MU-NLPC/Calc-aqua_rat huggingface dataset:
The sum s of prime numbers that are greater than 60 but less than 70 is Choose the correct option.
A) 67 B) 128 C) 191 D) 197 E) 260

Solution: A prime number is a number that has only two factors: 1 and itself. Therefore, a prime number is divisible by two numbers only.   Let's list the numbers from 61 to 69.   61, 62, 63, 64, 65, 66, 67, 68, 69   Immediately we can eliminate the EVEN NUMBERS because they are divisible by 2 and thus are not prime.   We are now left with: 61, 63, 65, 67, 69   We can next eliminate 65 because 65 is a multiple of 5.   We are now left with 61, 63, 67, 69.   To eliminate any remaining values, we would look at those that are multiples of 3. If you don’t know an easy way to do this, just start with a number that is an obvious multiple of 3, such as 60, and then keep adding 3.   We see that 60, 63, 66, 69 are all multiples of 3 and therefore are not prime.   Thus, we can eliminate 63 and 69 from the list because they are not prime.   Finally, we are left with 61 and 67, and we must determine whether they are divisible by 7. They are not, and therefore they must be both prime. Thus, the sum s of 61 and 67 is 128.   Answer 128.
Answer: B
A room is 15m long, 4m broad and 3m height. Find the cost of white washing its four walls at 50p per m2 ?	Answers:  A) 33  B) 57  C) 88  D) 26  E) 19

Solution: 2 *3(15 + 4) = 114   114 * 1/2 = Rs.57   \Answer:57
Answer: B
If x varies inversely as (y2 - 1) and is equal to 24 when y = 10, the value of x when y = 5 will be ?	Choose the correct option:
A) 100
B) 101
C) 99
D) 98
E) 97

Solution: Let X = K/(Y2 - 1).   Now 24 = K/(100 - 1)   Or K = 24 x 99.   X = K/(Y2 – 1)   When Y = 5, X = 24 × 99/(25 - 1 ) = 99   ANSWER:99
Answer: C
A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
Select the correct option: A) 230 B) 278 C) 266 D) 555 E) 255

Solution: Relative speed = 120 + 80= 
120 + 80 = 200
200 km/hr.= 200 * 5/18 = 500/9 m/sec.   Let the length of the other train be x m.   Then, (x + 270)/9 = 500/9 => x = 230.   230nswer:230
Answer: A
if 50% of (x-y) = 20% of (x+y) then what percent of x is y?	Choose the correct choice
A) 2.5% B) 10% C) 5% D) 15% E) 43%

Solution: 50% of (x-y)=20% of(x+y)   (50/100)(x-y)=(20/100)(x+y)   5(x-y)=2(x+y)   3x=7y   x=7/3y   therefore required percentage   =((y/x) X 100)% = ((y/(7/3)y) X 100) =43%   Answer is 43%.
Answer: E
A bag of candy contained 360 pieces. A group of 25 students divided the candy so that the 11 boys received twice as much candy as the girls. How many pieces of candy did the boys get? Choose the correct answer:  A) 12  B) 14  C) 16  D) 18  E) 20

Solution: girls candy = x   boys candy = 2x   # boys = 11   # girls = 25 - 11= 
25 - 11 = 14
14   14x + 11(2x)= 360   14x + 22x = 360   36x = 360   x = 10   boys candy = 2x = 2(10) = 20   Answer: 20
Answer: E
a boy perform 5 times a reaction and his reading are 2,2.1,2,2.2 but unfortunately
5th reading clearly not visible because a drop of chemical fall onto it.but luckily he
have mean of all reading which is 2.please help him in finding 5th reading. Choices
A) 2	B) 1.7	C) 1.9	D) 1.8	E) 2.1

Solution: solution   let 5th reading be x   (2+2.1+2+2.2+x)/5=2   8.3+x=10   x=1.7   answer 1.7
Answer: B
Out of a group of 10 contestants, 2 are to be selected at random. What is the maximum number of male contestants possible if the probability that both selected contestants are male is less than 20% ?
Select
A) 0  B) 1.51  C) 2  D) 2.12  E) 4

Solution: Let y be the number of males.   Total contestants = 10   Probability that the first contestant selected is a male = y/10   Probability that the second contestant selected is also a male = y-1/9   Total probability = y(y-1)/ 90 < 1/20 (this probability is less than 20%)   Solving for y we get, y(y-1)< 9/2. This implies that the maximum value of y can be 2.12.   Answer 2.12!
Answer: D
A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the
second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take
both the punctures together to make it flat ?
Choose the correct answer:
A) 315min	B) 325min	C) 335min	D) 345min	E) None of these

Solution: Explanation:   Do not be confused, Take this question same as that of work done question's. Like work done by 1st   puncture in 1 minute and by second in 1 minute.   Lets Solve it:   1 minute work done by both the punctures =   (19+16)=(518)   So both punctures will make the type flat in   (185)mins=335mins   Answer: 335min
Answer: C
Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:  Choose the most appropriate option:	A) 40	B) 80	C) 90	D) 100	E) 120

Solution: Let the numbers be 3x, 4x and 5x.   Then, their L.C.M. = 60x.   So, 60x = 2400 or x = 40.   The numbers are (3 x 40), (4 x 40) and (5 x 40).   Hence, required H.C.F. = 40.   40nswer: Option 40
Answer: A
The average of seven numbers is 22. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number? Options
A) 25
B) 27
C) 29
D) 32
E) 55

Solution: The total of seven numbers = 7X22 = 154   The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99   So, the middle number is  (154 - 99 )= 
 (154 - 99 ) = 55
55   55
Answer: E
In a graduating class, 40 percent of the students are male. In this class, 60 percent of the male students and 40 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old? Choose the correct choice from the following answers.
A) 0.4 B) 0.44 C) 0.48 D) 0.52 E) 0.56

Solution: Let x be the total number of students.   The number students who are younger than 25 is 0.4*0.4x+0.6*0.6x = 0.52x   The answer is 0.52. 0.4*0.4 +0.6*0.6= 
 0.4*0.4 +0.6*0.6 = 0.52
0.52x   The answer is 0.52.
Answer: D
Oak trees line both sides of a street for a length of 7/10 of a kilometer. If there is 14 meters of space between the trees, and each tree is 1 meter wide, how many trees are there along the street? Options:
A) a)	22	B) b)	23	C) c)	24	D) d)	44	E) e)	48

Solution: There is a gap of 16 m between every 2 trees , each tree is 1 m wide.   7/10 of 1 km = 700 m   Lets assume that x trees are planted So equation is   x*1 +(x-1)*14 = 700   Solve for x and we get x = 48, answer is e)	48
Answer: E
P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 6), the remainder is also D. If P/Q = 1020.75 and P/(Q + 6) = 816.6, then which of the following gives the correct set of {D, Q}? Choose the correct option:
A) {6, 12} B) {6, 15} C) {9, 12} D) {9, 15} E) {18, 24}

Solution: p/q= d=p/q+6   d= .75 q   d= .6(q+6)   we get d = 18 and q = 24. Answer = {18, 24}.
Answer: E
In an election between two candidates, 70% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 655200 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.
Choose the correct choice:
A) 1300000
B) 12500
C) 14000
D) 12000
E) None of these

Solution: Explanation :   Solution: let the total number of votes enrolled be x. then, number of votes cast = 70% of x. valid votes = 96% of(70% of x). .'. 75% of(96% of (70% of of x)) = 655200.   (75/100 * 96/100 * 70/100 * x) = 655200.   => x = (655200*100*100*100)/(75*96*70)= 
(655200*100*100*100)/(75*96*70) = 1_300_000
1300000   1300000nswer : 1300000
Answer: A
Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was: Choose the correct choice from the following choices: A) three times as much B) twice as much C) the same D) half as much E) A third as much

Solution: Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.   Speed = Distance/Time.   I.E Time = Distance/Speed.   times taken to covered a distance of 50 miles on his first trip = 50/x hr.   And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.   = 100/x hr.   So we can clearly see that his new time compared with the old time was: twice as much.CORRECT ANSWER : twice as much
Answer: B
Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?	Select:
A) 18
B) 20
C) 24
D) 36
E) 42

Solution: Use weighted average:   2% and 12% solutions mix to give 5% solution.   w1/w2 = (A2 - Avg)/(Avg - A1) = (12 - 5)/(5 - 2) = 7/3   You need 7 parts of 2% solution and 3 parts of 12% solution to get 10 parts of 5% solution.   If total 5% solution is actually 60 litres, you need  7*6= 
 7*6 = 42
42 litres of 2% solution and 3*6= 
3*6 = 18
18 litres of 12% solution.   Answer (42)
Answer: E
If a, b and c are the sides of a triangle, and a2 + b2 + c2 = bc + ca + ab, then the triangle is Choose the correct choice from the following choices.
A) equilateral
B) isosceles
C) right-angled
D) obtuse-angled
E) None of these

Solution: Explanation :   We know that (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac = 3ab + 3bc + 3ac   Now assume values of a, b, c and substitute in this equation to check the options.   Shortcut:   (a – b)2 + (b – c)2 + (c – a)2 = 0.   Hence, a = b = c.   equilateralnswer : equilateral
Answer: A
jhon has 10 choclates, jennifer has 5 choclates. Totally how many choclates they have in all?	Pick one:
A) 5 B) 10 C) 15 D) 20 E) 14

Solution: 10+5= 
10+5 = 15
15. Answer is 15
Answer: C
One vessel contains a mixture of 5 parts pure wine and 3 parts soda, whereas the other vessel contains a mixture of 9 parts pure wine and 3 parts soda. Compare the strength of the wine.
Choose the correct choice from the following
A) 35;36  B) 15 : 18  C) 7 : 4  D) 14 : 5  E) None of these

Solution: 5/8 : 9/12   LCM of 8,12 = 24   (5/8)*24 : (9/12)*24   15:18   Answer is 15 : 18.
Answer: B
Find the third proportional to 63 and 29.9?  Pick one:
A) 14.09
B) 14.29
C) 14.19
D) 14.16
E) None of these

Solution: Explanation:   Formula = Third proportional = (b × b)/a   A = 63 and B = 29.9   (29.9 × 29.9)/ 63 = 894.01/63 = 14.19   Answer: Option 14.19
Answer: C
A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
Choose one:
A) 120%  B) 190%  C) 100 percent  D) 200%  E) 101%

Solution: MP = 100   100 percentP = 75   SP = 150   ------   75 ---- 75   100 ---- ? => 100%   Answer:100 percent
Answer: C
The ratio of the number of females to males at a party was 1:2 but when 3 females and 3 males left, the ratio became 1:3. How many people were at the party originally?
Choose the correct choice from the following answers:	A) 14	B) 16	C) 18	D) 20	E) 22

Solution: The total number of people are x females + 2x males.   3*(x-3) = 2x - 3   x = 6   There were 3x = 18 people at the party originally.   The answer is 18.
Answer: C
The average (arithmetic mean) of 20, 40, and 60 is 5 more than the average of 10, 50, and what number?	Choose the correct choice from the following options
A) 40 B) 45 C) 55 D) 45 E) 50

Solution: a1 = 120/3= 
120/3 = 40
40   a2= a1 -5 = 35   sum of second list = 35*3= 
35*3 = 105
105   therefore the number= 105 -60= 
105 -60 = 45
45   45
Answer: D
In a certain candy store, 22% of the customers are caught sampling the candy and are charged a small fine, but 8% of the customers who sample the candy are not caught. What is the total percent of all customers who sample candy?  Choices:  A) 22%  B) 23.9%  C) 24%  D) 25%  E) 34%

Solution: Since 8% of the customers who sample the candyare notcaught, then 88% of the customers who sample the candyarecaught:   {% of customers who sample candy}*0.92 = 0.22;   {% of customers who sample candy} = 0.239.   Answer: 23.9%.
Answer: B
The least number which must be subtracted from 6709 to make it exactly divisible by 9 is:  Choose the correct choice from the following
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: On dividing 6709 by 9, we get remainder= 4   Therefore, required number to be subtracted= 4   ANSWER:4
Answer: C
10 is added to a certain number, the sum is multiplied by 2, the product is divided by 2 and 2 is subtracted from the quotient. The remainder left is half of 88. What is the number?  Choose the correct choice from the following answers.
A) 21
B) 20
C) 25
D) 36
E) 45

Solution: Let number is X.   When 10 added to it,   = (X+10)   2 multiplied to sum,   = 2 *(X +10)   Now,   = [{2 *(X +10)} /2]   And,   = [{2 *(X +10)} /2] - 2   According to question,   [{2 *(X +10)} /2] - 2 = half of 88   [(2X + 20) /2) = 44 +2   X + 10 = 46   X + 10 = 46   X = 46 - 10= 
46 - 10 = 36
36   So, required number is: 36.   ANSWER : 36
Answer: D
If f(a)=4a+6b+8, what is the value of (f(3a)-f(2b)) ? Select the correct option
A) 6a+8b+6	B) 8a-6b	C) 5a+3b-8	D) 6a+7b+3	E) 8a-2b+9

Solution: f(a)=4a+6b+8   f(3a) = 12a+6b+8   f(2b) = 4a+12b+8   (f(3a)-f(2b)) = 12a+6b+8-4a-12b-8 = 8a-6b   Answer is 8a-6b
Answer: B
A train 200 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is? Choose the correct choice
A) 10  B) 20  C) 30  D) 40  E) 50

Solution: S = (200 + 300)/45 = 500/45 * 18/5= 
500/45 * 18/5 = 40
40   ANSWER:40
Answer: D
A square and a rectangle have equal areas. If their perimeters are p1 and p2 respectively, then	Select the correct option
A) p1 < p2	B) p1 = p2	C) p1 > p2	D) none of these	E) Cannot be determined

Solution: Solution   A square and a rectangle with equal areas will satisfy the relation p1 < p2.   p1 < p2nswer p1 < p2
Answer: A
Mr. stenley employed a certain number of typist for his project. 8 days later 20% of the typist left the job and it was found that it took as much time to complete the rest work from then as the entire work needed with all the employed typists. The average speed of a typist is 20 pages/hour. Minimum how many typist could be employed?  Choose the most appropriate option.
A) 10 B) 5 C) 15 D) 4 E) 3

Solution: Explanation:   Since 20% (i.e 1/5) typists left the job. So, there can be any value which is multiple of 5 i.e, whose 20% is always an integer. Hence, 5 is the least possible value.   Answer: 5
Answer: B
A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
Select.
A) Rs. 4980	B) Rs. 4991	C) Rs. 4996	D) Rs. 4997	E) Rs. 5000

Solution: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.   Required sale = Rs. [ (6500 x 6) - 34009 ]   = Rs. (39000 - 34009)   = Rs. 4991.   Rs. 4991)
Answer: B
An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 5 o’clock in the afternoon?
Options:	A) 60°	B) 90°	C) 270°	D) 320°	E) None of these

Solution: Sol.   Angle traced by the hour hand in 9 hours = [360/12 * 9= 
360/12 * 9 = 270
270°   Answer 270°
Answer: C
A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. He sellis the radio for Rs 300. The profit percent of the retailer is
Choose the correct choice from the following options
A) 22 B) 32 C) 25 D) 88 E) 11

Solution: Explanation:   cost price = (225 + 15)= 
(225 + 15) = 240
240 sell price= 300   gain = (60/240)*100= 
(60/240)*100 = 25
25%   Answer: 25) 25%
Answer: C
A train 125 m long passes a person, running at 5 km/hr in the same direction in which that the train is going, in 10 seconds. The speed of the train is: Choose the correct option.
A) 40 km/hr
B) 60 km/hr
C) 55 km/hr
D) 50 km/hr
E) 65 km/hr

Solution: speed of train related to a person = 125/10 m/s   =>25/2   (25/2*18/5) km/hr   =45 km/hr   so speed consider as x and relative speed consider (x-5)   x-5 = 45 => x = 50 km/hr   ANSWER 50 km/hr
Answer: D
How many three-digit numbers that do not contain the digits 2 or 5 are there?
Answers
A) 488
B) 996
C) 228
D) 456
E) 1986

Solution: We can have 7 digits ( 1,3,4,6,7,8,9) for the first place ( hundred's place).   and similarly 8 digits for tenth's and unit digit. ( 0,1,3,4,6,7,8,9)   So in total 7*8*8= 488   Hence 996
Answer: B
Each of the following equations T has at least one solution EXCEPT  Select the correct option.
A) T=–2^n = (–2)^-n	B) T=2^-n = (–2)^n	C) T=2^n = (–2)^-n	D) (–2)^n = –2^n	E) (–2)^-n = –2^-n

Solution: While it is possible to reason out which of these choices must not work, we may not have time or the confidence to do so. However, this problem has variable in its answer choice, and relatively simple math. Therefore, an easy alternative is picking numbers.   Since we're dealing with exponents, we want to keep things as easy as possible. Hence, we'll start with the easiest exponent possible: n = 1. A, B, and C are not solved (x^-n = 1/(x^n), so we're comparing integers to fractions), but choices D and E both end up valid, eliminating them from contention.   In the process of doing this, however, we've uncovered a major clue to our next step: A, B, and C, all compared integers to fractions, and the only integer equal to it's reciprocal is 1, which is equal to 1/1. This, in turn, tells us the we need to pick n = 0. Remember, for all non-zero x, x^0 = 1.   If we plug n = 0 into choices B and C, we end up with 1 = 1 both times. Choice A, however, results in the false 1 = -1. Thus, we conclude that the first choice has no valid solutions, and is therefore the correct answer.
Answer: A
A and B complete a work in 4 days. A alone can do it in 8 days. If both together can do the work in how many days?  Choose the most appropriate option.
A) 3.75 days	B) 3.78 days	C) 3.25 days	D) 3.15 days	E) 2.7 days

Solution: 1/4 + 1/8 = 3/8   8/3 = 2.7 days   Answer: 2.7 days
Answer: E
The average age of students in section A of 50 students is 14 years and the average age of students in section B of 30 students is 6 years. Find the average age of students in both sections taken together?
Answers
A) 20years B) 15years C) 18years D) 9years E) 11years

Solution: The required average = (50*14+30*6)/50+30 = 11 years   Answer is 11years
Answer: E
The length of the bridge, which a train 150 meters long and travelling at 45 km/hr can cross in 30 seconds, is?	Options:
A) 266	B) 288	C) 245	D) 776	E) 225

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (150 + X)/30 = 25/2 ==> 2(150 + X) = 750 ==> X   = 225 m.   Answer:225
Answer: E
Find the middle one when The sum of three consecutive even numbers is 36?	Options
A) 10  B) 12  C) 14  D) 15  E) 16

Solution: 3 consecutive numbers can be a - 1, a, a + 1   So sum of numbers = 3a = 36.   Hence a = 12.   12
Answer: B
What is the value of âˆš81% ?  Choose one:
A) 25% B) 36% C) 42% D) 60% E) 90%

Solution: 90%xplanation: br>âˆš81%   =âˆš81/âˆš100   =9/10   =90/100=90%   correct answer is 90%)90%
Answer: E
26 men can complete a piece of work in 8 days. In how many days will 25 men complete the same work?	Choose the correct answer:	A) 7 1/3 days	B) 9 1/3 days	C) 8 2/3 days	D) 8 1/3 days	E) 9 1/3 days

Solution: Let the required number of days be p   More men, less days (indirect proportion)   Hence we can write as   26 : 25 :: p : 8   26*8=25*p   p=26*8/25   p=8 1/3 days   ANSWER:8 1/3 days
Answer: D
A train 110 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is
Select the correct option:	A) 54 kmph	B) 60 kmph	C) 66 kmph	D) 72 kmph	E) 82 kmph

Solution: speed of train relative to man: 110/6 * 18/5 km/hr   = 66 km/hr   let speed of train= x   therefore x+6 = 66   x= 66-6= 
66-6 = 60
60 km/hr   ANSWER:60 kmph
Answer: B
How many 6 letter words ( with or without meaning) can be formed using all the following 5 lettersV, P,Q,R,S,and T so that letter P is to the left of letter R? Choose the correct answer
A) 320 B) 300 C) 400 D) 480 E) 360

Solution: Two positions can be selected out of 6 positions in 6C2 ways = 15ways.   And the remaining 4 letters can be placed in 4 posions in 4! Ways = 24 ways.   So the final Answer = number of ways letters P and R can be arranged x number   of ways the other 4 letters can be arranged   Final Answer = 24 x 15 =360 ways   360
Answer: E
If sq. root of(x)/|y| = -1 which of the following must be true? Choose the correct choice from the following:
A) x = -y B) x = y C) x = y^2 D) x^2 = y^2 E) x^3 = y^3

Solution: sq. root of(x)/|y| = -1   sq. root of(x)= -1 |y|   Squaring both sides   + or - (x) = (-1 |y|) ^2= y^2   x = y^2 is the answer
Answer: C
35 - [23 - {15 - x}] = 12 × 2 ÷ 1/2
Pick.
A) 34
B) 32
C) 17
D) 27
E) 28

Solution: Explanation:   35 - [23 - {19 - (15 - x)}] = 12 × 2 × 2 = 48   => 35 - 23 + (19 - 15 + x) = 48   => 12 + 4 + x = 48   => x = 48 - (4 + 12)= 
48 - (4 + 12) = 32
32   Answer: Option 32
Answer: B
A boat goes 100 km downstream in 8 hours, and 75 Km upstream in 15 hours. The speed of the stream is?  Choose the correct choice from the following answers.
A) 3 B) 6.5 C) 5.5 D) 4 E) 3.75

Solution: 100 --- 10 DS = 12.5   ? ---- 1   75 ---- 15 US = 5   ? ----- 1 S = (12.5 - 5)/2= 
(12.5 - 5)/2 = 3.75
3.75 kmph.Answer:3.75
Answer: E
A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is
Choose the correct choice from the following answers
A) 33
B) 77
C) 12
D) 88
E) 91

Solution: S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205. S.I. for 5 years = Rs. (2205/3) x 5 = Rs. 3675 Principal = Rs. (9800 - 3675) = Rs. 6125. Hence, rate = (100 x 3675)/( 6125 x 5) % = 12%   Answer: 12:
Answer: C
Set M contains numbers that satisfy the condition that, if integer x is in the set then x-3 will also be in the set M. If -4 is one of the value in the set, which of the following numbers must also be present in the set M.
I.-7
II. -1
III. 2
Select the correct option:
A) I only
B) II only
C) I and II only
D) II and III only
E) I, II and III

Solution: Notice that we are askedwhich of the following numbers MUST also be present in the set MnotCOULD be in the set.   Now, if -4 is in the set, then -4-3=-7mustbe in the set. Could -1 or 2 be in the set? Certainly, but we don't know that for sure.   I onlynswer: I only.
Answer: A
Carol spends 1/4 of her savings on a stereo and 1/6 less than she spent on the stereo for a television. What fraction of her savings did she spend on the stereo and television? Pick.
A) 1/4
B) 2/7
C) 5/12
D) 1/2
E) 11/24

Solution: Total Savings = S   Amount spent on stereo = (1/4)S   Amount spent on television = (1-1/6)(1/4)S = (5/6)*(1/4)*S = (5/24)S   (Stereo + TV)/Total Savings = S(1/4 + 5/24)/S = 11/24   Answer: 11/24
Answer: E
A man can swim in still water at 3 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? Choose the correct choice
A) 1
B) 7.5
C) 2.25
D) 1.5
E) 4

Solution: M = 3   S = x   DS = 3 + x   US = 3 - x   3 + x = (3 - x)2   3 + x = 3 -2x   3x = 3   x = 1   1NSWER:1
Answer: A
By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 4 p.c?  Choose the correct answer:
A) 28000
B) 29000
C) 37000
D) 38400
E) 40000

Solution: Option B   Explanation:   CP + CP/8 = 45000   CP = 40000   SP = 40000*(96/100)= 
40000*(96/100) = 38_400
38400   Option 38400
Answer: D
You have 5 sticks of lengths 10, 20, 30, 40, 50 centimeters. The number of non-congruent triangles that can be formed by choosing three of the sticks to make the sides is	Choose the correct answer:
A) 3
B) 6
C) 7
D) 10
E) 12

Solution: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.   Based on this there can be only 3 triangles formed: (20, 30, 40), (20, 40, 50), (30, 40, 50)   3nswer; 3.
Answer: A