MU-NLPC/Calc-aqua_rat huggingface dataset:
In the last set of tests, a student scored marks in each of 5 subjects in the ratio 4:5:6:7:8 and got an overall score of 72%. If a mark of 50% in a subject is a pass and the maximum marks of each subject is the same, how many subjects did the student pass? Choose the most appropriate option:
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: The tests scores are 4k, 5k, 6k, 7k, and 8k.   The sum of the test scores is 30k.   The average test score is 30k/5 = 72. Then k = 12.   The test scores are 48, 60, 72, 84, and 96.   The student passed 4 subjects.   The answer is 4.
Answer: D
7^6n -1^ 6n When n is an integer > 0 is divisible by  Choose the correct choice from the following:
A) 119	B) 127	C) 141	D) 154	E) 165

Solution: 127   127
Answer: B
What annual installment will discharge a debt of Rs. 1428 due in 3 years at 12% simple interest? Choose the correct choice from the following choices:
A) 315
B) 345
C) 425
D) 335
E) None of them

Solution: Let each Installment be Rs. x   Then, ( x+ ((x*12*1)/100)) + (x+ ((x*12*2)/100) ) + x = 1428   =((28x/25) + (31x/25) + x) = 1428 ïƒ› (28x+31x+25x)=(1428*25)   x= (1428*25)/84 = Rs.425.   Therefore,	Each installment = Rs. 425.   Answer is 425.
Answer: C
A sells a Cricket Bat to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays $228 for it, the cost price of the Cricket Bat for A is:  Choose the correct choice from the following answers:
A) 152	B) 120	C) 130	D) 160	E) 210

Solution: 152   152   125% of 120% of 152 = 228   125/100 * 120/100 * 152= 
125/100 * 120/100 * 152 = 228
228   152= 228 * 2/3= 
228 * 2/3 = 152
152.
Answer: A
What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 14%?	Answers.
A) 20% B) 28% C) 29% D) 40% E) 70%

Solution: SP2 = 2/3 SP1   29%P = 100   SP2 = 86   2/3 SP1 = 86   SP1 = 129   100 --- 29 => 29%   Answer:29%
Answer: C
An investment E gained an interest payment of $250 each month when the annual interest rate was 8%, how much more should we invest annually if we want to gain 12% more per month with a new annual interest rate of 7.5% ?  Choose the correct choice from the following choices:
A) $9,360 B) $9,100 C) $8,250 D) $7,300 E) $7,150

Solution: Answer is D : 7,300   An investment E gained an interest payment of $250 each month when the annual interest rate was 8%,Interest per annum with 8% interest rate is = 250* 12 = Principal * Interest Rate(8/100)   This gives Principal as 37,500$   For an revised interest of 12% more and new interest rate of 7.5% , ie. 250* 12 * 1.12 = Principal * Interest Rate (7.5/100)   This gives the new Principal as 44,800.   The question is how much more should we invest, so 44,800 - 37,500 = 7,300.$7,300
Answer: D
A is a working partner and B is a sleeping partner in a business. A puts in 50,000 and B 60,000. A gets 12.5% of the profit for managing the business, and the rest is divided in proportion to their capitals. Find the share of A in profit of 8800.  Select.
A) 3500	B) 4600	C) 5400	D) 4800	E) None of these

Solution: The amount A gets for managing   = 12.5% of Rs. 8800 = 1100   Remaining profit = 8800 – 1100 = 7700   This is to be divided in the ratio 5 : 6.   Share of A = 5/11 of 7700 = 3500   ⇒ Total share of A = 3500 + 1100= 
3500 + 1100 = 4_600
4600.   Answer 4600
Answer: B
The average weight of 8 persons increases by 4.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?	Select:  A) 75 kg  B) 65 kg  C) 55 kg  D) 85 kg  E) 101 kg

Solution: Total weight increased = (8 x 4.5) kg = 36 kg.   Weight of new person = (65 + 36)= 
(65 + 36) = 101
101 kg.   Answer: 101 kg
Answer: E
If it takes 12 identical printing presses exactly 5 hours to print 12,000 newspapers, how long would it take 6 of these presses to print 8,000 newspapers?
Choose the correct choice from the following options:
A) 6 hrs 40 mins
B) 6 hrs 50 mins
C) 6 hrs 30 mins
D) 5 hrs 40 mins
E) 6 hrs 50 mins

Solution: 12 presses - 12,000 newspapers - 5 hours ;   6 presses - 6,000 newspapers - 5 hours ; (300 mins)   6 presses - 8,000 newspapers - 300/6000*8000 = 400 mins = 6 hrs 40 mins   6 hrs 40 minsnswer : 6 hrs 40 mins
Answer: A
The volumes of two cones are in the ratio 1 : 20 and the radii of the cones are in the ratio of 1 : 2. What is the ratio of their heights?	Choose the correct choice from the following answers
A) A)2:5  B) B)2:7  C) C)1:5  D) D)2:1  E) E)2:9

Solution: The volume of the cone = (1/3)πr2h   Only radius (r) and height (h) are varying.   Hence, (1/3)π may be ignored.   V1/V2 = r12h1/r22h2 => 1/20 = (1)2h1/(2)2h2   => h1/h2 = 1/5   i.e. h1 : h2 = 1 : 5   Answer: 1:5
Answer: C
A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?	Answers:  A) 7  B) 8  C) 9  D) 4  E) 3

Solution: 30 --- 3 DS = 10   ? ---- 1   18 ---- 3 US = 6   ? ---- 1 M = ?   M = (10 + 6)/2= 
(10 + 6)/2 = 8
8   Answer: 8
Answer: B
A certain junior class has 100 students and a certain senior class has 80 students. Among these students, there are 6 siblings pairs each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?  Choose the correct option:
A) 3/40000  B) 1/3600  C) 9/2000  D) 3/4000  E) 1/15

Solution: Let's see   Pick 6/100 first   Then we can only pick 1 other pair from the 800   So total will be 6 / 80 *100   Simplify and you get 3/4000   Answer is 3/4000
Answer: D
A train sets off at 2 p.m. at the speed of 50 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 75 kmph. At what time the trains will meet?	Choose the correct choice from the following options.
A) 6.37 p.m	B) 6.20 p.m	C) 6.30 p.m	D) 6.38 p.m	E) 6.10 p.m

Solution: D = 50 * 1 Â½ = 75 km   RS = 75 â€“ 50 = 25   T = 75/25= 
75/25 = 3
3 h     3.30 + 3= 
  3.30 + 3 = 6.3
6.30 p.m.   Answer: 6.30 p.m
Answer: C
In a recent election, Geoff received 0.5 percent of the 6,000 votes cast. To win the election, a candidate needed to receive more than x% of the vote. If Geoff needed exactly 3,000 more votes to win the election, what is the value of x ?	Choose the most appropriate option:
A) 50  B) 50.5  C) 56  D) 60  E) 63

Solution: Word problems are tricky in somehow more than other problem because you have the additional step to translate.   50.5reaking the problem: Geoff how many votes he receives ?? 30 votes   he needs 3571 more votes so :   30+3000= 
  30+3000 = 3_030
3030   Now what's the problem wants ?? a x %........3030 is what % of total votes 6000........translating: 3030= x/100 * 6000 ---   x= 50.5 %..........50.5
Answer: B
In a class of 32 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?  Pick:
A) 3 B) 5 C) 8 D) 11 E) 15

Solution: Total # of students = 32   Avg # of books per student = 2   Total # of books = 32*2= 
32*2 = 64
64   # of student borrowed at least 3 books= 32-2-12-10= 
32-2-12-10 = 8
8   # of books borrowed by above 8 students= 60-(12*1)+(10*2) = 32   Considering that 7 out of above 8 students borrowed only 3 books, # of books borrowed = 7*3= 
7*3 = 21
21   So maximum # of books borrowed by any single student= 32 -21= 
32 -21 = 11
11   option 11
Answer: D
A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855, the total profit is:  Choose the correct choice from the following answers
A) Rs. 1425
B) Rs. 1500
C) Rs. 1537.50
D) Rs. 1576
E) Rs. 1600

Solution: Explanation:   Let the total profit be Rs. 100.   After paying to charity, A's share = Rs.(95 X 3/5)=Rs. 57   If A's share is Rs. 57, total profit = Rs. 100.   If A's share Rs. 855, total profit =(100/57 X 855)=1500.   ANSWER IS Rs. 1500
Answer: B
A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 2 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?
Select:
A) 0.5< t < 0.75 B) 1.75< t < 2.0 C) 2.0 < t < 2.5 D) 2.5 < t < 3.0 E) 3 < t < 3.5

Solution: D=2, and R=1   circumference thus is 2pi miles   we know that she walked 2mph   knowing the formula rt=D, we can deduce that t= D/r   D is 2pi miles and r is 2mph   t = 2pi/2   pi can be rewritten as 22/7   2*22/7 = 44/7 and multiply this by 1/2 = 44/14. This is greater than 3, but less than 3.5, therefore, 3<t<3.5. Answer choice 3 < t < 3.5.
Answer: E
From the numbers given below select the √11?  Choose the correct choice.
A) 1.5	B) 2.9	C) 4.0	D) 3.1	E) 3.3

Solution: 3.3 is the correct answer   Let us simply square all the numbers    3.3*3.3= 
 3.3*3.3 = 10.89
10.89   3.1*3.1= 
3.1*3.1 = 9.61
9.61   Difference    11 - 10.89= 
 11 - 10.89 = 0.11
0.11   11 - 9.61= 
11 - 9.61 = 1.39
1.39   Since 0.11 is lesser of the both, 3.3 is closer   Answer is 3.3
Answer: E
When tossed, a certain six-sided die has an equal probability of landing on any of the six sides. If the die is tossed 2 times, what is the probability that it will land on the same side each time?  Pick
A) 1/2 B) 1/6 C) 1/12 D) 1/36 E) 1/60

Solution: On the first toss, the die will land on one of the sides.   On the second toss, the probability of landing on the same side is 1/6.   P(same side both times)=1/6.   The answer is 1/6.
Answer: B
Eight years ago, Rhea was half of Rick in age. If the ratio of their present ages is 3:4, what is the total of their present ages?	Choose the correct choice from the following.
A) 25 years B) 28 years C) 32 years D) 26 years E) 28 years

Solution: let rhea age be x   rick age be y   given   x-8=1/2(y-8)......a   also given   x/y=(3/4)   =>x=3/4(y).......b   by solving a and b   we get y=16   x=12   then x+y=12+16= 
12+16 = 28
28   ANSWER:28 years
Answer: B
You are standing in one of the biggest palaces in the world "Hofburg Palace, Vienna". In palace five commando are staying. Each commando has allotted five big rooms and each room contains five huge Tigers.
Each huge tiger has five small tigers.
We all know a tiger has 4 legs.
So how many legs are there in the palace ?  Choose the most appropriate option:
A) 3012
B) 3011
C) 3010
D) 3013
E) 3015

Solution: Solution:   3012   Explanation:   3012)   Five Commando alloted 5 room each, Number of rooms = 5 * 5= 
5 * 5 = 25
25   Number of huge Tiger= 25 * 5= 
25 * 5 = 125
125   Number of small Tigers= 125 * 5= 
125 * 5 = 625
625   Total tigers= 625 + 125= 
625 + 125 = 750
750   Number of legs of tigers= 750 * 4= 
750 * 4 = 3_000
3000 ..............................(1)   B)   There are 5 soldiers=>   Number of legs of soldiers = 5*2= 
5*2 = 10
10 .......................(2)   C)   Your leg= 2 ............(3)   Summing all , 3000 + 10 + 2 = 3012   3012nswer 3012
Answer: A
John's age is 86 years. If he is 4 more than twice the age of his son, find the age of his son.	Choose the correct choice from the following answers:  A) 20 years  B) 22 years  C) 40 years  D) 50 years  E) 60 years

Solution: Let Mike's son age be x.   4 + 2 x = 84   x = 40   Hence Mike's son age is 40 years   Answer : 40 years
Answer: C
The L.C.M of two numbers is 48. The numbers are in the ratio 2:3. The sum of numbers is:	Pick one:  A) 28  B) 30  C) 40  D) 50  E) 60

Solution: Let the numbers be 2x and 3x.   Then, their L.C.M = 6x. So, 6x = 48 or x = 8.   The numbers are 16 and 24.   Hence, required sum = (16 + 24)= 
(16 + 24) = 40
40.   ANSWER:40
Answer: C
Veena ranks 73rd from the top in a class of 182. What is her rank from the bottom if 22 students have failed the examination? Pick.
A) 88  B) 108  C) 110  D) 90  E) 93

Solution: total student=182   failed=22   paasd student=182-22= 
182-22 = 160
160   from bottom her rank is=160-73+1= 
160-73+1 = 88
88   88NSWER:88
Answer: A
How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
Choose the correct choice
A) 690 B) 720 C) 740 D) 760 E) 780

Solution: The word 'LOGARITHMS' has 10 different letters.   Hence, the number of 3-letter words(with or without meaning) formed by using these letters   = 10P3   =   10   ×   9   ×   8   =   720   Option 720
Answer: B
If a man lost 4% by selling oranges at the rate of 16 a rupee at how many a rupee must he sell them to gain 28%?  Choose the most appropriate option.
A) 12  B) 13  C) 14  D) 15  E) 10

Solution: 96% ---- 16   128% ---- ?     96/128 * 16= 
  96/128 * 16 = 12
12   12nswer: 12
Answer: A
Stock / Number of shares
V ------------ 68
W ---------- 112
X ------------ 56
Y ------------ 94
Z ------------ 45
The table shows the number of shares of each of the 5 stocks owned by Mr Sami. If Mr. Sami was to sell 20 shares of Stock X and buy 22 shares of stock Y, what would be the increase in the range of the numbers of shares of the 5 stocks owned by Mr. Sami?	Answers:
A) 4	B) 6	C) 9	D) 13	E) 20

Solution: Based on the original number of shares, the range would be: 112 - 45= 
112 - 45 = 67
67   However, the prompt tells us that two of the values in the table are going to change. After the changes, the values will be:   V 68   W 112   X 36   Y 116   Z 45   Now the range is   116 - 36= 
  116 - 36 = 80
80   The INCREASE in the range requires us to compare thenewrange to theoldrange:   80 - 67= 
  80 - 67 = 13
13   13
Answer: D
A boy is travelling from his home to school at 3 km/hr and reached 7 min late. Next day he traveled at 12 km/hr and reached 8 min early. Distance between home and school?	Choose the correct choice from the following.
A) 1km
B) 3km
C) 4km
D) 5km
E) 6km

Solution: Let the distance be x   T1 = x/3 hr   T2 = x/12hr   Difference in time = 7+8= 
7+8 = 15
15=1/4hr   x/3-x/12 = 1/4   x/4 = 1/4   x = 1 km   1kmnswer is 1km
Answer: A
The average of five results is 46 and that of the first four is 45. The fifth result is?
Choose the correct choice:
A) 18  B) 50  C) 27  D) 23  E) 12

Solution: 5 * 46 – 4 * 45   = 50   Answer:50
Answer: B
For covering 88km a wheel revolve 1000 times.what is the radius of wheel?
Select the correct option:
A) 14 m
B) 24 m
C) 28 m
D) 40 m
E) none of the above

Solution: distance travel in 1 round=88000/1000= 
88000/1000 = 88
88 m   perimeter=88 m,2πr=88,2R=[88*7/22= 
88*7/22 = 28
28 m   hence, diameter=28 m   answer 28 m
Answer: C
A chair is bought for Rs.600/- and sold at a loss of 10% find its selling price
Choose the correct choice from the following answers
A) Rs.540/- B) Rs.550/- C) Rs.560/- D) Rs.590/- E) Rs.580/-

Solution: 100 % ------> 600 (100 * 6 = 600)   90 % ------> 540 (90 * 6 = 540)   Selling price = Rs.540/-   Rs.540/-)
Answer: A
A florist has 2 azaleas, 4 buttercups, and 5 petunias. The florist puts two flowers together at random in a bouquet. However, the customer calls and says that she does not want two of the same flower. What is the probability that the florist does not have to change the bouquet?
Choose the correct choice.
A) 43/55
B) 38/55
C) 17/55
D) 8/11
E) 7/11

Solution: The probability that two of the same flowers were chosen:   P(AA) = 2/11 * 1/10 = 2/110   P(38/5538/55) = 4/11 * 3/10 = 12/110   P(PP) = 5/11 * 4/10 = 20/110   The sum of these probabilities is 17/55   P(two flowers are different) = 1 - 17/55 = 38/55   The answer is 38/55.
Answer: B
The H.C.F. of two numbers is 38 and the other two factors of their L.C.M. are 12 and 10. The larger of the two numbers is: Choose the correct choice from the following answers:
A) 678
B) 456
C) 234
D) 476
E) 432

Solution: :	Explanation:   Clearly, the numbers are (38 x 12) and (38 x 10).   {\color{Blue} \therefore } Larger number = (38 x 12) = 456.   Answer: 456)456
Answer: B
In one alloy there is 12% chromium while in another alloy it is 8%. 10 kg of the first alloy was melted together with 30 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.  Choose one:
A) 9.4%
B) 9.6%
C) 9%
D) 9.8%
E) 10%

Solution: The amount of chromium in the new 10+30= 
10+30 = 40
40 kg alloy is  0.12*10+0.08*30= 
 0.12*10+0.08*30 = 3.6
3.6 kg, so the percentage is  3.6/40*100= 
 3.6/40*100 = 9
9%.   Answer: 9%
Answer: C
The length of a side of a hexagon is 7 inches. What is the perimeter? Answers:
A) 48
B) 42
C) 44
D) 45
E) 40

Solution: Hexagon. It means 6 equal sides.   p = 6(7) = 42 inches   Answer 42
Answer: B
How much is 80% of 40 is greater than 4/5 of 25?  Answers:
A) 17	B) 19	C) 11	D) 12	E) 10

Solution: (80/100) * 40 – (4/5) * 25   32 - 20= 
32 - 20 = 12
12   Answer: 12
Answer: D
A chemical lab is scheduled to go through two air ventilation systems, a basic system and a more advanced system that takes forty minutes and 3 hours respectively to fully ventilate the room. If both ventilation systems were to operate at the same time with their respective constant rates, how many hours would it take to fully ventilate the chemical lab?
Choose the correct choice from the following options
A) 4/9  B) 2/3  C) 7/12  D) 6/11  E) 3/5

Solution: The rate of the basic system is 1 room/ (2/3 of an hour) = 3/2 rooms per hour   The rate of the advanced system is 1/3 of a room per hour   The combined rate is 11/6 rooms per hour.   The time to ventilate one room is 6/11 of an hour.   The answer is 6/11.
Answer: D
A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?  Choose the correct choice from the following options:
A) 228	B) 375	C) 219	D) 111	E) 121

Solution: Explanation:   CP1 = 100 SP1 = 120   CP2 = 80 SP2 = 80 * (125/100)= 
80 * (125/100) = 100
100   20 ----- 100   75 ----- ?=> 375   Answer:375
Answer: B
Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 110 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?	Select:
A) 280
B) 400
C) 540
D) 550
E) 840

Solution: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month:   2/3*3/4 = 1/2 survived the first month.   Of the geese that survived the first month, 3/5 did not survive the first year:   (1-3/5)*1/2 = 1/5 survived the first year.   110 geese survived the first year:   1/5*(total) = 110 --> (total) = 550.   Answer: 550.
Answer: D
In February Wilson’s earnings were 40 percent of his family’s total income. In March Wilson earned 25 percent less than in February. If the rest of his family’s income was the same in both months, then, in March, Wilson’s earnings were approximately what percent W of his family’s total income?  Choose the correct choice from the following:
A) 15%	B) 17%	C) 24%	D) 30%	E) 33%

Solution: Lets suppose the Total Family income in Feb = 100x   Wilson's earning in Feb = 40% of 100x = 40x   33%arnings of remaining family in Feb = 100x - 40x = 60x   Wilson's earning in March 100  - 40= 
100  - 40 = 60
60x   Wilson's earning in March= 75% of Wilson's Feb earnings = 75% of 40x = 30x   33%arnings of remaining family in March = 33%arnings of remaining family in Feb = 60x   Thus Wilson's earning as % of Total family income in March W= 30x/ (30+60)x = 30x/90x = 33.33%   Thus Answer is 33%
Answer: E
To mail a package, the rate is 20 cents for the first pound and 5 cents for each additional pound. Two packages weighing 4 pounds and 6 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved? Choices.
A) Separately, with a saving of 10 cents
B) Combined, with a saving of 25 cents
C) Combined, with a saving of 20 cents
D) Combined, with a saving of 15 cents
E) Separately, with a saving of 5 cents

Solution: 4 pounds cost = 20+3*5= 
20+3*5 = 35
35   6 pounds cost= 20+5*5= 
20+5*5 = 45
45   Total= 80   10 pounds cost = 20+ 9*5= 
20+ 9*5 = 65
65 dif. 80-65=15   Answer : Combined, with a saving of 15 cents
Answer: D
is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B? Choose the correct choice from the following answers.
A) 7
B) 8
C) 9
D) 10
E) 11

Solution: Let C's age be x years.   Then, B's age = 2x years.   A's age = (2x + 2) years.   (2x + 2) + 2x + x = 27   5x = 25 => x = 5   Hence, B's age = 2x = 10 years.   ANSWER:10
Answer: D
{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number selected will be a solution of the equation (x+5)(x+10)(2x-5) = 0?  Choose the correct choice:
A) 1/12 B) 1/6 C) 1/4 D) 1/3 E) 1/2

Solution: Roots of the equation (x-5)(x+10)(2x-5)=0 are x=-5,x=-10andx=5/2=2.5. So, three solutions present in our set of 12 distinct numbers, therefore P=3/12=1/4.   Answer: 1/4.
Answer: C
B @ K I 9 D Â© 5 2 T $ M 4 E J # U R 1 A Î´ K 5 W 6 % F Q 7 H P 8 Z
Which of the following should come in place of the question mark(?) in the following series based on the elements in the above arrangement?
K9D 2$M JUR ?
Choose the correct option:  A) Î´KW  B) Î´K5  C) Î´56  D) Î´W6  E) None of these

Solution: None of thesexplanation:   K +6 2 +6 J +6 Î´   9 +6 S +6 U +6 5   D +6 M +6 R +6 W   ANSWNone of theseR IS None of these
Answer: E
For any positive integer Y, the sum of the first Y positive integers equals Y(Y+1)/2 . If X and Y are positive integers and X > Y, what is the sum of all the integers between X and Y, inclusive?	Options
A) X(X+1)/2 + Y(Y+1)/2
B) X(X+1)/2 - Y(Y-1)/2
C) X(X+1)/2 - Y(Y+1)/2
D) X(X+1)/2 + Y(Y-1)/2
E) X(Y+1)/2 - Y(X-1)/2

Solution: The sum of all the integers between X and Y,inclusiveis the sum of the first X positive integersminusthe sum of the first Y-1 positive integers.   The sum of the first X positive integers is X(X+1)/2;   The sum of the first Y-1 positive integers is (Y-1)Y/2;   Therefore the answer is X(X+1)/2 - (Y-1)Y/2.   Answer: X(X+1)/2 - Y(Y-1)/2.
Answer: B
Rectangular tile each of size 60cm by 56cm must be laid horizontally on a rectangular floor of size 560cm by 240cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:
Select the correct option:
A) 50	B) 54	C) 47	D) 40	E) 45

Solution: Area of tile = 60*56= 
60*56 = 3_360
3360   Area of floor= 560*240= 
560*240 = 134_400
134400   No of tiles= 134400/3360= 
134400/3360 = 40
40   So, the no of tile= 40   ANSWER:40
Answer: D
The length of a rectangular landscape is 4times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/3rd of the total landscape. What is the length of the landscape?
Choose the correct choice from the following answers:
A) 100
B) 110
C) 120
D) 130
E) 140

Solution: Sol. x * 4x = 3 * 1200   x = 30   Length = 4 * 30= 
4 * 30 = 120
120   120
Answer: C
Let f(x) = x^2 + bx + c. If f(1) = 0 and f(-8) = 0, then f(x) crosses the y-axis at what y-coordinate? Choose the correct choice
A) -8	B) -1	C) 0	D) 1	E) 8

Solution: When x = 1 and when x = -8, the expression f(x) = x² + bx + c equals 0.   Then f(x) = (x-1)(x+8)   f(0) = -8   The answer is -8.
Answer: A
A man can swim in still water at 1.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? Choose the correct choice from the following choices:
A) 1.7
B) 0.5
C) 1.1
D) 1.5
E) 1.9

Solution: M = 1.5   S = x   DS = 1.5 + x   US = 1.5 + x   1.5 + x = (1.5 - x)2   1.5 + x = 3 -2x   3x = 1.5   x = 0.5   Answer:0.5
Answer: B