divelab/Sys2Bench huggingface dataset:
Question: 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 10 mat-weavers in 10 days?
Options:
A)25
B)19
C)39
D)61
E)16
Rationale: Let the required number of bottles be x.
More weavers, More mats (Direct Proportion)
More days, More mats (Direct Proportion)
Wavers	4	:	10 :: 4 : x
Days	4:10
4 * 4 * x = 10 * 10 * 4
x =	(10 * 10 * 4)/(4 x 4)
x = 25.
Answer is A.
Answer: A
Question: A grocer wants to arrange 13 fruits in a line among which 3 are mangoes, 4 are apples, 2 are oranges, 1 pineapple and remaining are guavas. In how many different ways can he do so, if fruits of one kind are identical?
Options:
A)13!/{(2!)(3!^2)(4!)}
B)13!/{(2!)(3!^2)}
C)13!/{(2!)(4!)}
D)13!
E)13!/(3!^2)
Rationale: The total number of ways in which a total N items, out of which p are identical of one type, q are identical of another type and rest are different, can be arranged in a line is N!/{p!q!}
Here we have 13 fruits out of which there are 3 alike mangoes, 4 alike apples, 2 alike oranges, 3 alike guavas and 1 pineapple.
Hence the number of ways in which he can arrange these in a line are 13!/(3!4!2!3!) = 13!/{(2!)(3!^2)(4!)}
Ans A
Answer: A
Question: In how many ways 6 persons can be formed from 8 men and 7 women?
Options:
A)5005
B)6452
C)4516
D)2313
E)3564
Rationale: Total number of persons = 15
Required number of ways = 15C6 = 5005
Answer is A
Answer: A
Question: If x = 4 and y = −2, what is the value of (x − 2y)^y?
Options:
A)−100
B)0.015
C)0.25
D)4
E)8
Rationale: Quickly we can spot that answer is neither integer nor negative. Eliminate A, DE
by inversing and squaring 0.015
Answer: B
Answer: B
Question: At a certain college there are twice as many Economics majors as history majors and three times as many Economics majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors?
Options:
A)6 to 1
B)6 to 4
C)2 to 3
D)1 to 5
E)1 to 6
Rationale: This is how I translated the question:
At a certain college there are twice as many economics majors as history majors
E = 2H
and three times as many economics majors as mathematics majors.
E = 3M
What is the ratio of the number of history majors to the number of mathematics majors?
What is H:M?
Just set E equal to each other to get the ratio in terms of H and M.
2H = 3M
H/M = 3/2
The answer is 6:4
Answer : B
Answer: B
Question: Simplify: 6005-6000+10
Options:
A)4505
B)4509
C)5405
D)4508
E)None of them
Rationale: 6005-6000+10
=6005-(6000/10)
=6005-600
=5405.
Answer is C
Answer: C
Question: The total age of A and B is 16 years more than the total age of B and C. C is how many year younger than A
Options:
A)A)11
B)B)12
C)C)13
D)D)16
E)E)15
Rationale: Explanation:
Given that A+B = 16 + B + C
=> A – C = 16 + B – B = 16
=> C is younger than A by 16 years
Answer: Option D
Answer: D
Question: If selling price of 12 pens is equal to the cost price of 18 pens, find the profit percent.
Options:
A)40%
B)33.3%
C)50%
D)25%
E)None of these
Rationale: Explanation:
Selling price of 12 pens = cost price of 18 pens
Therefore, the profit is 6 pens and cost price is 12 pens.
% profit = profit/cost price * 100
= 6/12 * 100
= 50%
ANSWER C
Answer: C
Question: Eggs are sold in packages of six or eleven only. If Doris bought 70 eggs exactly, what could be the number of large packs Doris bought?
Options:
A)6.
B)2.
C)3
D)5.
E)4
Rationale: Let number of packs of six = s
let number of packs of eleven = e
6s + 11e = 70
Now , we need to test for values of e .
Since sum 70 is even and 6s will always be even , e can't be odd .
Now , we can test for values e = 2 , 4 and 6
11*2 + 6*8 = 22 + 48 = 70
Answer B
Answer: B
Question: If p and q are positive integers each greater than 1, and 17(p+1)=25(q+1), what is the least possible value of p+q?
Options:
A)36
B)42
C)40
D)46
E)none
Rationale: 17(p+1)=29(q+1) --> (p+1)/(q+1) = 29/17 --> the least positive value of p+1 is 25, so the least value of p is 24 and the least positive value of q+1 is 17, so the least value of q is 16 --> the least value of p+q is 24+16=40.
Answer: C.
Answer: C
Question: The length of a rectangular field is 7/5 its width. If the perimeter of the field is 432 meters, what is the width of the field?
Options:
A)50
B)60
C)70
D)80
E)90
Rationale: Let L be the length and W be the width. L = (7/5)W
Perimeter: 2L + 2W = 432, 2(7/5)W + 2W = 432
Solve the above equation to find: W = 90 m and L = 126 m.
correct answer E)90
Answer: E
Question: In case N is the only individual sewing on committee B, which among the following shouldserve on committee A?
Options:
A)V and U
B)V and T
C)U and S
D)O and P
E)T and U
Rationale: O and P should serve on A
ANSWER:D
Answer: D
Question: What percent is 350 gm of 1 kg?
Options:
A)25%
B)40%
C)35%
D)8%
E)12%
Rationale: 1 kg = 1000 gm
350/1000 Ã— 100 = 35000/1000
=35 %
Answer is C
Answer: C
Question: If in a certain sequence of consecutive multiples of 100, the median is 650, and the greatest term is 1000, how many terms that are smaller than 650 are there in the sequence?
Options:
A)6
B)4
C)8
D)12
E)13
Rationale: Since the median is 650 we know there must be a even number of integers
So the list around 625 must go. 600 ( 650) 700 800 900 1000
Since we know there are 4 numbers greater than 650 then there must be 4 numbers less then 650.
B
Answer: B
Question: Three bodies D, E and F start moving around a circular track of length 240m from the same point simultaneously in the same direction at speeds of 6 m/s, 10 m/s and 18 m/s respectively. When will they meet for the first time after they started moving?
Options:
A)120 seconds
B)60 seconds
C)30 seconds
D)20 seconds
E)50 seconds
Rationale: If they all meet after T seconds, it means they covered the distances 6T, 10T, and 18T respectively.
Since they all arrive to the same spot, it means that the differences taken pairwise between the distances must be positive integer multiples of the length of the track, which is 240m. So, 4T, 8T, and 12T must all be multiples of 240. 4T multiple of 240 means T multiple of 60. The smallest T with this property is 60 and is on the list of answers.
Answer B.
Answer: B
Question: If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 7 kmph, then the speed of the boat in still water is :
Options:
A)2.5 km/hr
B)4.5 km/hr
C)5 km/hr
D)10.5 km/hr
E)None of these
Rationale: Solution
Speed of stream = 1/2 (17-8) km/hr= 4.5kmph . Answer B
Answer: B
Question: A trader sells 80 meters of cloth for Rs. 9000 at the profit of Rs. 23.5 per metre of cloth. What is the cost price of one metre of cloth?
Options:
A)22
B)89
C)90
D)78
E)80
Rationale: SP of 1m of cloth = 9000/80 = Rs. 112.5
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 112.5 - Rs. 23.5 = Rs. 89.
Answer: B
Answer: B
Question: A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
Options:
A)10.39
B)10.36
C)10.3
D)10.33
E)10.31
Rationale: D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3.30 + 7 h = 10.30 p.m.
Answer: C
Answer: C
Question: 55 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be :
Options:
A)84 m
B)88 m
C)120 m
D)70 m
E)None
Rationale: Sol.
Let the length of the wire b h.
Radius = 1/2 mm = 1/20 cm. Then,
22/7 * 1/20 * 1/20 * h = 55 ⇔ = [55 * 20 * 20 * 7 / 22] = 7000cm = 70 m.
Answer D
Answer: D
Question: What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?
Options:
A)1245
B)1683
C)1773
D)1650
E)1760
Rationale: Explanation:
LCM of 5, 6, 7 and 8 = 840
Hence the number can be written in the form (840k + 3) which is divisible by 9.
If k = 1, number = (840 × 1) + 3 = 843 which is not divisible by 9.
If k = 2, number = (840 × 2) + 3 = 1683 which is divisible by 9.
Hence 1683 is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder.
Answer: Option B
Answer: B
Question: Solve 2x – 5 = 1
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Sol.
2x – 5 = 1
=> 2x = 1 + 5
=> 2x = 6
=> x = 3.
Answer : C
Answer: C
Question: A room is 4 meters 37 cm long and 3 meters 23cm broad. It is required to pave the floor with minimum square slabs. Find the number of slabs required for this purpose?
Options:
A)485
B)431
C)391
D)381
E)481
Rationale: HCF of 323, 437 = 19
323 * 437 = 19 * 19 * x
x = 391
ANSWER:C
Answer: C
Question: Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 40 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?
Options:
A)205
B)220
C)240
D)247
E)294
Rationale: Car Y began travelling after 72 minutes or 1.2 hours.
Let t be the time for which car Y travelled before it stopped.
Both cars stop when they have travelled the same distance.
So,
35(t+1.2) = 40t
t=8.4
Distance traveled by car X from the time car Y began traveling until both cars stopped is
35 x 8.4
= 294 miles
Answer:- E
Answer: E
Question: The guidelines at a certain college specify that for the introductory English class, the professor may choose one of six specified novels, and choose two plays from a list of 5 specified plays. Thus, the reading list for this introductory class has one novel and two plays. How many different reading lists could a professor create within these parameters?
Options:
A)50
B)55
C)60
D)65
E)70
Rationale: 6C1*5C2 = 6*10 = 60
The answer is C.
Answer: C
Question: One hour before John started walking from P to Q, a distance of 33 miles, Ann had started walking along the same road from Q to P. Ann walked at a constant speed of 3 miles per hour and John at 2 miles per hour. How many miles had Ann walked when they met?
Options:
A)6 miles
B)8,4 miles
C)9 miles
D)9,6 miles
E)21 miles
Rationale: Ann walks from Q to P at a speed of 3 miles/hr for one hour. She covers 3 miles in 1 hour and now distance between John and Ann is 33 - 3 = 30 miles.
Ann walks at 3 mph and John at 2 mph so their relative speed is 3+2 = 5 mph.
They have to cover 30 miles so it will take them 30/5 = 6 hours to meet.
In 6 hrs, Ann would have covered 6 hrs * 3 miles per hour = 18 miles.
Adding this to the 3 miles she covered before John, Ann covered a total of 3 + 18 = 21 miles.
Answer (E)
Answer: E
Question: What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, x
Options:
A)2643
B)5464
C)3456
D)7554
E)3158
Rationale: 12
12 × 3 + 2 = 38
38 × 3 + 2 = 116
116 × 3 + 2 = 350
350 × 3 + 2 = 1052
1052 × 3 + 2 = 3158
E
Answer: E
Question: A certain clock marks every hour by striking a number of times equal to the hour,and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 55 seconds. at 12:00 ,how many seconds elapse between the beginning of the first stroke and the end of the last stroke?
Options:
A)A.72
B)B.115
C)C.48
D)D.46
E)E.44
Rationale: At 6:00 it'll chime 6 times. If we assume that the time taken to chime is x, then time between chimes is also x. So you have 6 chimes, which is 6x and 5 time intervals between chimes. This means that 11x = 55 seconds. Thus x = 5 seconds.
By a similar logic, at 12:00, there are 12 chimes and 11 intervals so the total time is (12+11)x = 23x = 115 seconds.
Answer B
Answer: B
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 894 in 4 years. The sum is:
Options:
A)s. 650
B)s. 690
C)s. 698
D)s. 700
E)s. 578
Rationale: S.I. for 1 year = Rs. (894 - 815) = Rs. 79.
S.I. for 3 years = Rs.(79 x 3) = Rs. 237.
Principal = Rs. (815 - 237) = Rs. 578.
Answer: Option E
Answer: E
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
Options:
A)7m
B)8m
C)3m
D)2m
E)4m
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer: D
Answer: D
Question: A carpenter is building a frame for a wall painting. The painting is in the shape of a rectangle. If the sides of the rectangle are in the ratio of 3:2 and the shorter side has a length of 23 inches, how many inches of framing material does the carpenter need to frame the painting?
Options:
A)12
B)22 1/2
C)37 1/2
D)50
E)29
Rationale: (23/2) ( 2+3) * 2 = 29 =E
Answer: E
Question: The perimeter of a triangle is 22 cm and the inradius of the triangle is 3.5 cm. What is the area of the triangle?
Options:
A)22
B)35
C)77
D)54
E)38
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 3.5 * 22/2
= 38.5 cm2
Answer:E
Answer: E
Question: A car mechanic purchased four old cars for Rs. 1 lakh. He spent total 2 lakh in the maintenance and repairing of these four cars. what is the average sale price of the rest three cars to get 70% total profit if he has already sold one of the four cars at Rs. 1.2 lakh?
Options:
A)1.8 lakh
B)1.3 lakh
C)1.9 lakh
D)8.1 lakh
E)6.1 lakh
Rationale: Explanation:
Total cost of 4 cars = 1+2 = 3 lakh
Total SP of 4 cars = 3 x 1.7 = 5.1 lakh
SP of 1 car = 1.2 lakh
SP of rest 3 cars = 5.1 - 1.2 = 3.9 lakh
Average SP of all the 3 cars = 1.3 lakh
Answer: B)
Answer: B
Question: A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 12% microphotonics; 24% home electronics; 15% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research?
Options:
A)43°
B)10°
C)18°
D)36°
E)52°
Rationale: Here all percentage when summed we need to get 100% . As per data 12+24+15+29+8 = 88%.
So remaining 12% is the balance for the astrophysics.
Since this is a circle all percentage must be equal to 360 degrees.
100% ---- 360 degrees
Then 12% will be 43 degrees..
IMO option A.
Answer: A
Question: Calculate the percentage gain if a trader bought a bicycle for Rs.640 and sold it for Rs.720?
Options:
A)14.5%
B)11.5%
C)15.5%
D)12.5%
E)18.5%
Rationale: C.P. = 640
S.P. = 720
Gain = 720-640 ---- 80
% Gain => 80/640*100 => 12.5%
Answer:D
Answer: D
Question: Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.
Options:
A)1:2
B)2:3
C)3:4
D)3:5
E)4:5
Rationale: Req = 60:90 = 2:3
ANSWER B
Answer: B
Question: A tank with a volume of 30 cubic feet has one inlet pipe and 2 outlet pipes. The inlet pipe fills water into the tank at the rate of 5 cubic inches/min and the 2 outlet pipes empty it out at the rates of 9 cubic inches/min and 8 cubic inches/min respectively. If all 3 pipes are opened when the tank is full, how many minutes does it take to empty the tank? (1 foot = 12 inches)
Options:
A)1440
B)2340
C)3240
D)4320
E)5420
Rationale: The tank is emptied at this rate: 9 + 8 - 5 = 12 cubic inches/min
The tank has a volume of 30*12*12*12 = 51840 cubic inches.
The time it takes to empty the tank is 51840/12 = 4320 minutes.
The answer is D.
Answer: D
Question: A square of side 8 cm has been made to a rectangle by combining it with a rectangle of dimensions of length 8cm and breadth 4cm. What is the perimeter of the newly formed rectangle?
Options:
A)10
B)20
C)40
D)60
E)80
Rationale: Dimensions of newly formed rectangle, length= 8+4 = 12cm breadth= 8cm
Perimeter of the new rectangle= 2x(12=8)= 40cm
Answer: C
Answer: C
Question: If X = 2 + 1/(1+1/(1-1/2))then the value of 2x+7/3?
Options:
A)9 2/3
B)10 1/3
C)7
D)11 2/3
E)12
Rationale: X = 2 + 1/(1+1/(1-1/2))
= 2 + 1/(1+2)
= 2 + 1/3
X = 7/3 ==> 2X + 7/3 => 2(7/3) + 7/3
==> 14/3 + 7/3
==> 21/3
==> 7.
C)
Answer: C
Question: Of the land owned by a farmer, 90 percent was cleared for planting. Of the cleared land, 80 percent was planted with barley and 10 percent of the cleared land was planted with potato. If the remaining 90 acres of cleared land was planted with tomato, how many acres did the farmer own?
Options:
A)850
B)950
C)1025
D)975
E)1000
Rationale: 80% of 90% = 72%, 10% 0f 90% = 9% so the remaining 90-72-9=9%=90 acres or 10% of 90%=9% --> 90/9*100=1000 acres Answer (E)
Answer: E
Question: In a 5 digit ID number, what is the probability of exactly three digits are the digit 0?
Options:
A)12/2507
B)9/2500
C)11/9800
D)13/2500
E)14/2751
Rationale: Total number of 5 digit numbers = 99999-10000+1=90,000
No. of ways of arranging 3 digits as 0 = 4C3=4.
Arrangements are as follows. Here X can be any digit other than 0
1) X000X ==> no. of ways - 81
2) XX000 ==> no. of ways - 81
3) X0X00 ==> no. of ways - 81
4) X00X0 ==> no. of ways - 81
Probability = (81*4)/90000
=9/2500
Ans - B
Answer: B
Question: There are 9 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair. what is the number of pair that can be formed.
Options:
A)62
B)70
C)72
D)71
E)76
Rationale: First of all you should remember that there is a difference in left and right sock.
now no. of way to select any of the sock = 9
and for second = 8
so total methods = 9*8 = 72
ANSWER:C
Answer: C
Question: The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 524 different signs. If the company used 522 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 524 signs?
Options:
A)46
B)248
C)2092
D)15,128
E)30,256
Rationale: # of 2-letter codes possible from 524 different signs = 524*524.
# of 2-letter codes possible from 522 different signs = 522*522.
The difference = 524^2 - 522^2 = (524 -522)(524 + 522) = 2092.
Answer: C.
Answer: C
Question: The mean of 50 observations was 40. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is
Options:
A)40.46
B)36.1
C)36.5
D)39.1
E)None
Rationale: Sol.
Therefore correct sum
= ( 40 × 50 + 48 – 23)
= 2023.
Therefore correct mean
= 2023 / 50
= 40.46.
Answer A
Answer: A
Question: A baker filled with a measuring cup with 1/3 cup water. He poured 1/2 of the water into the batter, and then spilled 1/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?
Options:
A)1/8 cup
B)3/8 cup
C)11/24 cup
D)1/2 cup
E)7/8 cup
Rationale: 1/3 is the original water in cup .half in batter.So left is 1/6 out which 1/8 is spilled out.So again left with 1/24.
so 50% more than what he started was = 1/3+1/2*(1/3)=1/2
Amount of water needed to add = 1/2 - 1/24=11/24
C
Answer: C
Question: Excluding stoppages, the speed of a train is 30 kmph and including stoppages it is 21 kmph. Of how many minutes does the train stop per hour?
Options:
A)16
B)17
C)12
D)15
E)18
Rationale: T = 9/30 * 60
= 18
Answer: E
Answer: E
Question: A certain taxi company charges $2.80 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long?
Options:
A)15.6
B)16.0
C)18.4
D)18.7
E)19.1
Rationale: A certain taxi company charges $2.80 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long?
A. 15.60
B. 16.00
C. 17.50
D. 18.70
E. 19.10
1/5 miles = 0.2 miles.
The cost of 8 miles long ride would be $2.80 for the first 0.2 miles plus (8-0.2)/0.2*0.4 = $2.8 + $15.6 = $18.4.
Answer: C.
Answer: C
Question: What is the least possible value that can be subtracted from 2^586 so that the result is a multiple of 7?
Options:
A)2
B)3
C)5
D)7
E)11
Rationale: We need to subtract something to make 2^586 a multiple of 7.
So let us try to write 2^586 in a from from which we can convert it in terms of 7
We know that 2^3 = 8 and 8 = (7+1)
Hence we will write 2^586 in powers of 8
2^586 = 2*2^585 = 2*8^195 = 2*(7+1)^195
All of the terms of (7+1)^195 will be multiple of 7 apart from the last term - "1"
Hence 2*(7+1)^195 = 2(Multiples of 7 + 1) = 2*Multiples of 7 + 2
Therefore we need to subtract 2 to make 2^586 a multiple of 7
ANSWER:A
Answer: A
Question: In a psychology school the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Joey’s grade at the end of the first year is 30, what will be his grade at the end of the third year?
Options:
A)44
B)56
C)64
D)75
E)80
Rationale: Cool question!
There's a lot of information given here, so let's eat slow here.
Joey scores a 30 at the end of his first year. That means that he's currently 15 years old (since given per instruction, after the first year one's grade is determined by doubling his/her age).
Now, come next year, or his second year at this psychology school, he's technically 16 years old. To find out the second year's grade, we want to double his age PLUS half of his previous grade.
Well, his second year is then going to be 16(2) + 15 = 41.
Now let's tackle the main question: what's his grade going to be the third year?
Well, he will be at an age of 17 on his third year at this school. Again, to find out his third year's grade, you're going to double his age (17x2), plus half of his previous year's grade (as calculated for his second year, his grade is 41; therefore, 41/2)
Having said that, the final answer would be 17(2) + 41/2 = 34 + 20.5 = 64.5 ~= 64--> (C)
Answer: C
Question: A student is to take her final exams in two subjects. The probability that she will pass the first subject is 3/4 and the probability that she will pass the second subject is 2/3. What is the probability that she will pass one exam or the other exam?
Options:
A)5/12
B)1/2
C)7/12
D)5/7
E)11/12
Rationale: Let the two subjects be X (probability of passing 3/4) and Y (probability of passing 2/3)
The probability of passing in X only is 3/4 times 1/3 (failing in Y) = 1/4
The probability of passing in Y only is 2/3 times 1/4 (failing in X) = 1/6
Therefore the total probability = 1/4 + 1/6 = 5/12
Hence A
Answer: A
Question: In 1995, the Johny spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johny cut back their water usage. By how much must the Johny have reduce their 1996 water usage to pay exactly the same amount in 1996 as they paid in 1995?
Options:
A)a)	33 1/3 %
B)b)	40 %
C)c) 50 %
D)d)	66 2/3 %
E)e)	100 %
Rationale: Let x be the water usage and c be the cost water of Johny
We have
xc =800, c=800/x
Y(1.5c)=800 where Y is the water usage in 1996
Y= 800/ (1.5*800/x)= 1/1.5x=2/3x
Thus reduction will be x-2/3x=1/3x=A
Answer: A
Question: How many pages the book have, if total 309 digits are used to form the page numbers?
Options:
A)135 pages
B)136 pages
C)137 pages
D)138 pages
E)139 pages
Rationale: First 9 pages .. 9 digits
next 90 pages .. 180 digits
next 40 pages ... 120 digits
----------------------
Total ...139 pages ...309 digits
ANSWER:E
Answer: E
Question: Pipes A can fill a tank in 5 hours and Pipe B can fill it in 6 hours . If the two pipes are opened together, then the tank will be filled in:
Options:
A)3 4/11 hours.
B)2 8/11 hours.
C)2 3/11 hours.
D)5 2/11 hours.
E)4 3/11 hours.
Rationale: Explanation:
Pipes A can fill the tank in 5 hours . Therefore,
part filled by pipe A in 1 hour =1/5 Pipe B can fill the tank in 6 hours. Therefore,
part filled by pipe B in 1 hour = 1/6
Net part filled by Pipes A,B together in 1 hour
=1/5+1/6=11/30
i.e., the tank can be filled in 30/11=2 8/11 hours.
Answer: Option B
Answer: B