mathewhe/aqua_rat huggingface dataset:
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1000 resolutions?
(A) 1408 m
(B) 1704 m
(C) 1479 m
(D) 1427 m
(E) 1297 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 1000 resolutions.
= 1000 * 2 * 22/7 * 22.4
= 140800 cm
= 1408 m
Answer:A
Answer: (A) 1408 m
Question: Two trains are moving in opposite directions @100kmph and 120kmph. Their length are 500m and 700m. The time taken by the slower train to cross faster train in second is?
(A) 15sec
(B) 18.3sec
(C) 19.6sec
(D) 20.4sec
(E) 22.5sec
Rationale: Relative speed = 100+120 = 220*5/18 = 550/9 m/s
Distance covered = 500+700 = 1200m
Required time= 1200*9/550 = 19.6sec
Answer is C
Answer: (C) 19.6sec
Question: A vendor bought dog for Rs. 1, and a cat for Rs. 1.20, a pig for Rs.1.34, He totally purchased 100 animals for 100 Rs. Then find no of cats.
(A) 10
(B) 12
(C) 14
(D) 15
(E) 16
Rationale: 50 - pigs
10 - cats
ANSWER:A
Answer: (A) 10
Question: A man can row a boat at 24 kmph in still water. If the speed of the stream is 8 kmph, what is the time taken to row a distance of 54 km downstream?
(A) 27/16 hours
(B) 27/33 hours
(C) 28/13 hours
(D) 27/13 hours
(E) 30/13 hours
Rationale: Speed downstream = 24 + 8 = 32 kmph.
Time required to cover 54 km downstream = d/s = 54/32 = 27/16 hours.Answer:A
Answer: (A) 27/16 hours
Question: A certain auto manufacturer sold 2% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.3 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?
(A) 22,50,000
(B) 22,80,000
(C) 22,90,000
(D) 22,95,000
(E) 23,00,000
Rationale: Let's assume in 2006 the manufacturer sold X.
In 2007 he sold X-2/100(X)
If sales in 2006,X= 2.3 million find X-2/100(X)
(2.3 x 10^6)-2/100(2.3 x 10^6)
2300000-46000=22,54,000-----> 22,50,000(approx)
Answer-A
Answer: (A) 22,50,000
Question: You have a bag of 9 letters: 3 Xs, 3 Ys and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different R ways can you place one letter into each area such that there are no rows or columns with 2 or more of the same letter?
(A) 5
(B) 6
(C) 9
(D) 12
(E) 18
Rationale: Consider one particular arrangement of the first row: XYZ, then we can construct only two boxes with so that no rows or columns have 2 or more of the same letter:
XYZ
YZX
ZXY
And:
XYZ
ZXY
YZX
Now, the first row itself can be arranged in 3!=6 ways (since there are three distinct letter), hence the total number of boxes possible R is 2*6=12.
Answer: D.
Answer: (D) 12
Question: Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:
(A) 10
(B) 50
(C) 40
(D) 20
(E) 30
Rationale: Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x.
So, 60x = 2400 or x = 40.
{\color{Blue} \therefore } The numbers are (3 x 40), (4 x 40) and (5 x 40).
Hence, required H.C.F. = 40.
Answer: Option C
Answer: (C) 40
Question: A discount dealer professes to sell his goods at cost price
but uses a weight of 960 gms for a Kg weight .Find his gain %?
(A) 25%
(B) 6%
(C) 6/25%
(D) 25/6%
(E) 42%
Rationale: Gain%=[(error*100)/(true value-error)]%
=[(40*100)/1000-40)]%=25/6%
ANSWER D 25/6%
Answer: (D) 25/6%
Question: eight family members: 5 grandchildren (3 brothers and 2 sisters) and their 3 grandparents are to be seated around a circular table. How many different seating arrangements are possible so that 2 sisters are seated between any two of the three brothers?
(A) 120
(B) 288
(C) 1440
(D) 2880
(E) 8640
Rationale: Answer: B.
Answer: (B) 288
Question: A large tanker can be filled by two pipes A and B in 30 and 15 hours respectively. How many hours will it take to fill the tanker from empty state if A and B fill it together?
(A) 8hr
(B) 10hr
(C) 12hr
(D) 9hr
(E) 5hr
Rationale: Part filled by A in 1hr = 1/30
Part filled by B in 1hr = 1/15
part filled by A+B = 1/30 + 1/15 = 1/10
Both the pipes can fill the tank in = 10 hours
Answer is B
Answer: (B) 10hr
Question: In the fifth grade at Parkway elementary school there are 450 students. 320 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?
(A) 69.
(B) 73.
(C) 81.
(D) 95.
(E) 108.
Rationale: Total students = 450
Boys = 320, Girls = 130
Total playing soccer = 250
86%of 250 = 215 are boys who play soccer.
Girls who play soccer = 35.
Total girls who do not play soccer = 130 - 35 = 95.
Correct option: D
Answer: (D) 95.
Question: 8 is 4% of a, and 4 is 8% of b. c equals b/a. What is the value of c?
(A) 1/32
(B) 1/4
(C) 1
(D) 4
(E) 5
Rationale: Explanation :
Given,
=>4a/100=8.
=>a=8×(100/4)=200. ---------(i)
And,
=>(8/100)×b=4.
=>b=50. ---------(ii)
Now, c=b/a ( from (i) and (ii) )
=>50/200.
=>1/4.
Answer : B
Answer: (B) 1/4
Question: A sock drawer contains seven socks, each one a different solid color. The colors of the socks are blue, indigo, and violet. A person reaches into the drawer, pulls out two socks, and puts a single sock on each foot. If each sock can fit either the left or the right foot, and if it matters whether a particular sock is on the left or the right foot, how many different sock fashion combinations could the person make from the three socks?
(A) 12
(B) 15
(C) 21
(D) 36
(E) 6
Rationale: It's a question of permutation since order matters here ....
It can be deduced to-
3P2 = 3!/1! = 3*2 = 6 .........Answer is - E
Answer: (E) 6
Question: A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 3, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following ?
(A) 1/625
(B) 2/625
(C) 4/625
(D) 50/625
(E) 25/625
Rationale: I think most of the answers are missing a point. Let me try to put it across:
Total number of possible numbers are : 5x5 = 25
Correct number =1
Case 1: When he gets it right in first attempt: P(E1) = 1/25
Case 2: He gets 1st attempt wrong and second right:
When he gets it wrong then the probability of getting wrong is 24/25.
Now there are 24 cases with him and he chooses the right one this time.
Probability of right case is 1/24
Thus, P(E2) = 24/25 x 1/24
=1/25
Probability of getting it right in at most two cases = P(E1) + P(E2)
= 1/25 + 1/25
= 2/25
= 50/625
Option (D) is therefore right as most of you mentioned but the method employed was wrong.
Answer: (D) 50/625
Question: If b=4p where p is a prime number greater than 2, how many different positive even divisors does b have, including b?
(A) two
(B) three
(C) four
(D) six
(E) eight
Rationale: b=2, 2, p (p is in the prime factorization since were told it is a prime number in the question)
2
4 (because of 2*2)
2p (because of 2 * p)
4p (because of 2 * 2 * p)=C
Answer: (C) four
Question: A watch was sold at a loss of 10%. If the watch was sold for $20 more, there would have been a gain of 6%. What is the cost price?
(A) $95
(B) $105
(C) $115
(D) $125
(E) $135
Rationale: 0.9x + 20 = 1.06x
0.16x = 20
x = 125
The answer is D.
Answer: (D) $125
Question: a goes to place x and b goes to place y.
after a travelled 180 km more than b they together meet at a point between xy. they together had their lunch for half an hour. after that a took 2 hrs to reach x and b took 4.5 hrs to reach y. find distance between x and y?
(A) 900km
(B) 540km
(C) 720km
(D) 820km
(E) 920km
Rationale: let speed of A be-------Sa
let speed of B be--------Sb
let the distance covered by B while going to position XY be-----------x
so distance covered by A in same time while going to XY is----------180 +x(it's given in the question)
so total distance b/w X and Y is=x+(x+180)
while going to position XY :-
time taken by A = time taken by B
(x+180)/Sa= x/Sb
Sa/Sb=(x+180)/x---------------------1
After lunch:-
A.C.T(according to question)
Sa=x/2
Sb=(x+180)/4.5
dividing Sa/Sb=(x*4.5) / ((x+180)*2)--------------------2
equating equations 1 and 2
9/4 = (x+180)^2 / x^2
now taking square root on both sides we get
3/2 = (x+180) / x
x=360
therefore distance between x and y =x+(x+180)=900km
ANSWER:A
Answer: (A) 900km
Question: The length of the bridge, which a train 180 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 195 m
(B) 156 m
(C) 245 m
(D) 156 m
(E) 156 m
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time
= 30 sec. Let the length of bridge be x meters. Then, (180 + X)/30 = 25/2
==> 2(180 + X) = 750 ==> X
= 195 m.
Answer: A
Answer: (A) 195 m
Question: A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1.2 cm when a man gets on it. The mass of man is
(A) 72 kg
(B) 60 kg
(C) 72 kg
(D) 96 kg
(E) None
Rationale: Solution
Volume of water displaced	= (3 x 2 x 0.012)m3
= 0.072 m3.
Mass of man	=Volume of water displaced ×Density of water
= (0.072×1000) kg
= 72 kg.
Answer A
Answer: (A) 72 kg
Question: The ‘moving walkway’ is a 300-foot long conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a combined rate (including both walkway and foot speed) of 6 feet per second, reaches the group of people, and then remains stationary until the walkway ends. What is Bill’s average rate of movement Z for his trip along the moving walkway?
(A) 2 feet per second
(B) 2.5 feet per second
(C) 3 feet per second
(D) 4 feet per second
(E) 5 feet per second
Rationale: I get E.
Their rate is 3 ft/sec and his is 6 ft/sec. Their distance is d-120 and his distance is d.
So we get two equations:
3t=d-120
6t=d
Substituting, we get 3t=6t-120, or t=40 which means that d=240 so Bill traveled 240 ft and they traveled 120 ft. (They were at 240 on the conveyor belt when they met.
So, Bill's average rate of movement is Z:
He traveled 6 ft/sec for 240 ft and 40 seconds. He traveled 3 ft/sec for the remaining 60 ft for 20 seconds.
(240+60)/(20+40)= 5 ft/sec=E
Answer: (E) 5 feet per second
Question: The average of runs of a cricket player of 10 innings was 40. How many runs must he make in his next innings so as to increase his average of runs by 4?
(A) 87
(B) 16
(C) 10
(D) 84
(E) 17
Rationale: Average after 11 innings = 44
Required number of runs
= (44* 11) - (40* 10) = 484- 400
= 84.
Answer: D
Answer: (D) 84
Question: The average age of the district level hockey team of eleven is 26 years.The average age gets increased by 2 year when the coach age is also included.what is the age of the coach ?
(A) 40 yrs.
(B) 50 yrs.
(C) 45 yrs.
(D) 48 yrs.
(E) 52 yrs.
Rationale: Explanation:
Total age of players in team = 26 x 11 = 286
When coach is included, total members = 12, Avg age increases by two becomes 28
Total age when coach is included = 28x12 = 336
Age of coach = 336-286 = 50 yrs.
Answer: B
Answer: (B) 50 yrs.
Question: A glucose solution contains 20 grams of glucose per 1000 cubic centimeters of solution. If 500 cubic centimeters of the solution were poured into an empty container, how many grams of glucose would be in the container?
(A)  10.00
(B)  15.00
(C)  11.50
(D)  10.50
(E)  9.75
Rationale: We are given that a glucose solution contains 20 grams of glucose per 1000 cubic centimeters of solution. Since we are dealing with a solution, we know that the grams of glucose is proportional to the number of cubic centimeters of solution. Thus, to determine how many grams of glucose would be in the container when we have 500 cubic centimeters of solution, we can set up a proportion.
We can say: “20 grams of glucose is to 1000 cubic centimeters of solution as x grams of glucose is to 500 cubic centimeters of solution.” Let’s now set up the proportion and solve for x.
20/1000 = x/500
When we cross multiply we obtain:
(20)(500) = 1000x
10000 = 1000x
10 = x
There are 10.00 grams of glucose in the solution in the container.
The answer is A.
Answer: (A)  10.00
Question: The area of a triangle is with base 3m and height 4m?
(A) 4 m2
(B) 6 m2
(C) 18 m2
(D) 19 m2
(E) 12 m2
Rationale: 1/2 * 3 * 4
= 6 m2
Answer: B
Answer: (B) 6 m2
Question: .01 x .3 ÷ .4 x .5 = ?
(A) .015
(B) .0375
(C) .00375
(D) .1
(E) None of these
Rationale: Answer
Given expression = .01 x .3 ÷ .4 x .5
= .0015 ÷ .4
= .00375
Option: C
Answer: (C) .00375
Question: Which of the following is divisible by the first six positive integer multiples of 19?
(i) 52440
(ii) 114600
(iii) 19038
(A) None
(B) i only
(C) iii only
(D) ii and iii only
(E) i and ii only
Rationale: A positive integer x is divisible by 19, 2*19,...,6*19 if and only if it is divisible by their least common multiple, which in this case is 3*4*5*19. In particular, x is divisible by 10, so iii is not divisible by the first six positive integer multiples of 19.
3*4*5*19=60*(20-1)=1140. 1140*100=114000, so clearly (ii) is not divisible by the first six positive integer multiples of 19.
It remains to verify (i). 52440-40*1140=52440-45600=6840=6*1140, so (i) is divisible by 1140.
Answer B.
Answer: (B) i only
Question: Machine A and machine W are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine W. Machine W produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?
(A) 6
(B) 6.6
(C) 60
(D) 100
(E) 110
Rationale: [Reveal]Spoiler:
TimeW: 660/x
TimeA: [660/x+10]
660/x = [660/x+10] *110/100
660/x =66*11/x+10
660x+10= 66*11*x
660x +6600 = 66*11*x
x= 100
plug in back to timeA
660/100+10 => 660/110 = 6=A
Answer: (A) 6
Question: A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B ?
(A) 160 km
(B) 180 km
(C) 200 km
(D) 220 km
(E) 240 km
Rationale: Down Stream Speed :(14+4)km/hr =18 km/hr
Up Stream Speed:(14-4)km/hr=10km/hr
(x/18)+(x/2/20)=19
x=180km
ANSWER:B
Answer: (B) 180 km
Question: A cube has a volume of 27 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?
(A) 216
(B) 48
(C) 64
(D) 80
(E) 100
Rationale: Volume = 27 = side^3
i.e. Side of Cube = 3
New Cube has dimensions 6, 6, and 6 as all sides are twice of teh side of first cube
Volume = 6*6*6 = 216 square feet
Answer: option A
Answer: (A) 216
Question: Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion. In 16 years from now, Lyn the circus Lion will be exactly half as old as Ele, the circus Elephant. How old is Ele today?
(A) 47
(B) 48
(C) 43
(D) 42
(E) 41
Rationale: Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion.
Ele = 3*Lyn
Usually, ages are integers so there is a good possibility that the age of Ele is 48 (the only option that is a multiple of 3).
Then age of Lyn would be 16. In 16 yrs, Ele would be 64 and Lyn would be 32 - so Lyn would be half as old as Ele.
Answer (B)
Answer: (B) 48
Question: What is the smallest number which when increased by 3 is divisible by 18, 70, 100 and 21?
(A) 5037
(B) 5447
(C) 5867
(D) 6297
(E) 6617
Rationale: When increased by 3, the number must include at least 2^2*3^2*5^2*7 = 6300
The answer is D.
Answer: (D) 6297
Question: What is the probability of flipping a fair coin four times and the coin landing on heads on exactly three flips?
(A) 1/3
(B) 1/4
(C) 2/3
(D) 2/5
(E) 1/8
Rationale: Probability = (Favorable combination)/(Total combination)
Favorable combination = (HHHT, HHTH, HTHH,THHH) ==> 4
Total combination = 8 (2^4)
Probability = (4)/(16) = 1/4
(B)
Answer: (B) 1/4
Question: Rectangular Floors X and Y have equal area. If Floor X is 14 feet by 18 feet and Floor Y is 9 feet wide, what is the length of Floor Y, in feet?
(A)  13 1/2
(B)  18
(C)  18 3/4
(D)  21
(E)  28
Rationale: The area of a rectangle is: Area = length x width
We are given that floor X is 14 feet by 18 feet and that floor Y is 9 feet wide. So we can say:
length of X = 14
width of X = 18
width of Y = 9
length of Y = n
We also can say:
Area of Floor X = Area of Floor Y
(length of X)(width of X) = (length of Y)(width of Y)
(14)(18) = 9n
(14)(2) = n
28 = n
Answer E.
Answer: (E)  28
Question: There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability W that the number of men is equal to that of women?
(A) W=18/35
(B) W=16/35
(C) 14/35
(D) 13/35
(E) 12/35
Rationale: METHOD-1:
Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36
Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70
Probability = 36/70 = 18/35
A
METHOD-2:Also see the mistake done by the person who posted this question
Probability of First selected person being Man = 4/8
Probability of Second selected person being Man = 3/7
Probability of First selected person being Woman = 4/6
Probability of Second selected person being Woman = 3/5
i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35
The important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here
When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well
The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2!
A
Answer: (A) W=18/35
Question: If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many Z such committees are possible?
(A) 20
(B) 40
(C) 50
(D) Z=80
(E) Z=120
Rationale: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 5C3=10.
But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.
Total # of ways: 5C3*2^3=80.
Answer: D.
Answer: (D) Z=80
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?
(A) 09:30 p.m
(B) 11:23 p.m
(C) 10:30 p.m
(D) 07:30 p.m
(E) 05:93 p.m
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) 10:30 p.m
Question: 4, 5, 7, 11, 19, (...)
(A) 32
(B) 22
(C) 35
(D) 27
(E) 28
Rationale: 4
4 × 2 - 3 = 5
5 × 2 - 3 = 7
7 × 2 - 3 = 11
11 × 2 - 3 = 19
19 × 2 - 3 = 35
Answer is C
Answer: (C) 35
Question: Two pyramids are thrown with faces 1,2,4,6. Find the probability to get a sum of even number on an their faces?
(A) 5/8
(B) 3/4
(C) 1/4
(D) 7/4
(E) 3/5
Rationale: 1 pyramid can show 4 different kind of arrangements
1,2,4=7
1,2,6=9
1,4,6=11
2,4,6=12
So, out of 4 outcomes
3 are odd and 1 is even.
In question given two pyramids are thrown.
So, to make some of their faces as even
Condition 1: some of both individual faces of each pyramid is odd
3/4 * 3/4
=9/16
Condition 2: some of both individual faces of pyramid is even
1/4 + 1/4
=1/16
Total such conditions = 9/16 + 1/16
= 10/16
= 5/8
ANSWER:A
Answer: (A) 5/8
Question: A certain number when divided by 39 leaves a remainder 17, what is the remainder when the same number is divided by 13?
(A) 7
(B) 8
(C) 9
(D) 6
(E) 4
Rationale: Explanation:
39 + 17 = 56/13 = 4 (Remainder)
Answer: E
Answer: (E) 4
Question: Average of all prime numbers between 30 to 50
(A) 37
(B) 37.8
(C) 39
(D) 39.8
(E) 40
Rationale: Explanation:
Prime numbers between 30 and 50 are:
31, 37, 41, 43, 47
Average of prime numbers between 30 to 50 will be
(31+37+41+43+47 / 5)=199 / 5=39.8
Option D
Answer: (D) 39.8
Question: A snail, climbing a 42 feet high wall, climbs up 4 feet on the first day but slides down 2 feet on the second. It climbs 4 feet on the third day and slides down again 2 feet on the fourth day. If this pattern continues, how many days will it take the snail to reach the top of the wall?
(A) 20
(B) 26
(C) 32
(D) 39
(E) 51
Rationale: total transaction in two days = 4-2 = 2 feet
in 38 days it will climb 38 feet
on the 39th day , the snail will climb 4 feet , thus reaching the top
therefore , total no of days required =39
D
Answer: (D) 39
Question: Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then
(A) XB > CD
(B) XB < YD
(C) AX > XB
(D) AX < CD
(E) AX > AB
Rationale: A--X------B
C-----Y---D
AX < CD.
Answer: D.
Answer: (D) AX < CD
Question: The letters D, G, I, I , and T can be used to form 5-letter strings as DIGIT or DGIIT. Using these letters, how many 5-letter strings can be formed in which the two occurrences of the letter I are separated by at least one other letter?
(A) 12
(B) 18
(C) 24
(D) 36
(E) 48
Rationale: Total no of ways arranging 5 letter with one letter redundant is 5!/2!=60
No of ways two I's can be together 4!=24
no of ways at least one alpha is between two I's =60-24=36
ANS:D
Answer: (D) 36
Question: A 8% stock yields 20%. The market value of the stock is:
(A) Rs 48
(B) Rs 45
(C) Rs 40
(D) Rs 50
(E) Rs 55
Rationale: Explanation:
For an income of Rs. 20, investment = Rs. 100.
For an income of Rs 8, investment =Rs.100/20 X8 =Rs 40
Market value of Rs. 100 stock = Rs 40
Answer is C
Answer: (C) Rs 40
Question: At what rate percent on simple interest will Rs.750 amount to Rs.825 in 5 years?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 75 = (750*5*R)/100
R = 2%.Answer: A
Answer: (A) 2
Question: In the formula V = 1/(2r)^3, if r is halved, then V is multiplied by?
(A) 16
(B) 8
(C) 1
(D) 1/8
(E) 1/64
Rationale: Say r=1 => V1 = 1/8
when r=1/2; V2 = 1
V2 = 1*V1.
Answer : B
Answer: (B) 8
Question: If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:
(A) 0
(B) 1
(C) 2
(D) 3
(E) None of these
Rationale: Explanation:
Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3.
x = 2.
ANSWER IS C
Answer: (C) 2
Question: A vending machine randomly dispenses four different types of fruit candy. There are twice as many apple candies as orange candies, twice as many strawberry candies as grape candies, and twice as many apple candies as strawberry candies. If each candy cost $0.4, and there are exactly 90 candies, what is the minimum amount of money required to guarantee that you would buy at least three of each type of candy?
(A) $3.00
(B) $20.75
(C) $33.20
(D) $42.75
(E) $45.00
Rationale: Let number of Apple , Orange , strawberry and grape candies be A, O ,S and G respectively .
A= 2O
S= 2G
A= 2S
A= 4G
A+O+S+G = 90
=>A + A/2 + A/2 +A/4 = 90
=> 9A/4 = 90
=> A = 40
O = 20
S = 20
G = 10
Cost of each candy = .25 $
Mininum amount of money required to guarantee that you would buy at least three of each type of candy
We can buy 40 Apple candies , 20 orange candies , 20 strawberry candies and 3 grape candies to ensure atleast 3 of each type of candies .
Total = 83 candies
Amount required = 83 * .4 = 33.20 $
Answer C
Answer: (C) $33.20
Question: A computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $5 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
(A) $28
(B) $82
(C) $110
(D) $138
(E) $195
Rationale: by the question, the equation would be 150 p - 85*150 - 16500 = 0
p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component.
solving the equation, we get p = $ 195. Answer E for me.
Answer: (E) $195