divelab/Sys2Bench huggingface dataset:
Question: 2 gears one with 12 teeth and other one with 14 teeth are engaged with each other. One teeth in smaller and one tooth in bigger are marked and initially those 2 marked teeth are in contact with each other. After how many rotations of the smaller gear with the marked teeth in the other gear will again come into contact for the first time?
Options:
A)6
B)7
C)8
D)9
E)2
Rationale: Assume the distance between the teeth is 1 cm. Then the circumference of first gear is 12 cm and the second is 14 cm.
Now LCM (12, 14) = 84. So to cover 84 cm, the first gear has to rotate 84128412 = 7 rounds (the second gear rotates 84 / 14 = 6 rounds as it is bigger)
Correct Option : A
Answer: A
Question: A total of m different points are selected on a particular line, and a total of n different points are selected on another line parallel to the first, where each of m and n is greater than 1. In how many different ways can a triangle be made with its vertices at three of the selected points?
Options:
A)m^2n+mn^2
B)mn(m+n-2)
C)mn(m+n−2)/2
D)(m+n)(m+n−1)(m+n−2)/6
E)(m+n)!/m!n!
Rationale: ase 1: One point on particular line and other 2 points on parallel line. #ways=
m* nc2
Case 2: one point on parallel line and other 2 on particular line.
n* mc2
Total
m* nc2+ n* mc2
mn(m+n-2)
ANS:B
Answer: B
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is?
Options:
A)25/42
B)25/46
C)25/48
D)25/18
E)25/29
Rationale: Total fruits = 9
Since there must be at least two apples,
(⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃
= 25/42.
Answer: A
Answer: A
Question: At what rate percent on simple interest will Rs.1750 amount to Rs.2000 in 5 years?
Options:
A)4 %
B)3 6/7 %
C)2 6/7 %
D)5 %
E)6 %
Rationale: Explanation:
250 = (1750x5xR)/100
250 = (175xR)/2
500 = (175xR)
R = 500/175
R = 2 6/7 %
Answer: Option C
Answer: C
Question: How many times the keys of a writter haveto be pressedin order to write first 400 counting no.'s?
Options:
A)998
B)1000
C)1092 times
D)1100
E)1200
Rationale: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 400 = 301 * 3 = 903
-----------
1092
C
Answer: C
Question: In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
Options:
A)1/3
B)2/3
C)1/4
D)1/5
E)2/5
Rationale: Total number of balls = (8 + 7 + 6) = 21.
Let E	= event that the ball drawn is neither red nor green
= event that the ball drawn is blue.
n(E) = 7
=>7/21 = 1/3
ANSWER A
Answer: A
Question: The average age of 25 students of a class is 25 years. Out of these, the average age of 10 students is 22 years and that of the other 14 students is 28 years. The age of the 25th student is?
Options:
A)10
B)15
C)13
D)11
E)9
Rationale: Age of the 25th student = 25*25 - (10*22+14*28) = 625-612 = 13 years
Answer is C
Answer: C
Question: A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 95, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
Options:
A)74
B)75
C)76
D)77
E)81
Rationale: ratio is 4:6:5 , numbers are 4x, 6x, 5x
total scores of each class is (65*4x + 6x * 95 + 77*5x) = 260x+570x+385x = 1215x
total number of students = 15x
average = 1215x/15x = 81
E is the answer
Answer: E
Question: A train 280 m long is running with a speed of 60 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)15
B)6
C)7
D)9
E)5
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 280 * 3/55 = 15 sec.Answer: A
Answer: A
Question: How many integers between 324,805 and 458,705 have tens digit 1 and units digit 3?
Options:
A)1,349
B)1,353
C)10,040
D)1,354
E)10,400
Rationale: There is one number in hundred with 1 in the tens digit and 3 in the units digit: 13, 113, 213, 313, ...
The difference between 324,805 and 458,705 is 458,705-324,805=134,900 - one number per each hundred gives 134,900/100=1,349 numbers.
Answer: A.
Answer: A
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 90 kmph. In how much time will the trains cross each other?
Options:
A)11
B)10
C)12
D)13
E)14
Rationale: Relative speed = (54 + 90)* 5/18 = 7 * 5 = 40 mps.
The time required = d/s = (100 + 100 + 200)/40
= 400/40 = 10 sec.
Answer: B
Answer: B
Question: Find the least number which when divided by 35 and 11 leaves a remainder of 1 in each case.
Options:
A)366
B)236
C)367
D)365
E)386
Rationale: Explanation:
The least number which when divided by different divisors leaving the same remainder in each case
= LCM(different divisors) + remainder left in each case.
Hence the required least number
= LCM(35, 11) + 1 = 386.
Answer: E
Answer: E
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
Options:
A)8
B)4
C)3
D)2
E)6
Rationale: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer: B
Answer: B
Question: A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
Options:
A)76 hrs
B)97 hrs
C)35 hrs
D)16 hrs
E)12 hrs
Rationale: Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.
1/x + 2/x + 4/x
= 1/5
7/x = 1/5 => x = 35 hrs.
Answer: C
Answer: C
Question: If a positive even number n is not divisible by 3 or 4, then the product (n + 6)(n + 8)(n + 10) must be divisible by which of the following?
I. 24
II. 32
III. 96
Options:
A)None
B)I only
C)II only
D)I and II only
E)I, II, and III
Rationale: n is a multiple of 2 but not a multiple of 3 or 4
Possible values of n = 10, 14, 22.....
@n=10 : (n + 6)(n + 8)(n + 10) = 16*18*20 i.e. Divisible by 24, 32 and 96 all
@n=14 : (n + 6)(n + 8)(n + 10) = 20*22*24 i.e. Divisible by 24, 32 and 96 all
@n=22 : (n + 6)(n + 8)(n + 10) = 28*30*32 i.e. Divisible by 24, 32 and 96 all
Answer: Option E
Answer: E
Question: Mysoon collects glass ornaments. Ten more than 1/6 of the ornaments in her collection are handmade, and 1/2 of the handmade ornaments are antiques. If 1/10 of the ornaments in her collection are handmade antiques, how many ornaments are in her collection?
Options:
A)36
B)60
C)108
D)144
E)300
Rationale: The number of ornaments = a
Ten more than 1/6 of the ornaments in her collection are handmade => Handmade = 10+a/6
1/2 of the handmade ornaments are antiques => Handmade ornaments = 1/2*(10+a/6) = 5 + a/12
1/10 of the ornaments in her collection are handmade antiques => Handmade ornaments = a/10
=> 5 + a/12 = a/10 => a = 300
Ans: E
Answer: E
Question: Every letter in the alphabet has a number value that is equal to its place in the alphabet. Thus, the letter A has a value of 1, the letter B has a value of 2, the letter C has a value of 3, etc... The number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word. What is the number value of the word "COW"?
Options:
A)120
B)123
C)126
D)129
E)132
Rationale: "COW" = (3+15+23)*3=123.
The answer is B.
Answer: B
Question: The owner of a cell phone shop charges his customer 23% more than the cost price. If a customer paid Rs.7,011 for a cell phone, then what was the cost price of the cell phone?
Options:
A)Rs.5,845
B)Rs.6,750
C)Rs.5,700
D)Rs.6,925
E)None of these
Rationale: Explanation:
123% of CP =SP
Therefore, CP = Rs.7,011x100/123 = Rs.5700
Answer: Option C
Answer: C
Question: A cube of edge 5 cm is cut into cubes of each edge 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to
Options:
A)1 : 5
B)1 : 25
C)1 : 125
D)1 : 625
E)None
Rationale: Solution
Required ratio	=(6x1x1 / 6x5x5)
‹=› 1/ 25
‹=› 1 : 125.
Answer B
Answer: B
Question: In a school of 650 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
Options:
A)173
B)163
C)153
D)143
E)117
Rationale: 44 + 28 + 10 = 82%
100 – 82 = 18%
650 * 18/100 = 117
ANSWER:E
Answer: E
Question: Mr Amin borrowed some money from Mr Vishwas. The rate of interest for first two years is 8% p.a., for the next three years is 11 % p.a. and for the period beyond 5 years 14% p.a. Mr Vishwas got an amount of 10920 as an interest at the end of eight years. Then what amount was borrowed by Mr Amin ?
Options:
A)12000
B)15000
C)1400
D)Data inadequate
E)None of these
Rationale: Let ‘x’ be the amount borrowed by Mr Amin.
∴ x×2×8/100+x×3×11/100+x×3×14/100=10920
or, 91⁄100x = 10920 or x = 10920×100/91=12000
Answer A
Answer: A
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 W for his trip along the moving walkway?
Options:
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 W is:
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
Question: In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?
Options:
A)144
B)119
C)113
D)88
E)31
Rationale: Greatest Possible Number taken both should be 144 (As it is maximum for One)
Smallest Possible Number taken both should be given by
Total - Neither = A + B - Both
Both = A+B+Neither - Total (Neither must be 0 to minimize the both)
So 144 + 119 + 0 - 232 = 31
Greatest - Smallest is 144-31 = 113
So answer must be C. 113
Answer: C
Question: In a certain circle there are 9 points. What is the number of the triangles connecting 3 points of the 9 points?
Options:
A)12
B)84
C)108
D)120
E)132
Rationale: IMO : B
HERE we have to select 3 points out of 9 points. Order is not important
So the answer will be 9c3 = 84
answer B
Answer: B
Question: In an office, 10 percent of the workers have at least 5 years of service, and a total of 16 workers have at least 10 years of service. If 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but fewer than 10 years of service?
Options:
A) 16
B) 64
C) 50
D) 144
E) 160
Rationale: (10/100)Workers = 16 = > number of workers = 160
(10/100)*Workers = x+16 = > x = 16
Answer A
Answer: A
Question: John makes $50 a week from his job. He earns a raise andnow makes $75 a week. What is the % increase?
Options:
A)15%
B)16.66%
C)50%
D)19%
E)21%
Rationale: Increase = (25/50)*100 = (1/2)*100 = 50%.
C
Answer: C
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1000 resolutions?
Options:
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
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?
Options:
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
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.
Options:
A)10
B)12
C)14
D)15
E)16
Rationale: 50 - pigs
10 - cats
ANSWER:A
Answer: A
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?
Options:
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
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?
Options:
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
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?
Options:
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
Question: Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:
Options:
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
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 %?
Options:
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
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?
Options:
A)120
B)288
C)1440
D)2880
E)8640
Rationale: Answer: B.
Answer: B
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?
Options:
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
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?
Options:
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
Question: 8 is 4% of a, and 4 is 8% of b. c equals b/a. What is the value of c?
Options:
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
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?
Options:
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
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 ?
Options:
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
Question: If b=4p where p is a prime number greater than 2, how many different positive even divisors does b have, including b?
Options:
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
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?
Options:
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
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?
Options:
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
Question: The length of the bridge, which a train 180 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
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
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
Options:
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
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?
Options:
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
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?
Options:
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
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 ?
Options:
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
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?
Options:
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
Question: The area of a triangle is with base 3m and height 4m?
Options:
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
Question: .01 x .3 ÷ .4 x .5 = ?
Options:
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