MU-NLPC/Calc-aqua_rat huggingface dataset:
The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 14 cm each. The radius of the sphere is  Select:
A) 3 cm
B) 4 cm
C) 6 cm
D) 7 cm
E) None

Solution: Solution   4Î R2	= 2Î 7x14   â‡’ R2 = (7x14/2)   â‡’ 49   â‡’ R = 7 cm.   Answer 7 cm
Answer: D
A train 110 m long is running with a speed of 36 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going? Options:
A) 5
B) 6
C) 7
D) 9
E) 5

Solution: Speed of train relative to man = 36 + 6= 
36 + 6 = 42
42 km/hr.= 42 * 5/18 = 35/3 m/sec.   Time taken to pass the men = 110 * 3/35 = 9 sec.Answer: 9
Answer: D
A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 106. What was the number he chose?
Choose the correct choice:
A) 123
B) 267
C) 277
D) 122
E) 120

Solution: Let xx be the number he chose, then   2â‹…xâˆ’138=106   x=122   Answer:122
Answer: D
In a camp, there is a meal for 160 men or 220 children. If 160 children have taken the meal, how many men will be catered to with remaining meal?  Choose the correct choice.
A) 41
B) 16
C) 15
D) 14
E) 20

Solution: B   16   There is a meal for 200 children.   180 children have taken the meal.   Remaining meal is to be catered to 20 children.   Now, 200 children 160 men.   20 children = (160/200)x 20= 16 men.
Answer: B
2 friends A n B running up hill and then to get down length of road 440 yads A on his return journey met B going up at 20 yards from top if A has finished race 5 minute earlier than B then how much time A had taken to complete the race ?  Choose the correct choice.
A) 100 minute  B) 110 minute  C) 120 minute  D) 130 minute  E) 140 minute

Solution: total journey= 440*2= 
440*2 = 880
880   A meet B 20 yards from top in getting down it means he has covered   440+20= 
  440+20 = 460
460 yards while B is 420 yards.so he is 40 yards ahead of B which is equals to 5 minute.   so 40 yards in 5 min   880 yards will be in 5*880/(40)= 
5*880/(40) = 110
110 minute   ANSWER:110 minute
Answer: B
Wilson can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows?
Choose the correct option.
A) 40 minutes. B) 1 hour and 30 minutes. C) 1 hour. D) 1 hour and 40 minutes. E) 2 hours and 15 minutes.

Solution: Rate =Output/Time   Wilson Rate=25/20=5/4   Dylan Rate=25/60=5/12   1 hour.ombined rate = 5/4+5/12= 20/12   1 hour.ombinedRate*1 hour.ombinedTime= 1 hour.ombinedOutput   20/12*t=150   t=90 mins => 1 hr 30 min
Answer: C
City A and City B are 140 miles apart. Train C departs City A, heading towards City B, at 4:00 and travels at 40 miles per hour. Train D departs City B, heading towards City A, at 5:00 and travels at 20 miles per hour. The trains travel on parallel tracks. At what time do the two trains meet? Select the correct option
A) 5:00
B) 5:30
C) 6:00
D) 6:30
E) 7:00

Solution: Train C has traveled 20 mi in the half hour before Train D has started its journey.   140-20= 
140-20 = 120
120   40+20= 
40+20 = 60
60 mph   120 mi/ 60 mph= 2 hrs   5:00pm + 2 hrs = 7:00pm   Answer:   E. 7:00
Answer: E
A sports equipment store sold ping pong rackets for a total of $735. If the average (arithmetic mean) price of a pair of rackets is $9.8, how many pairs were sold?  Choose the correct option.
A) 50
B) 100
C) 490
D) 500
E) 75

Solution: Average price for a pair of rackets = $9.8   Total cost = $9.8*x = $735   x = 75 pairs were sold.   ANSW75R:75
Answer: E
Each night before he goes to bed, Jordan likes to pick out an outfit to wear the next day. He has 11 different shirts, 10 different pairs of jeans, and 8 pairs of sneakers. If an outfit consists of 1 shirt, 1 pair of jeans, and 1 pair of sneakers, how many different outfits does Jordan have? Choose the correct answer:  A) 30  B) 90  C) 240  D) 480  E) 880

Solution: Total # of outfits = 11 * 10 * 8= 
11 * 10 * 8 = 880
880   Answer - 880
Answer: E
Lucy deposited $62500 in an investment fund that provided 20 percent annual return compounded quarterly. If she made no other transactions with the fund, in how much time, in months, did her investment earn a total interest of $5100?
Pick.
A) 0.5 B) 2.4 C) 3 D) 6 E) 6.1

Solution: A = P + I = 62500 + 5100= 
62500 + 5100 = 67_600
67600   67600= 62500(1 + 20/4*100)^(4t)   (676/625) = (105/100)^(4t)   t = 1/5 yrs = 2.4 months   Answer: 2.4
Answer: B
The amount of electrical current that flows through a wire is inversely proportional to the resistance in that wire. A wire originally carries 4 amperes of electrical current. Then the resistance is reduced to one-fourth of its original value. How many amperes of electrical current will flow through the wire? Choose the correct option
A) 2
B) 4
C) 8
D) 16
E) 24

Solution: Given that, I∝1/R, I*R is a constant value.   I1*R1 = I2*R2   I1*R1 = I2*R1/4   I2 = 4*I1 = 16 amperes   The answer is 16.
Answer: D
The average marks obtained by 120 cndidates in a certainexaminationis 35.if the average marks of passed candidate is 39 and that of the failedcandidates is 15,what is the number of candidates who passed the examination	Pick one.
A) 14 years  B) 14 years 5 month  C) 14 years 8 month  D) 15 years  E) 15 years 5 month

Solution: (d) Let No. of passed candidates are x   So, x * 39 + (120 – x) 15= 120 * 35   x = 100   2.(a) Total increase = 8 * 2= 
8 * 2 = 16
16 years   So, total age of two women= 35 + 45 +16= 
35 + 45 +16 = 96
96   Average age of two women=96/2= 
96/2 = 48
48 years   3(d) Total decrease= 20 * 2= 
20 * 2 = 40
40 month= 3 years 4 month   So, age of new boy = 18 years – 3 years 4 month   = 14 years 8 month   14 years 8 month
Answer: C
In a division sum, the divisor is 12 times the quotient and 6 times the remainder. If the remainder is 24, what is the divident?  Pick
A) 1738
B) 1752
C) 1846
D) 1648
E) None

Solution: Solution: Dividend= [Divisor*quotient]+Remainder ----> (1).   Given divisor=6*24= 
6*24 = 144
144. 12*quotient=144 => quotient=144/12= 
144/12 = 12
12.   substitute these values in the (1) then we get 1752 as dividend.   Answer 1752
Answer: B
What is the minimum number of square marbles required to tile a floor of length 3 metres 39cm and width 2 metres 26 cm? Options:
A) 176	B) 187	C) 540	D) 748	E) 6

Solution: The marbles used to tile the floor are square marbles.   Therefore, the length of the marble=width of the marble.the length of the marble=width of the marble.   As we have to use whole number of marbles, the side of the square should a factor of both 3 m 39 cm and 2m 26. And it should be the highest factor of 3 m 39 cm and 2m 26.   3 m 39 cm = 339 cm and 2 m 26 cm = 226 cm.   The HCF of 339 and 226 = 113.   Hence, the side of the square is 113.   The number of such square marbles required,   =339×226/113×113   =6 marbles   Option(6)
Answer: E
In how many different number of ways 5 men and 2 girls can sit on a shopa which can accommodate persons? Pick one: A) 180 B) 200 C) 210 D) 220 E) 240

Solution: 7p3 = 7 × 6 × 5 = 210   210)
Answer: C
In how many different ways can the letters of the word ‘ARMOUM’ be arranged?
Options
A) 213  B) 220  C) 230  D) 240  E) 360

Solution: ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360   360
Answer: E
Three pounds of 05 grass seed contain 5 percent herbicide. A different type of grass seed, 20, which contains 20 percent herbicide, will be mixed with three pounds of 05 grass seed. How much grass seed of type 20 should be added to the three pounds of 05 grass seed so that the mixture contains 15 percent herbicide?	Choose the correct option:
A) 3	B) 3.75	C) 4.5	D) 6	E) 9

Solution: 05 grass seed contains 5% herbicide and its amount is 3 pound   20 grass seed contains 20% herbicide and its amount is x   when these two types of grass seeds are mixed, their average becomes 15%   thus we have   3(5)+x(20)/(x+3) = 15   15+20x=15x +45   5x=30   or x=6   ANSWER:6
Answer: D
Machine–X produces 50% of the total output and Machine-Y produces 75% of the total output. An average of 16 units out of a thousand goods manufactured by Machine-X and 3 unit of 500 units produced by Machine-X prove to be defective. What is the probability that a unit chosen at random from the total daily output of the factory is defective? Answers:
A) 0.01
B) 0.02
C) 0.04
D) 0.06
E) 0.08

Solution: Suppose machine X produce 1000 units   total defective = 16   Machine Y then produces=1500 units   total defective=9   probability=25/2500= 
25/2500 = 1/100 = around 0.01
0.01   0.01nswer : 0.01
Answer: A
6 points are marked on a straight line and another 8 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?  Choose one:
A) 91 B) 105 C) 288 D) 21 E) 14

Solution: getting the answer 288 which is not in the choices, what is the source of the problem?   62882* 82881 + 82882* 62881 = 288   288
Answer: C
A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12400 after a year?
Choose the correct choice:
A) 3630  B) 9232  C) 3720  D) 3720  E) 2813

Solution: 6300:4200:10500   3:2:5   3/10 * 12400= 
3/10 * 12400 = 3_720
3720   Answer: 3720
Answer: C
I. c^2 - 9c + 20 = 0,
II. 2d^2 - 5d- 12 = 0 to solve both the equations to find the values of c and d?  Pick:  A) c< d  B) c ≤ d  C) the relationship between c and d cannot be established  D) c> d  E) a ≥ b

Solution: I. (c- 5)(c- 4) = 0   => c= 5, 4   II. (2d+ 3)(d- 4) = 0   => d= 4, -3/2 => c≥ d   Option a ≥ b
Answer: E
From the word 'CARRIAGE', how many independent words can be made with-out changing the order of the letters and using each letter only once ?
Choices
A) 5 B) 8 C) 3 D) 2 E) 9

Solution: Explanation:   The words formed are   3AR, AGE and RIAGE   Answer: 3) 3
Answer: C
The value of a machine depreciates at 23% per annum. If its present value is $1,50,000, at what price should it be sold after two years such that a profit of $24,000 is made?
Pick:
A) $252935  B) $432935  C) $122935  D) $112935  E) $152935

Solution: The value of the machine after two years = 0.77 * 0.77 * 1,50,000 = $88,935   SP such that a profit of $24,000 is made = 88,935 + 24,000 = $1,12,935   $112935
Answer: D
A train travels from New York to Chicago, a distance of approximately 480 miles, at an average rate of 40 miles per hour and arrives in Chicago at 6:00 in evening, Chicago time. At what hour in the morning, New York time, did the train depart for Chicago? (Note : Chicago time is one hour earlier than New York time)
Answers: A) 3:00 B) 4:00 C) 5:00 D) 6:00 E) 7:00

Solution: 6:00 in evening in Chicago = 7:00 in evening in New York. So, the train was in Chicago 7:00 in the evening, New York time.   The trip took T=D/R=480/40= 
480/40 = 12
12 hours. Therefore, the train depart from New York at 7:00 - 12 hours= 7:00 in the morning, New York time.   Answer: 7:00.
Answer: E
What is the remainder when 9^1 + 9^2 + 9^3 +...+ 9^9 is divided by 9? Options.
A) 2	B) 3	C) 0	D) 5	E) None of the above

Solution: Notice that in the brackets we have the sum of 9 odd multiples of 9, which yields remainder of 0 upon division by 9.   Answer : 0
Answer: C
A river 2m deep and 45 m wide is flowing at the rate of 3 kmph the amount of water that runs into the sea per minute is?  Pick one:
A) 4500
B) 2678
C) 2689
D) 2761
E) 2882

Solution: (3000 * 2 * 5)/60   = 4500 M3   4500nswer:4500
Answer: A
A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number ?  Choose the correct choice from the following answers:
A) 2	B) 4	C) 5	D) 8	E) 9

Solution: Explanation:   Let the number be v. Then, 3 (2x + 9) = 75.   2x + 9 = 25   => 2x = 16   => x = 8   Answer: 8) 8
Answer: D
Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 17 times as heavy as water? Choose the correct choice from the following answers
A) 1:2 B) 3:2 C) 4:1 D) 5:2 E) 6:5

Solution: G = 19W   4:1 = 9W   Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy   1gm gold + x gm copper = x+1 gm of alloy   19W+9Wx = x+1 * 17W   19+9x = 17(x+1)   x = 1/4   Ratio of gold with copper = 1:1/4 = 4:1   Answer is 4:1
Answer: C
In what time will the simple interest be 2/5 of the principal at 8 per cent per annum?
Choose the correct answer.
A) 8 years  B) 7 years  C) 6 years  D) 5 years  E) 4 years

Solution: Explanation:   Let sum = x.   Then, Amount =2/5 x ,R=8% pa   Here, S.I = 2/5 of sum   Time =( 100 X 2x/x X 5 X 8) = 5 Years   Answer: 6 years
Answer: C
A student needed to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What is the value of x?
Choose the correct choice from the following answers.
A) 7	B) 8	C) 9	D) 6	E) 5

Solution: (3+11+7+9+15+13+8+19+17+21+14+x)/12 =12   ⇒(137+x)/12=12   ⇒137+x=144   ⇒x=144−137=7   7nswer is 7.
Answer: A
The Pinedale bus line travels at an average speed of 60 km/h, and has stops every 5 minutes along its route. Yahya wants to go from his house to the Pinedale Mall, which is 9 stops away. How far away, in kilometers, is Pinedale Mall away from Yahya's house?  Choices:
A) 20 km
B) 30 km
C) 45 km
D) 50 km
E) 60 km

Solution: Number of stops in an hour: 60/5= 
60/5 = 12
12   Distance between stops: 60/12= 
60/12 = 5
5 km   Distance between Yahya's house and Pinedale Mall: 5 x 9= 45 km   IMO, correct answer is "45 km."
Answer: C
In a certain alphabet, 20 letters contain a dot and a straight line. 36 letters contain a straight line but do not contain a dot. If that alphabet has 60 letters, all of which contain either a dot or a straight line or both, how many letters contain a dot but do not contain a straight line? Select the correct option.
A) 4 B) 3 C) 14 D) 20 E) 28

Solution: We are told that all of the letters contain either a dot or a straight line or both, which implies that there are no letters without a dot and a line (no line/no dot box = 0).   First we find the total # of letters with lines:  20 +36= 
 20 +36 = 56
56;   Next, we find the total # of letters without line:  60 - 56= 
 60 - 56 = 4
4;   Finally, we find the # of letters that contain a dot but do not contain a straight line: 4 - 0= 
4 - 0 = 4
4.
Answer: A
Choose the missing terms out of the given alternatives.
JE, LH, OL, SQ, ?	Choose the correct option:
A) XW  B) DT  C) WV  D) WX  E) VW

Solution: A   XW   The first letter moves 2, 3, 4 ... steps forward. The second letter moves 3, 4, 5 ... steps forward
Answer: A
The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:	Choose the correct choice from the following choices: A) 9000 B) 9400 C) 9600 D) 9800 E) 9200

Solution: Greatest number of 4-digits is 9999.   L.C.M. of 15, 25, 40 and 75 is 600.   On dividing 9999 by 600, the remainder is 399.   Required number  (9999 - 399)= 
 (9999 - 399) = 9_600
9600.   Answer: Option 9600
Answer: C
A bag contains 40 black balls and 50 white balls. One ball is drawn at random. What is the probability that the ball drawn is white? Select: A) 2/5 B) 5/7 C) 1/2 D) 1/4 E) 1/3

Solution: Total number of balls = 40+50 = 70   no. of white balls = 50   probability of drawing a white ball = 50/70 = 5/7   Answer is 5/7
Answer: B
The owner of a furniture shop charges his customer 20% more than the cost price. If a customer paid Rs. 3600 for a computer table, then what was the cost price of the computer table?
Choose the correct choice from the following answers: A) 2299 B) 2699 C) 3000 D) 6725 E) 2601

Solution: CP = SP * (100/(100 + profit%))   = 3600(100/120) = Rs. 3000   Answer:3000
Answer: C
It takes John 5 minutes to walk to the car park and 45 to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.?
Answers:
A) 7:30 B) 7 C) 6:30 D) 6 E) 5

Solution: The time it takes John to get to work: time to walk to car park + time to drive     25 + 45= 
  25 + 45 = 70
70 minutes= 1 hour and 10 minutes   John needs to get out of the house 1 hour and 10 minutes before 9:00 am at   9:00 - 1:10 = 7:30 a.m.   7:30
Answer: A
A man purchased a grinder for Rs. 420 and sold it at a profit of 10%. The selling price is:  Choose the correct choice from the following options.
A) Rs. 462
B) Rs. 812
C) Rs. 684
D) None of these
E) Cannot be determined

Solution: s.p.=110/100 × 420=462   Rs. 462nswer: Rs. 462
Answer: A
A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?	Choose the correct choice from the following answers.
A) 320 m  B) 350 m  C) 650 m  D) None of these  E) Cannot be determined

Solution: Solution   Speed	= (300 / 18) m/sec   = (50 / 3) m/sec.   Length of the platform be x metres.   Then	= x + 300 /39   = 50 / 3 m/sec   = 3 (x + 300) =1950 .   = 350 m   Answer 350 m
Answer: B
A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance? Choose one
A) 91 (1/3) kmph
B) 21 (1/3) kmph
C) 81 (1/3) kmph
D) 21 (1/7) kmph
E) 23 (1/3) kmph

Solution: Let the total distance be x km   total time taken   = (x/4)/16 + (3x/4)/24   = x/64 + x/32 = 3x/64   Average speed = x/(3x/64)   = 64/3kmph = 21 (1/3)kmph.   Answer:21 (1/3) kmph
Answer: B
How many odd integers from 1 to 100 (both inclusive) have odd number of factors?
Choose the correct choice from the following choices.
A) 13  B) 14  C) 5  D) 6  E) 7

Solution: Integers having odd number of factors will be perfect squares. Odd numbers will have odd perfect squares. Thus, the possible values for the perfect squares are :   1,9,25,49,81 and the corresponding integers are 1,3,5,7,9 (more than 4). Thus 5 is the correct answer .
Answer: C
At the faculty of Aerospace Engineering, 302 students study Random-processing methods, 232 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering? Choose the most appropriate option:
A) 444
B) 432
C) 346
D) 422
E) 448

Solution: 302 + 232 - 112 (since 112 is counted twice )= 422   422 is the answer
Answer: D
20 beavers, working together in a constant pace, can build a dam in 18 hours. How many hours will it take 12 beavers that work at the same pace, to build the same dam?
Choose the correct choice from the following
A) 22.
B) 24.
C) 30.
D) 36
E) 38.

Solution: Total Work = 20*18= 
20*18 = 360
360 Beaver hours   12 Beaver * x=360 Beaver hours   x=360/12= 
360/12 = 30
30   ANSWER:30.
Answer: C
An Office used three types of envelopes: small,medium and large. They used 80 small envelopes. The no.of Medium envelopes used was 5 times, the no.of small envelopes plus 5/20 of the number of envelopes. The no.of.large envelopes was equals to the no.of small envelopes plus 5/20 of the no.of medium envelope. Altogether, How many envelope did they use? Choose the correct choice from the following answers: A) 950 B) 960 C) 972 D) 970 E) 980

Solution: Let the total no. of envelopes be x   No. of small envelopes = 80   No. of medium envelopes =5*80+5/20*x = 400+5/20*x   No. of large envelopes = 80 +5/20(400+5/20*x) = 180+25/400*x   Sum of small, medium and large envelopes = x   80 + 400+5/20*x + 180+25/400*x = x   660 + 5/16*x = x   11/16*x = 660   x = 960   ANSWER:960
Answer: B
Simplify: 1005-1000+10	Select the correct option.
A) 900	B) 926	C) 1001	D) 905	E) None of them

Solution: 1005-1000+10   =1005-(1000/10)   =1005-100= 
1005-100 = 905
905.   Answer is 905
Answer: D
One ball will drop from a certain height. The height it will reach after rebounding from the floor is 50 percent of the previous height. The total travel is 250cm when it touches the floor on third time. What is the value of the original height?	Answers.
A) 80cm
B) 90cm
C) 100cm
D) 120cm
E) 130cm

Solution: when Ball comes down, Then i have indicated the distance covered in green   when Ball goes up, Then i have indicated the distance covered in red   Distance travelled uptil the ball touches the floor 3rd time:h+0.5h+0.5 h+0.5*0.5 h+0.5*0.5 h   h + 2 * 0.5 * h + 2 * 0.25 * h = h (1+2*0.5+2* 0.25) = h (1+1+0.5) = 250   2.5 h = 250   h = 100.   100cm is the answer.
Answer: C
A drum has a combination of 2 liquids X and Y in the proportion 7:5 when 9 L of combination are taken out and the Drum is filled with Y, the proportion of X and Y becomes 7:9. Then how many litres of liquids X was obtained by the Drum initially?
Choose one:
A) 21 litres B) 22 litres C) 23 litres D) 24 litres E) 25 litres

Solution: Explanation :   => If the Drum has 7a and 5a litres of combinations X and Y correspondingly. 21 litresmount of Combination taken out is 9 litres   Some of X in Combination left = [ 7a - (7/12)*9] litres   = [ 7a - (21/4) ] litres   Some of Y in combination left = [ 5a - (5/12)*9 ] litres   = [ 5a - (15/4) ] litres   => Since the combination is in the ratio 7:9,   { [7a - (21/4)] / [ 5a - (15/4) ]+9 } = (7/9) => [ (28a - 21) / (20a + 21) ] = (7/9)   =>252a – 189 = 140a + 147   => 112a = 336   => a = 3   Some of liquid X, has in the Drum initially is (7*3)= 
(7*3) = 21
21 litres   21 litresnswer : 21 litres
Answer: A
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 10 minutes, then the area of the park (in sq. m) is: Select:  A) 153601  B) 153600  C) 153602  D) 153603  E) 240000

Solution: Perimeter = Distance covered in 10 min. =(12000/60) x 10m = 2000 m.   Let length = 3x metres and breadth = 2x metres.   Then, 2(3x + 2x) = 2000 or x = 200.   Length = 600 m and Breadth = 400 m.   Area = (600 x 400) m2 = 240000 m2.   Answer: 240000
Answer: E
The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person? Choices:  A) 76 kg  B) 80 kg  C) 85 kg  D) 90 kg  E) None

Solution: Solution   Total weight increased	= (8 x 2.5)kg   = 20 kg.   Weight of new person	= (65 + 20)= 
(65 + 20) = 85
85 kg.   Answer 85 kg
Answer: C
A soccer store typically sells replica jerseys at a discount of 30 percent to 70 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent of the list price is the lowest possible sale price?
Choices:  A) 20  B) 25  C) 30  D) 40  E) 50

Solution: Let the list price be 2x   for min sale price, the first discount given should be 70%, 2x becomes x here   now, during summer sale additional 20% off is given ie sale price becomes 0.8x   it is given lise price is $80   => 2x = 80   => x = 40   and 0.8x = 32   so lowest sale price is 32, which is 40% of 80   hence, 40 is the answer
Answer: D
21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement. Choices:
A) 2/31	B) 4/35	C) 9/42	D) 8/41	E) 9/67

Solution: The probability that first toy shows the even number,   =1021=1021   Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.   Hence, probability that second toy shows the even number,   =920=920   Required probability,   =(1021)×(920)=(1021)×(920)   =9/42   9/42
Answer: C
In a local school district, the high school and middle school each received r dollars toward funding for the student arts program. The high school enrolled 400 students and the middle school enrolled 200 students. Later, the middle school transferred s dollars to the high school so that they would have received the same funding per student. Which of the following is equivalent to s? Choose the correct choice from the following
A) r/2 B) r/3 C) r/4 D) r/5 E) r/8

Solution: Total per head = 2r/600   After s transfer both schools have total for head.   So at High School it will be:   r+s = (400)* (2r/600) = 8r/6=4r/3   i.e. s = 4r/3 - r/1 =4r-3r/3=r/3   Answer : r/3
Answer: B