128nswer = 1/128   1/128nswer - 1/128
Answer: A
A girl was asked to multiply a certain number by 43. She multiplied it by 34 and got his answer less than the correct one by 1251. Find the number to be multiplied. Pick.
A) 130 B) 132 C) 134 D) 136 E) 139

Solution: Let the required number be x. Then,   43x – 34x = 1251 or 9x = 1251 or x = 139.   Required number = 139.   ANSW139R:139
Answer: E
The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?	Choices: A) 7% B) 4% C) 5% D) 2% E) 1%

Solution: 65*(90/100)*((100-x)/100)   = 56.16   x = 4%   Answer: 4%
Answer: B
How many words can be formed from the letters of the word "SIGNATURE" so that vowels always come together. Answers:
A) 17280 B) 4320 C) 720 D) 80 E) None of thsee

Solution: Explanation:   word SIGNATURE contains total 9 letters.   There are four vowels in this word, I, A, U and E   Make it as, SGNTR(IAUE), consider all vowels as 1 letter for now   So total letter are 6.   6 letters can be arranged in 6! ways = 720 ways   Vowels can be arranged in themselves in 4! ways = 24 ways   Required number of ways = 720*24= 
720*24 = 17_280
17280   Option 17280
Answer: A
15 + sqrt(- 6 + 8Ã—5Ã·4) =?
Options.
A) 31	B) 32	C) 33	D) 34	E) 35

Solution: According to order of operations, inner brackets first where 8x5Ã·4 is first calculated since it has a multiplication and a division.   8x5Ã·4 = 40Ã·4 = 10   Hence   15 + sqrt(- 6 + 8Ã—5Ã·4) = 15+ sqrt(- 6 + 10)   = 15 + sqrt(4) = 15 + 16= 
15 + 16 = 31
31   correct answer 31)31
Answer: A
How many of the positive factors of 63 , 84 and how many common factors are there in numbers?  Answers.
A) 2
B) 4
C) 3
D) 5
E) 1

Solution: factors of 63 - 1,3,7,9,21,63   factors of 84 - 1,2,3,4,6,7,12,14,21,28,42,84   Comparing both, we have three common factors of 63 and 84- 1,3,7,21   Answer(4)
Answer: B
A numberais squared and then multiplied by negative 3. The result of this operation R is equal to three times the sum of three timesaand two. What is one possible value ofa?	Choose the correct choice from the following answers
A) -3  B) -2  C) 1  D) 2  E) 3

Solution: R=-3*a^2=3(3a+2)   a= -2 or -1   a=-2=-2
Answer: B
Let the number which when multiplied by 13 is increased by 180. Options.
A) 14	B) 20	C) 15	D) 28	E) 30

Solution: Solution   Let the number be x .   Then, 13x - x = 180   ‹=›12x = 180   x ‹=› 15.   Answer 15
Answer: C
5 persons a, b, c, d, e are to be lined up in a row. If a, b, and c adhere always together, how many possible cases are there?	Choose the correct option.
A) 24 B) 36 C) 48 D) 72 E) 144

Solution: firstly it is not GEOMETRY but COMBINATIONS, so changing the TAG accordingly..   total 5 are there..   take a,b, and c as one,so total =3..   these 3 can be arranged in 3! ways..   a,b, and c can be arranged within themselves in 3! ways ..   TOTAL = 3!*3!=36   36
Answer: B
A rower whose speed is 4 km/hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 2 km/hr. What is the rower's average speed (in km/hr) for the total journey?
Choose the correct answer: A) 6 B) 4 C) 9 D) 3 E) 2

Solution: time upstream = d / 2   time downstream = d / 6   total time = d/2 + d/6 = 2d/3   average speed = 2d / (2d/3) = 3 km/hr   The answer is 3.2  / (2 /3)= 
2  / (2 /3) = 3
3 km/hr   The answer is 3.
Answer: D
What is the probability of getting exactly 2 heads in a single throw of four fair coins?	Choose the correct choice from the following choices
A) 1/2
B) 3/4
C) 3/8
D) 3/16
E) 5/16

Solution: One possible case is HHTT.   P(HHTT) = 1/2*1/2*1/2*1/2 = 1/16   There are 4C2 = 6 possible cases.   P(2 heads) = 6*1/16 = 3/8   The answer is 3/8.
Answer: C
The sale price sarees listed for Rs.750 after successive discount is 20% and 15% is?  Choose the correct choice from the following.
A) 227
B) 570
C) 342
D) 680
E) 230

Solution: 750*(80/100)*(85/100)   = 570   Answer: 570
Answer: B
The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher  Choose the correct answer:	A) 49	B) 88	C) 25	D) 18	E) 11

Solution: Total age of students is 32X16 = 512 Years   Total age inclusive of teacher = 33X (16+1) = 561   So, Teacher's age is 561-512= 
561-512 = 49
49 Yrs   49nswer: 49
Answer: A
How many odd factors does 520 have? Select the correct option.
A) 3  B) 4  C) 5  D) 6  E) 8

Solution: Start with the prime factorization: 520 = 2*5*13   For odd factors, we put aside the factor of two, and look at the other prime factors.   set of exponents = {1, 1}   plus 1 to each = {2, 2}   product = 2*2= 
2*2 = 4
4   Therefore, there are 4 odd factors of 520.   Answer: 4.
Answer: B
Population of a city in 20004 was 1300000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city at the end of the year 2007 Choose the correct choice from the following options
A) 354354
B) 545454
C) 465785
D) 456573
E) 2818075/2

Solution: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)   = P (1 + 15/100)(1 - 35/100)(1 + 45/100)   = 2818075/2   2818075/2
Answer: E
Find the area of a parallelogram with base 32 cm and height 14 cm?  Choose the most appropriate option:
A) 498 cm2
B) 384 cm2
C) 430 cm2
D) 128 cm2
E) 448 cm2

Solution: Area of a parallelogram   = base * height   = 32 * 14= 
32 * 14 = 448
448 cm2   Answer:448 cm2
Answer: E
The probability of Sam passing the exam is 1/5. 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?  Pick one
A) 1/24.  B) 1/2.  C) 5/6.  D) 2/3.  E) 2/5

Solution: 1/5 *1/m= 1/6 , 1/m = 5/6   Answer 5/6.
Answer: C
A shipment of 8 television sets contains 2 black-and-white sets and 4 color sets. If 2 television sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black-and-white set?	Select:  A) 1/7  B) 1/4  C) 5/14  D) 11/14  E) 13/28

Solution: I get 11/14, which is not in the answer choices.   the probability of getting at least one b/w TV is 1-(the probability of getting 2 color TVs)   1-C(4,2)/C(8/2)=22/28=11/14   11/14
Answer: D
An office supply store stocks three sizes of notebooks, each in five colors: blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 3 notebooks of the same size and the same color or 3 notebooks of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?	Choose the correct choice from the following answers:
A) 24
B) 30
C) 42
D) 45
E) 60

Solution: First let's consider the small notebooks.   There are 5 ways to choose 3 notebooks of the same color.   The number of ways to choose 3 notebooks with different colors is 5C3=10.   There are 15 different packages we can make with the small notebooks.   We can use the same process to find 15 different packages with medium and large notebooks.   The total number of different packages is 45.   The answer is 45.
Answer: D
A train 175 m long pass a telegraph pole in 5 seconds. Find the speed of the train	Choose the correct answer:	A) 66 km/hr	B) 68.4 km/hr	C) 72 km/hr	D) 126 km/hr	E) None

Solution: Sol.   Speed = [175/6] m/sec = [352 * 18/5] km/hr = 126 km/hr.   Answer 126 km/hr
Answer: D