MU-NLPC/Calc-aqua_rat huggingface dataset:
Two sets A and B consists only of positive integers such that mean of set A is 55 . If set R consist of all the elements of both A and B such that mean of R is 80 then the mean of set B is =>  Select the correct option.
A) [A] 65
B) [B] 60
C) [C] 70
D) [D] 55
E) [E] cannot be determined

Solution: For this question, we have zero information about the size of two sets, sets AB. These two sets may have the same size or may be wildly different. Thus, the answer is (E), the mathematical answer cannot be determined. This is a very weak math question. As someone who writes GMAT practice questions, I would give this a grade of anD-as a question.   Answer [E] cannot be determined
Answer: E
What decimal of an hour is a second ? Choices: A) .0025 B) .0256 C) .00027 D) .000126 E) None of these

Solution: Explanation:   Required decimal =	1=	1= .00027   60 x 60=3600   Answer- .00027
Answer: C
A store owner estimates that the average price of type A products will increase by 35% next year and that the price of type B products will increase by 10% next year. This year, the total amount paid for type A products was $4500 and the total price paid for type B products was $8300. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?	Choose the correct choice from the following answers.
A) $14,755  B) $15,205  C) $16,000  D) $16,225  E) $17,155

Solution: cost of type A products next year = 1.35 * 4500= 
1.35 * 4500 = 6_075
6075   cost of type $15,205 products next year= 1.1 * 8300= 
1.1 * 8300 = 9_130
9130   total 6075 + 9130= 
6075 + 9130 = 15_205
15205 option $15,205
Answer: B
Average of five numbers is 27. If one number is excluded the average becomes 25. The excluded
number is  Choose the most appropriate option
A) 35	B) 45	C) 55	D) 65	E) 75

Solution: Explanation:   Number is (5*27) - (4*25) = 135-100= 
135-100 = 35
35   35nswer: Option 35
Answer: A
A gambler bought $3,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 13 chips, and then cashed in the remainder. If the number of $20 chips lost was 3 more or 3 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back?	Pick one
A) $2,040
B) $2,120
C) $2,240
D) $1,920
E) $1,400

Solution: In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost.   So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 13: x+x-3=13 --> x=8: 8 $20 chips were lost and 8-2= 
8-2 = 6
6 $100 chips were lost.   Total worth of chips lost is   8*20+6*100= 
  8*20+6*100 = 760
$760, so the gambler kept $3,000-$760=$2,240.   Answer: $2,240.
Answer: C
An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
Choose the correct choice:	A) 33 1/8%	B) 33 8/3%	C) 33 1/3%	D) 35 1/3%	E) 32 1/3%

Solution: 675 ---- 225   100 ---- ? => 33 1/3%   Answer: 33 1/3%
Answer: C
The measures of the 2 acute angles of a triangle are in the ratio of 2:7. What are the measures of the 2 angles? Pick
A) 40° B) 70° C) 80° D) 100° E) 180°

Solution: If the ratio of the two angles is 2:7, then the measures of two angles can be written as 2x and 7x. Also the two acute angles of a triangle is equal to 90°. Hence   2x + 7x = 90   9x = 90   x = 10   Measures of the two acute angles are   2x = 2 × 10 = 20°   7x = 7 × 10 = 70°   70°
Answer: B
Find the area of a parallelogram with base 22 cm and height 14 cm?
Choose the correct option:
A) 298 cm2  B) 384 cm2  C) 308 cm2  D) 286 cm2  E) 276 cm2

Solution: Area of a parallelogram = base * height = 22 * 14= 
22 * 14 = 308
308 cm2   Answer:308 cm2
Answer: C
24 oz of juice P and 25 oz of juice V are mixed to make smothies M and Y . The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie M?
Choose the correct option:  A) 5  B) 10  C) 15  D) 20  E) 25

Solution: The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.p1 + p2 = 24   v1 + v2 = 25   p1 = 4v1   p2 = v2/5   4v1 + v2/5 = 24   v1 + v2 = 25   4v2 - v2/5 = 76   19v2/5 = 76 => v2 = 20   => v1 = 5   => p1 = 20   Answer - 20
Answer: D
If n = 30! + 27, then n is divisible by which of the following?
I. 25
II. 27
III. 29 Choose the correct choice from the following options
A) None  B) I only  C) II only  D) I and II  E) II and III

Solution: 27 divides 30! so 27 also divides 30! + 27.   25 and 29 divide 30! so they do not divide 30! + 27.   The answer is II only.
Answer: C
The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 6400 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units? Choose the correct answer:
A) 140 sq.units
B) 320 sq.units
C) 367sq.units
D) 178sq.units
E) 176sq.units

Solution: Given that the area of the square = 6400 sq.units   => Side of square = √6400 = 80 units   The radius of the circle = side of the square = 80 units Length of the rectangle = 2/5 * 80= 
2/5 * 80 = 32
32 units   Given that breadth= 10 units   Area of the rectangle = lb = 32 * 10= 
32 * 10 = 320
320 sq.units   Answer:320 sq.units
Answer: B
The least number,which when divided by 48,60,72,108 and 140 leaves 38,50,62,98 and 130 as remainder respectively, is : Choose the correct choice:  A) 11115  B) 15110  C) 15120  D) 15210  E) 12510

Solution: Solution   Here (48 - 38)= 
(48 - 38) = 10
10 , (60 - 50)= 10,(72 - 62) = 10,(108 - 98) = 10 & (140 - 130)= 
(140 - 130) = 10
10.   So, Required number= (L.C.M. of 48,60,72,108,140) - 10 = 15120 - 10= 
15120 - 10 = 15_110
15110. Answer 15110
Answer: B
A buffet costs rs300. owner reduced the price 20% less. he got profit of 25% on its revenue. what is the percentage increase in number of customers?
Select:	A) 56%	B) 57%	C) 58%	D) 45%	E) 35%

Solution: let assume he sells 1 buffet daily,   now   then 300*1 = revenue (eq -1)   if he reduced his price by 20% then ,   240*(customer) = 125/100*revenue   customer = 1.25*300/240 = 1.56   means 56 % increase in customer.   56%NSWER:56%
Answer: A
The population of a village is 10000. It increases annually at the rate of 20% p.a. What will be its population after 2 years?
Choose the correct choice from the following
A) 10000 B) 12000 C) 13000 D) 14000 E) 14400

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   10000 × 120/100 × 120/100 = 14400   14400
Answer: E
For any integer k greater than 1, the symbol k* denotes the product of all the fractions of the form 1/t, where t is an integer between 1 and k, inclusive. What is the value of 5*/6* ?
Choose the correct choice from the following answers:
A) 5  B) 5/4  C) 4/5  D) 1/4  E) 1/5

Solution: When dealing with 'Symbolism' questions, it often helps to 'play with' the Symbol for a few moments before you attempt to answer the question that's asked. By understanding how the Symbol 'works', you should be able to do the latter calculations faster.   Here, we're told that K* is the PRODUCT of all the fractions of the form 1/T, where T is an integer between 1 and K, inclusive.   Based on this definition....   IF....   K = 2   K* = (1/1)(1/2) = 1/2   IF....   K = 3   K* = (1/1)(1/2)(1/3) = 1/6   We're asked to find the value of 5*/4*   Now that we know how the Symbol 'works', solving this problem shouldn't be too difficult. You can actually choose to do the math in a couple of different ways....   5* = (1/1)(1/2)(1/3)(1/4)(1/5)   1/4on't calculate this just yet though....since we're dividing by 4*, many of those fractions will 'cancel out.'   4* = (1/1)(1/2)(1/3)(1/4)   We're looking for the value of:   (1/1)(1/2)(1/3)(1/4)(1/5) / (1/1)(1/2)(1/3)(1/4)   Since the first four fraction in the numerator and denominator cancel out, we're left with just one fraction:   1/4   1/4
Answer: D
A man can row upstream at 25 kmph and downstream at 41 kmph, and then find the speed of the man in still water? Choose the correct answer.
A) 33
B) 67
C) 30
D) 15
E) 17

Solution: US = 25   DS = 41   M = (41 + 25)/2= 
(41 + 25)/2 = 33
33   33nswer: 33
Answer: A
Let the polynomials be:
P1(x)=3x2−7x+4,
P2(x)=−5x2−4x+2,
P1(x)+P2(x)=	Choose the correct choice from the following answers.
A) 2x2 + 11x - 7
B) -2x2 - 11x + 6
C) -2x2 - 11x + 6
D) 2x2 - 9x + 7
E) None of these

Solution: Solution:   P1(x)+P2(x)=(3x2−7x+4)+(−5x2−4x+2)=P1(x)+P2(x)=(3x2−7x+4)+(−5x2−4x+2)=   3x2−7x+4−5x2−4x+2=3x2−7x+4−5x2−4x+2=   −2x2−11x+6   Answer -2x2 - 11x + 6
Answer: B
A certain galaxy is known to comprise approximately 10^11 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?  Select the correct option:
A) 800	B) 1,250	C) 2,000	D) 12,000	E) 80,000

Solution: 10^11   50 mln = 5*10^7   we divide 10^11 by 10^7 and we get 10^4=10,000 and divide by 5. the result is 2,000   2,000
Answer: C
A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length? Choose the correct choice.
A) 30 B) 50 C) 40 D) 60 E) 70

Solution: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= Distance/speed   = 500 * (2/25)= 
500 * (2/25) = 40
40 seconds   Answer: Option 40
Answer: C
In a race of 200 m, A can beat B by 40 m and C by 20 m. In how many meter race, C will beat B by 50m ?
Choose the correct choice from the following.
A) 225 m B) 285 m C) 200 m D) 250 m E) 150 m

Solution: Explanation:   A:B = 100 : 60   A:200 m = 100 : 80   =>B:200 m = 60:80 = 3:4   When 200 m covers 80 m , B 200 movers 60 m   When 200 m covers x m , B 200 movers   => x - 50 m   3x/4 = x - 50   x = 200 m   Answer: 200 m
Answer: C
There are two numbers. If 20% of the first number is added to the second number, then the second number increases to its five-fourth. What is the ratio of the first number to the second number?
Choose the correct answer
A) 2 : 9
B) 3 : 8
C) 8 : 5
D) 5 : 4
E) 7 : 3

Solution: Let the two numbers be x and y.   (2/10) * x + y = (5/4) * y   (2/10) * x = (1/4) * y   x/y = 10/8 = 5/4   The answer is 5 : 4.
Answer: D
Of 55 players on a cricket team, 37 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total? Choose the most appropriate option: A) 49 B) 55 C) 59 D) 71 E) 92

Solution: Total = 55   Thrower = 37   Rest = 55 - 37= 
55 - 37 = 18
18   Left Handed= 18/3= 
18/3 = 6
6   Right handed= 12   If all Thrower are right handed then total right handed is   37 + 12= 
  37 + 12 = 49
49   so A. 49 is the right answer
Answer: A
When the smallest of 3 consecutive odd integers is added to four times the largest, it produces a result 730 more than 4times the middle integer. Find the numbers?	Choose the correct choice from the following
A) 650
B) 678
C) 698
D) 710
E) 730

Solution: x + 4 (x + 4) = 730 + 4 (x + 2)   Solve for x and find all three numbers   x + 4 x + 16 = 730 + 4 x + 8   x = 722   x + 2 = 724   x + 4 = 726   Check: the smallest is added to four times the largest   722 + 4 * 726= 
722 + 4 * 726 = 3_626
3626   four times the middle   4 * 724= 
4 * 724 = 2_896
2896   3626 is more than 2896 by   3626 - 2896= 
3626 - 2896 = 730
730   730
Answer: E
What is the smallest number which when increased by 3 is divisible by 18, 70, 25 and 21?
Options:
A) 2327
B) 2757
C) 3147
D) 3587
E) 3997

Solution: When increased by 3, the number must include at least 2*3^2*5^2*7 = 3150   The answer is 3147.
Answer: C
A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it? Choices
A) 14 1/7 days  B) 15 1/7 days  C) 16 2/3 days  D) 17 1/7 days  E) 18 1/7 days

Solution: 5/10 + 20/x = 1   x = 40   1/30 + 1/40 = 7/120   120/7 = 17 1/7 days   ANSWER:17 1/7 days
Answer: D
An iron cube of side 10 cm is hammered into a rectangular sheet of thickness 0.5 cm. If the sides of the sheet are in the ratio 1 : 5, the sides are :  Choose the correct choice from the following answers
A) 10 cm20 cm
B) 2 cm10 cm
C) 100 cm20 cm
D) 30 cm100 cm
E) None

Solution: Sol.   Let the sides of the sheet be x and 5x. Then,   ⇒ x * 5x * 1/2 = 10 * 10 * 10 ⇒ 5x² = 2000 ⇒ x² = 400 ⇒ x = 20.   ∴ The sides are 20 cm and 100 cm.   10 cm20 cmnswer 10 cm20 cm
Answer: A
In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together ?	Pick: A) 120960 B) 135650 C) 115850 D) 142560 E) 185260

Solution: In the word 'MATHEMATICS' we treat the two vowels AEAI as one letter. Thus,we have MTHMTCS (AEAI)   Now, we have to arranged 8 letters, out of which M occurs twice, T occurs twice and the rest are different.   Number of ways of arranging these letters= 8!/(2!)(2!)=10080.   Now AEAI has 4 letters in which A occurs 2 times and the rest are different.   number of ways of arranging these letters =4!/2!=12.   Required number of ways =(10080*12)= 
(10080*12) = 120_960
120960.   120960nswer is 120960
Answer: A
The average age of 15 students of a class is 15 years. Out of these, the average age of 4 students is 14 years and that of the other 10 students is 16 years, The age of the 15th student is Answers.
A) 11  B) 12  C) 9  D) 14  E) 15

Solution: Explanation:   Age of the 15th student = [15 * 15 - (14 * 5 + 16 * 9)] = 9 years. Answer: 9
Answer: C
In one hour, a boat goes 19 km/hr along the stream and 11 km/hr against the stream. The speed of the boat in still water (in km/hr) is:	Choices:
A) 12 kmph
B) 13 kmph
C) 14 kmph
D) 15 kmph
E) 16 kmph

Solution: Explanation:   Let the speed downstream be a km/hr and the speed upstream be b km/hr, then   Speed in still water =1/2(a+b) km/hr   Rate of stream = 1/2(a−b) km/hr   Speed in still water = 1/2(19+11) kmph = 15 kmph.   Answer: Option 15 kmph
Answer: D
A runs twice as fast as B and gives B a start of 71m.How long should the racecourse be so that A and B might reach in the same time? Pick one
A) 75 m.  B) 80 m.  C) 150 m.  D) 142 m.  E) None of the above

Solution: ratio of speeds of a and b is 2:1   b is 71m away from a but we know that a covers 1 meter(2-1) more in every second than b   the time taken for a to cover 71m is   71/1= 
  71/1 = 71
71m   so the total time taken by a and b to reach=2*71= 
2*71 = 142
142m   ANSWER:142 m.
Answer: D
On a weekend, 11 college friends went to the beach and evenly split the cost of their beach house. If the amount paid by each person was an integer, which of the following could not have been the cost of the beach house?
Answers.
A) $121  B) $568  C) $484  D) $363  E) $319

Solution: Each of the seven persons evenly splitting the cost is an integer amount, therefore check the divisibility by 11 for all answer choices.   121/11= 
121/11 = 11
11   568/11= 51.64   484/11= 
484/11 = 44
44   363/11= 
363/11 = 33
33   319/11= 
319/11 = 29
29   B is not an integer amount.   Answer:$568
Answer: B
How many four-digit numbers are there such that all three digits are different and the first digit and last digit is not zero?
Choose the correct choice from the following options:
A) 2128
B) 3458
C) 4207
D) 5184
E) 8104

Solution: All three digits are different and first digit is not zero.   So first digit can be filled in 8 ways.   And, second digit can be filled in 9 ways.   And, third digit can be filled in 9 ways.   And, fourth digit can be filled in 8 ways.   Total ways = 8*9*9*8= 
8*9*9*8 = 5_184
5184   Hence option (5184).
Answer: D
A bus 75 m long is running with a speed of 21 km/hr. In what time will it pass a woman who is walking at 3 km/hr in the direction opposite to that in which the bus is going? Choose the correct answer:
A) 5.75
B) 7.62
C) 11.25
D) 4.25
E) 3.25

Solution: Speed of bus relative to woman = 21 + 3= 
21 + 3 = 24
24 km/hr.= 24 * 5/18 = 20/3 m/sec.   Time taken to pass the woman = 75 * 3/20= 
75 * 3/20 = 45/4 = around 11.25
11.25 sec.   Answer: 11.25
Answer: C
Find the fourth proportion to 2,5,12	Choose the correct choice from the following choices
A) 18  B) 12  C) 40  D) 30  E) 24

Solution: Explanation:   2:5 :: 12:x   => 2/5 = 12/x   => x = 60/2   => x = 30   Option 30
Answer: D
A container contains 40 litres of milk.From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container. Answers:
A) 29.19 litres	B) 29.96 litres	C) 99.16 litres	D) 29.16 litres	E) 23.16 litres

Solution: Answer: 29.16 litres) 29.16 litres
Answer: D
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 one.
A) 30229
B) 3000
C) 278
D) 274
E) 287

Solution: 60*5:36*6:75*3   100: 72: 75   100/247 * 7410= 
100/247 * 7410 = 3_000
3000   Answer:3000
Answer: B
The area of sector of a circle whose radius is 18 metro and whose angle at the center is 42Â° is?	Choices:
A) 52.6  B) 52.9  C) 52.8  D) 118.8  E) 52.2

Solution: 42/360 * 22/7 * 18 * 18= 
42/360 * 22/7 * 18 * 18 = 594/5 = around 118.8
118.8 m2   Answer: 118.8
Answer: D
There are 10 slate rocks, 11 pumice rocks, and 4 granite rocks randomly distributed in a certain field. If 2 rocks are chosen at random and without replacement, what is the probability that both rocks will be slate rocks?
Pick:  A) 3/20  B) 5/26  C) 7/34  D) 9/37  E) 11/49

Solution: 10/25*9/24 = 3/20   The answer is 3/20.
Answer: A
In a box, there are 8 orange, 7 black and 6 white balls. If one ball is picked up randomly. What is the probability that it is neither orange nor white? Choose the most appropriate option.
A) 2/3 B) 3/4 C) 7/19 D) 8/21 E) 10/21

Solution: total balls are 21   and neither black nor white .   so favor case will be only 8C1   and total case 21C1   probability will be 8C1/21C1=8/21   ANSWER:8/21
Answer: D
Two trains 110 meters and 200 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?	Answers
A) 4.85 B) 7.69 C) 6.85 D) 5.85 E) 6.15

Solution: T = (110+ 200)/ (80 + 65) * 18/5   T = 7.69   ANSWER:7.69
Answer: B
Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 7 = f(3x – 6)
Choose the correct choice from the following:
A) 0
B) 2
C) 6
D) 7
E) 13

Solution: Answer = 2 = 2   f(x) = 3x – 5   2*[f(x)] – 7 = f(3x – 6)   2(3x-5) -7 = 3 (3x-6) - 5   6x - 17 = 9x - 23   x = 2
Answer: B
A and B enter into partnership with capitals in the ratio 1 : 2. At the end of 10 months A withdraws,and the profits now are divided in the ratio of 5 : 6. Find how long B remained in the business? Pick one
A) 9 months
B) 8 months
C) 6 months
D) 7 months
E) None of these

Solution: Initially A’s investment = 1x and B’s investment = 2x   Let B remain in the business for ‘n’ months.   ⇒ 1x × 10 : 2x × n = 5 : 6   ∴ 1x × 10 × 6 = 2x × n × 5   ⇒ n = 6   Answer 6 months
Answer: C
A rectangular courtyard 3.78 metres long and 2.25 metres wide is to be paved exactly with square title, all of the same size. What is the largest size of the tile which could be used for the purpose ?	Choose the correct choice from the following
A) 11 cms B) 21 cms C) 42 cms D) None of these E) 46 cms

Solution: Solution   Largest size of the tile = H.C.F. of 378 cm an= 21 cm = 525 cm. Answer 21 cms
Answer: B
30 men can do a work in 40 days. When should 20 men leave the work so that the entire work is completed in 40 days after they leave the work?	Choose the correct choice from the following:
A) 22 days B) 10 days C) 77 days D) 88 days E) 55 days

Solution: Total work to be done = 30 * 40= 
30 * 40 = 1_200
1200   Let 20 men leave the work after 'P' days, so that the remaining work is completed in 40 days after they leave the work.   40P + (20 * 40)= 1200   40P = 400 => P = 10 days   Answer:10 days
Answer: B
Five players forms a team joins in a shooting game. The best shooter scored 78 points. If he had scored 95 points, the average score for the team would have been 85. The number of points, the team scored, was
Choose the correct choice from the following answers:
A) 288  B) 345  C) 408  D) 672  E) 578

Solution: Explanation :   Let the total score be x.   (x +95 - 78)/5 = 85 so x+17 = 425 so x=408   Answer : 408
Answer: C
Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 30% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of
Choices:
A) 18%
B) 20%
C) 30%
D) 23%
E) Cannot be determined

Solution: Answer: 30%.
Answer: C
David covered a distance of 50 miles on his first trip. On a later trip he traveled 150 miles while going three times as fast. His new time compared with the old time was:  Choose the correct answer.
A) twice as much	B) three times as much	C) the same	D) half as much	E) a third as much

Solution: Let t be the time of the first trip.   On the later trip, David can travel 150 miles in time t.   The answer is the same.
Answer: C
A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
Choose the most appropriate option
A) 7
B) 6
C) 9
D) 4
E) 2

Solution: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.   Given x + y = 18 --- (1)   and x - y = 10 --- (2)   From (1) & (2) 2x = 28 => x = 14, y = 4.   Answer: 4
Answer: D
In a group of 28 junior high school students, 7 take French, 10 take Spanish, and 2 take both languages. The students taking both French and Spanish are not counted with the 7 taking French or the 10 taking Spanish. How many students are not taking either French or Spanish?	Choose the correct choice.
A) 7  B) 6  C) 9  D) 4  E) 8

Solution: C   9   Add 7 + 10 + 2 to get 19   Then subtract 21 from the total students ⇒ 28 – 19 = 9.   Answer is 9
Answer: C
An equal number of desks and bookcases are to be placed along a library wall that is 15 meters long. Each desk is 2 meters long, and each bookshelf is 1.5 meters long. If the maximum possible number of desks and bookcases are to be placed along the wall, then the space along the wall that is left over will be how many meters F long?  Choose one:	A) 0.5	B) 1	C) 1.5	D) 2	E) 3

Solution: Let x be the number of desks and bookcases that are placed along the library wall.   2x + 1.5x < 15   3.5x < 15   Since x is a non negative integer, the largest number x can be is 4.   When x is 4, the desks and bookcases take up 3.5 * 4= 
3.5 * 4 = 14
14m, leaving 1m of empty space.   Thus, I believe the answer is 1) 1
Answer: B
Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -8 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions? Choices.
A) 54
B) 4032
C) 2,160
D) 2,916
E) 148,824

Solution: We have the rectangle with dimensions 9*8 (9 horizontal dots and 8 vertical). AB is parallel to y-axis and AC is parallel to x-axis.   Choose the (x,y) coordinates for vertex A: 9C1*8C1;   Choose the x coordinate for vertex C (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A);   Choose the y coordinate for vertex B (as x coordinate is fixed by A): 7C1, (8-1=7 as 1 vertical dot is already occupied by A).   9C1*8C*8C1*7C1=4032.   Answer: 4032.
Answer: B
Reeya obtained 55, 67, 76, 82 and 85 out of 100 in different subjects, What will be the average Select the correct option.
A) 70 B) 75 C) 73 D) 85 E) 90

Solution: Explanation:   (55+67+76+82+85 / 5)=73   Option 73
Answer: C