RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The respective ages of father and his son are 42 and 16 years. In how many years will the father be twice as old as his son ?
A.19 years
B.9 years
C.10 years
D.15 years
Answer: C.10 years
Explanation: Suppose x years later the father will be twice as old as his son.
x + 42 = 2 (x + 16)
x = 42 - 32 = 10 years
answer : C
Question: At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent W of the interns report no feelings of tiredness during their shifts?
A.6
B.14
C.19
D.20
Answer: C.19
Explanation: < 6 hours sleep>= 6 hours sleepTOTAL
Tired75--
Not Tired-0.7*X?
TOTAL80X100
Interns who receive< than 6 hours sleepandNot Tired= 80 - 75 = 5;
TOTAL interns who receive >= 6 hours sleep= 100 - 80 = 20, so interns who receive>= 6 hours sleepand areNot Tired= 0.7 * 20 =14;
Interns who areNot Tired W= 5 + 14 = 19.
Answer: C.
Question: If $100 is invested at x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?
A.10,000(x^n)
B.10,000(x/100)^n
C.100n(x/100)
D.10,000(1+x/100)^n
Answer: C.100n(x/100)
Explanation: I think answer D is for compound interest (which i assumed)
and answer C is for simple interest because it is not compounding
Question: A cylindrical container of radius 6 cm and height 15 cm is filled with ice-cream. The whole icecream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is four times the radius of its base, find the radius of the ice-cream cone.
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: volume of given ice cream =(pie)*6²*15=540(pie)
dividing to 10 children volume given to a child =54(pie)
let r be radius and h be the height of the cone,then
(pie)r²h/3 + 2(pie)r³/3=54(pie)
also given h=4r
4r³/3 +2r³/3=54
2r³=54
r³=27
r=3
ANSWER:C
Question: In Net's hair salon 48% of the customers dye their hair blond, 36% dye their eyebrows blond and 35% straighten their hair. 20% of the customers have none of these three procedures, while 12% take all of these three procedures. What percent of the customers come for exactly 2 of these 3 procedures?
A.5%
B.9%
C.12%
D.15%
Answer: D.15%
Explanation: Let a total of 100 people visit the salon.
Total = 100
Dye hair blonde (A) = 45 % = 45
Dye Eyebrows blonde (B) = 36% = 36
Straighten Hair (C) = 35% = 35
Neither = 20% = 20
All Three = 12% =12
Total = A+B+C - (Sum of Exactly Two group overlaps) - 2*(All three) + Neither
100 = 45+36+35 - (Sum of Exactly Two group overlaps) - 2*12 + 20
(Sum of Exactly Two group overlaps) = 9
%of customers coming for exactly 2 of the 3 procedures = 15%
D
Question: A shop owner sells 60mtr of cloth and gains SP of 10 mtrs. Find the gain %?
A.20%
B.40%
C.50%
D.60%
Answer: A.20%
Explanation: Here, selling price of 10 m cloth is obtained as profit.
Profit of 10 m cloth = (S.P. of 60 m cloth) – (C.P. of 60 m cloth)
Selling price of 50 m cloth = Selling Price of 60 m of cloth
Let cost of each metre be Rs. 100.
Therefore, cost price of 50 m cloth = Rs. 5000 and S.P. of 50 m cloth = Rs. Rs. 6000
Profit% = 10/50 × 100 = 20%
20
Profit of 20% was made by the merchant.
A
Question: If a fair die is rolled two times, what is the probability that a 3 occurs on at least one roll?
A.25/36
B.125/216
C.91/216
D.11/36
Answer: D.11/36
Explanation: Questions such as these that talk aboutat leastormaximumorminimumin probability questions should make sure realize that probability of any event (N) to occur = 1- P(Not N)
Thus, the probability of at least 1 roll = 1- Probability of NO 3s = 1- (5/6)(5/6) = 1-25/36 = 11/36.
5/6 is the probability of NOT getting a 3 in any 1 roll with 5 allowed numbers (=1,2,4,5,6) out of a total of 6 possibilities.
D is thus the correct answer.
Question: In 1937, the ship of the great sailor SINBAD left an Egyptian port heading Ivory coast at R mile/month .
One month later another ship of the greatest pirate ever CHENG I SAO was 5000 miles due south of the same Egyptian port and heading due north at Y miles/month. Six months later after the leaving of Sinbad’s ship from Egyptian port, how far apart were the ships? [Ivory coast is in the west of Egypt]
A.{ (6R)^2 + (5000-5y)^2 }^1/2
B.{ (36x)^2 + (5000-7y)^2 }^1/2
C.{ (16x)^2 + (5000-7y)^2 }^1/2
D.{ (7x)^2 + (5200-7y)^2 }^1/2
Answer: A.{ (6R)^2 + (5000-5y)^2 }^1/2
Explanation: The chinese ship sailed for 5 months i.e. 5Y miles @Y miles/month, therefore distance from Egyptian port is 5000-5Y. Since A is the only option with this value ...therefore A is the answer
Question: The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. What is the period (in years)?
A.1
B.2
C.3
D.3.5
Answer: B.2
Explanation: Explanation:
Let the period be n years
Then, amount after n years = Rs.(30000 + 4347) = Rs. 34347
P(1+R/100)T=34347
30000(1+7/100)n=34347
30000(107100)n=34347
(107/100)n=34347/30000=11449/10000=(107/100)2
n=2 years
Answer: Option B
Question: A sum of money becomes 7/6 of itself in 7 years at a certain rate of simple interest. The rate per annum is?
A.50/13
B.50/17
C.50/19
D.50/21
Answer: D.50/21
Explanation: Let sum = x. Then, amount = 7x/6
S.I. = 7x/6 - x = x/6; Time = 7 years.
Rate = (100 * x) / (x * 6 * 7) = 50/21 %.
Answer:D
Question: Ashok secured average of 77 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?
A.38
B.27
C.92
D.17
Answer: C.92
Explanation: Explanation:
Number of subjects = 6
Average of marks in 6 subjects = 77
Therefore total marks in 6 subjects = 77 * 6 = 462
Now, No. of subjects = 5
Total marks in 5 subjects = 74 * 5 = 370
Therefore marks in 6th subject = 462 – 370 = 92
ANSWER: C
Question: In the x-y plane, the area of the region bounded by the graph of |x+y| + |x-y| = 10 is
A.8
B.625
C.16
D.20
Answer: B.625
Explanation: I've never seen such kind of question in GMAT before.
OK there can be 4 cases:
|x+y| + |x-y| = 10
A. x+y+x-y = 10 --> x=5
B. x+y-x+y = 10 --> y=5
C. -x-y +x-y= 10 --> y=-5
D. -x-y-x+y=10 --> x=-5
The area bounded by 4 graphs x=5, x=-5, y=5, y=-5 will be square with the side of 4 so the area will be25*25=625
Answer: B
Question: A can do a piece of work in 6 days and B can do it in 6 days how long will they both work together to complete the work?
A.6/11
B.1/2
C.3/4
D.9/11
Answer: B.1/2
Explanation: Explanation:
A’s one day work = 1/5
B’s one day work = 1/6
(A+B)’s one day work = 1/6 + 1/6 = 2/3= => time = 3/2 = 1 1/2 days
Answer: Option B
Question: Three gentlemen and three ladies are candidates for two vacancies. A voter has to vote for two candidates. In how many ways can one cast his vote?
A.9
B.30
C.36
D.15
Answer: D.15
Explanation: Solution: There are 6 candidates and a voter has to vote for any two of them.
So, the required number of ways is,
= 6C2 = 6!/2!*4!
= 15.
Answer: Option D
Question: There were two candidates in an election. Winner candidate received 58% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?
A.776
B.1044
C.299
D.257
Answer: B.1044
Explanation: W = 58% L = 42%
58% - 42% = 16%
16% -------- 288
58% -------- ? => 1044
Answer:B
Question: A school has 4 section of Chemistry in Class X having 55, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the 4 sections. Determine the overall average of marks per student.
A.50.15
B.52.06
C.51.25
D.53.06
Answer: B.52.06
Explanation: Required average marks
= 55Ã—50+35Ã—60+45Ã—55+42Ã—45/55+35+45+42
= 2750+2100+2475+1890/162
= 9215â„177 = 52.06
Answer B
Question: The tax on a commodity is diminished by 15% and its consumption increased by 10%. The effect on revenue is?
A.8.5
B.6.5
C.5.5
D.5.6
Answer: B.6.5
Explanation: 100 * 100 = 10000
85 * 110 = 9350
-----------
10000-----------650
100-----------? => 6.5% decrease
Answer:B
Question: A takes twice as much time as B & C takes thrice as much time as B to finish a piece of work. Working together they can finish the work in 18 days. The no. of days need for B to do the work alone is?
A.30 days
B.31 days
C.33 days
D.41 days
Answer: C.33 days
Explanation: Let A takes x days to complete the work , then B takes
x/2
days and C takes
3x/2
days to complete the work.
A,B and C together complete the work in 18 days
In 1 day , all they together can do => 1/x+ 2/x+ 2/3x
= 1/18
3+6+2/3x = 1/18
3x23x2 = 18
X = 66 days
The number of days B alone takes to finish the work = x/2
= 33 days
C
Question: A fort had provision of food for 150 men for 45 days. After 15 days, 10 men left the fort. The number of days for which the remaining food will last, is:
A.32
B.37	1/4
C.42
D.54
Answer: A.32
Explanation: we have food for 150 men for 45 days.
After 15 days food left for 150 men for 30 days.
so
150 : 30
now we have 140 men and x days
140 : 150 :: 30 : x
x = (150*30)/140 = 32 days.
ANSWER:A
Question: The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
A.1209
B.6677
C.1200
D.3356
Answer: C.1200
Explanation: P --- 10 ---- 600
P --- 5 ----- 300
3P --- 5 ----- 900
------
=> 1200
Answer:C
Question: Train A and Train B began traveling towards each other from opposite ends of a 500-mile long track at 1:00 PM. If Train A traveled at 35 miles per hour and Train B traveled at 15 miles per hour, at what time did the trains meet?
A.5:40 PM
B.6:00 PM
C.7:20 PM
D.11:00 PM
Answer: D.11:00 PM
Explanation: This question tests your concepts of relative speed:
If two trains are moving in opposite direction, then distance will reduce at a rate of (Speed of 1 + Speed of 2)
If two trains are moving in same direction, then distance will reduce at a rate of (Speed of 1 - Speed of 2)
Here the trains are moving towards each other, hence in opposite direction.
Trains will cover the 500 mile track in a time of 500/(15 + 35) = 500/50 = 10 hours
Trains started at 1:00 PM, there they will meet at 11:00 PM
Option D
Question: Five Siblings are to be seated in a round table for lunch. If Daniel and David are among the five siblings, what is the probability that they sit next to each other
A. 5%
B. 10%
C. 15%
D. 20%
Answer: B. 10%
Explanation: Possible Sitting position is 5! = 120
Daniel and David sitting next to each other is 5 Combination 2
=5!/2!(5-2)!
=120/2(6)
=120/12
= 10
Answer = B
Question: During a sale, the price of a pair of shoes is marked down 10% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?
A.9%
B.10%
C.11%
D.15%
Answer: C.11%
Explanation: Assume the price = 100
Price during sale = 90
Price after sale = 100
Percent increase = 10/90*100 = 11% approx.
Correct Option: C
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.76800?
A.81000
B.97200
C.27772
D.29889
Answer: B.97200
Explanation: 76800* 9/8 * 9/8 = 97200.Answer:B
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 6 boys when a boy gets any no. of prizes?
A.216
B.220
C.289
D.240
Answer: A.216
Explanation: Ans.(A)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 6 ways, i.e. (6 x 6 x 6) ways = 63 ways = 216 ways Or nr ways = 63 ways = 216 ways
Question: What distance will be covered by a bus moving at 72 kmph in 30 seconds?
A.416.66 m
B.516.66 m
C.250 m
D.616.66 m
Answer: B.516.66 m
Explanation: 62 kmph = 62 * 5/18 = 17.22 mps
D = Speed * time = 17.22 * 30 = 516.66 m.
ANSWER:B
Question: A certain team has 9 members, including Joey. A three-member relay team will be selected as follows: one of the 9 members is to be chosen at random to run first, one of the remaining 8 members is to be chosen at random to run second, and one of the remaining 7 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?
A.1/1320
B.1/132
C.1/110
D.2/9
Answer: D.2/9
Explanation: Total outcomes= 9*8*7
Favorable Outcomes= 11*1*10 and 11*10*1
P=2*8*7*1/9*8*7
P=2/9
Ans D
Question: Gretzky Street begins at Orr Street and runs directly east for 5.6 kilometers until it ends when it meets Howe Street. Gretzky Street is intersected every 350 meters by a perpendicular street, and each of those streets other than Orr Street and Howe Street is given a number beginning at 1st Street (one block east of Orr Street) and continuing consecutively (2nd Street, 3rd Street, etc...) until the highest-numbered street one block west of Howe Street. What is the highest-numbered street that intersects Gretzky Street?
A.12th
B.13th
C.14th
D.15th
Answer: D.15th
Explanation: 5.6 km / 350 m = 16.
However, the street at the 5.6-km mark is not 16th Street; it is Howe Street.
Therefore, the highest numbered street is 15th Street.
The answer is D.
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is:
A.150
B.258
C.750
D.693
Answer: C.750
Explanation: Explanation:
Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750
Answer:C) 750
Question: Ten years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages
A.35
B.34
C.45
D.25
Answer: A.35
Explanation: Explanation:
Let the present age of P and Q be 3x and 4x respectively.
Ten years ago, P was half of Q in age
=> 2(3x – 10) = (4x – 10)
=> 6x – 20 = 4x – 10
=> 2x = 10
=> x = 5
Answer: Option A
Question: If the magician is not using a trick deck of cards, what is the possibility that he will draw a Jack or Diamond from a very well-shuffled deck of cards?
A.1 in 13
B.4 in 13
C.1 in 4
D.4 in 52
Answer: B.4 in 13
Explanation: This problem uses the principle of adding fractions with a common denominator. Add the number of suits in the deck to the number of cards in each suit in the deck. Use the denominator of number of cards total in the deck. (4/52 + 13/52 = 17/52). Now subtract the number of Jacks of Diamonds in the deck from you answer. (17/52 - 1/52 = 16/52). Further reduce this fraction. (16/52 = 4/13). Answer is B.
Question: A number is said to be prime saturated if the product of all the different positive prime factors of q is less than the square root of q. What is the greatest two digit prime saturated integer ?
A.99
B.98
C.97
D.96
Answer: D.96
Explanation: q 96 = 3 * 32 = 3 * 2^5
Answer is D.
Question: Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 20000, then find his savings?
A.Rs.3600
B.Rs.4000
C.Rs.3639
D.Rs.3632
Answer: B.Rs.4000
Explanation: Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively.
Income, 5x = 20000 => x = 4000
Savings = Income - expenditure = 5x - 4x = x
So, savings = Rs.4000
Answer: B
Question: The bus uses 80 gallons of fuel to fly 320 miles. At this rate, how many gallons of fuel are needed for a 800 mile bus?
A.100
B.300
C.150
D.200
Answer: D.200
Explanation: Number of gallons of fuel per mile = 320 /80 = 4 gallons per mile
Number of gallons of fuel for a 800 mile bus = 800/4= 200
ANSWER:D
Question: The average age of applicants for a new job is 30, with a standard deviation of 7. The hiring manager is only willing to accept applications whose age is within one standard deviation of the average age. What is the maximum number of different ages of the applicants?
A.8
B.14
C.15
D.18
Answer: C.15
Explanation: within one standard deviation of the average age means 31 +/- 7
23--30--37
number of dif.ages -23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
total=15
C
Question: Two trains of length 160 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
A.100/7 sec
B.80/7 sec
C.112/7 sec
D.120/7 sec
Answer: C.112/7 sec
Explanation: Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (160 + 100 + 300)/35
= 560/35 = 112/7 sec.
ANSWER:C
Question: If -3 < x < 0, which of the following must be true?
I. x^5 < x^2
II. x^5 < 2 – x
III. x^4 < x^2
A.I only
B.I and II only
C.II and III only
D.I and III only
Answer: B.I and II only
Explanation: I. x^5 < x^2 --> since x is always negative x^5 is always negative and x^2 is always positive therefore x^5 < x^2, so this statement is true.
II. x^5 < 2 – x --> x(x^4+1) < 2 --> negative*positive < 0 < 2, so this statement is also true.
III. x^4 < x^2 --> reduce by x^2 (we can safely do that since from -3 < x < 0 is follows that x^2>0): x^2 < 1. Since -3 < x < 0, then x^2 can be greater than 1. Hence, this statement is false.
Answer: B.
Question: In Orange County, one sixth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?
A.140
B.155
C.160
D.168
Answer: D.168
Explanation: The number must be a multiple of both 6 and 7 so the answer is 168.
The answer is D.
Question: A man can row his boat with the stream at 6 km/h and against the stream in 2 km/h. The man's rate is?
A.1 kmph
B.2 kmph
C.5 kmph
D.7 kmph
Answer: B.2 kmph
Explanation: DS = 6
US = 2
S = ?
S = (6 - 2)/2 = 2 kmph
Answer: B
Question: If M and N are positive integers that have remainders of 1 and 3, respectively, when divided by 9, which of the following could NOT be a possible value of M+N?
A.86
B.58
C.31
D.22
Answer: A.86
Explanation: M=9p+1
N=9q+3
We need M+N=9p+1+9q+3=9(p+q)+4
Pick numbers for pq
Since it is an addition of pq and the answer to this expression should be an integer (because all the numbers being added are integers),
we just need to choose values so that we get integer multiples of 6 so
p+q=0 ; M+n = 4
p+q=1 ; M+N = 13
P+q=2 ; M+N = 22
and so on, so basically you get something like - 4,13,22,31,40,..... all the other options were turning up.
Then I directly tried p+q=9 because it was closer to 86 for the first option, i got 85,
So Answer A.
Question: A cube of side one meter length is cut into small cubes of side 25 cm each. How many such small cubes can be obtained?
A.56
B.60
C.62
D.64
Answer: D.64
Explanation: Along one edge, the number of small cubes that can be cut
= 100/25 = 4
Along each edge 25 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut
= 4 * 4 * 4 = 64
Answer: D
Question: Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?
A.22
B.10
C.39
D.88
Answer: B.10
Explanation: Explanation:
Assume both trains meet after x hours after 7 am
Distance covered by train starting from P in x hours = 20x km
Distance covered by train starting from Q in (x-1) hours = 25(x-1)
Total distance = 110
=> 20x + 25(x-1) = 110
=> 45x = 135
=> x= 3
Means, they meet after 3 hours after 7 am, ie, they meet at 10 am
Answer: B) 10
Question: Each of the 59 members in a College class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 22 students sign up for the poetry club, 27 students for the history club, and 28 students for the writing club. If 6 students sign up for exactly two clubs, how many students sign up for all three clubs?
A.2
B.5
C.6
D.8
Answer: C.6
Explanation: Each of the 59 members in a College class is required to sign up for a minimum of one and a maximum of three academic clubs.Total = G1 + G2 + G3 - (# In exactly 2) - 2*(# in 3 sets)
59 = 22+27+28 - (6) - 2x
so, # In 3 sets = 6
Question: What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
A.20
B.21
C.12
D.22
Answer: A.20
Explanation: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such number =14
Required percentage =((14/70)x 100)% = 20%.
ANSWER A
Question: Evaluate: 30 - |-x + 6| for x = 10
A.16
B.26
C.36
D.46
Answer: B.26
Explanation: Substitute x by 10 in the given expression and evaluate
30 - |- (10) + 6| = 30 - |-10 + 6|
= 30 - | - 4 | = 30 - 4 = 26
correct answer B)26
Question: If c is 25% of a and 15% of b, what percent of a is b?
A. 2.5%
B. 15%
C. 25%
D. 125%
Answer: D. 125%
Explanation: Answer = D
25a/100 = 20b/100
b = 25a/20 = 125a/100 = 125%
Question: In a sports club with 30 members, 17 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis?
A.7
B.8
C.9
D.10
Answer: C.9
Explanation: There are a total of 30 members out of which two do not play either of the two sports... so the number of people of folks which play at least one of the sports mentioned is 28.
Now 17 play badminton and 19 play tennis out of 28.
The way I solved this was:
Badminton: (28 - 17 = 11 People)
Tennis (28 - 19 = 9 People)
Hence, the answer was 9 since it was the smaller number out of the two
ANSWER:C
Question: If 28a+30b+31c=520.
then a+b+c=?.a,b,c are natural numbers
A.18
B.20
C.17
D.42
Answer: C.17
Explanation: have a look on your calender
since,we all knw a year consist of 365 days
february is d only month which has 28 days
4 months in a year has 30 days
and,rest 7 months has 31 days..
so,following d given eq. we can write 28*1 + 30*4 + 31*12..
hence values of a,b and c are 1, 4 and 12 respectively..
a+b+c=17
ANSWER:C
Question: If x : y = 1 : 2, find the value of (2x + 3y) : (x + 4y)
A.5 : 6
B.7 : 8
C.8 : 9
D.9 : 10
Answer: C.8 : 9
Explanation: x : y = 1 : 2 means x/y = 1/2
Now, (2x + 3y) : (x + 4y) = (2x + 3y)/(x + 4y) [Divide numerator and denominator by y.]
= [(2x + 3y)/y]/[(x + 4y)/2] = [2(x/y) + 3]/[(x/y) + 4], put x/y = 1/2
We get = [2 (1/2) + 3)/(1/2 + 4) = (1 + 3)/[(1 + 8)/2] = 4/(9/2) = 4/1 × 2/9 = 8/9
Therefore the value of (2x + 3y) : (x + 4y) = 8 : 9
Answer is C
Question: There are 5,480 feet in 1 mile and 12 inches in one foot. How many inches are in a mile?
A.5,280 - 12
B.5,480*12
C.12(5,280)
D.12^2(5,280)
Answer: B.5,480*12
Explanation: 1 feet = 12 inches
1 mile = 5480 feet
1 mile = 5480*12 inches
Ans: B
Question: closed cylindrical tank contains 36pi cubic feet of water and its filled to half its capacity. When the tank is placed upright on its circular base
on level ground, the height of water in the tank is 4 feet. When the tank is placed on its side on level ground, w hat is the height, in feet, of the
surface of the water above the ground?
A.1 ft
B.2 ft
C.3 ft
D.4 ft
Answer: C.3 ft
Explanation: We know that the volume of cylinder = πr^2h
Given tank height = 4ft.
⇒ π r^2 4 = 36π
⇒ r = 3
So the radius is 3 which means the diameter is 6.
As the cylinder is filled to initially exactly half of the capacity, When this cylinder is placed on its side, Water comes up to the height of the radius.
So water comes up to 3 ft
ANSWER:C
Question: Which of the following are orthogonal pairs? a. 3i+2j b. i+j c. 2i-3j d. -7i+j ???
A.a,b
B.a,c
C.b,c
D.a,d
Answer: B.a,c
Explanation: a. 3i+2j
and
c. 2i-3j
are orthogonal pair.
as the dot product of two vectors is zero;so they are orthogonal.
ANSWER:B
Question: By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent of solution B. If 250 grams of solution A are mixed with 700 grams of solution B, then liquid X accounts for what percent of the weight of the resulting solution?
A.1.46%
B.1.93%
C.10%
D.15%
Answer: A.1.46%
Explanation: I think there is a typo in question.
It should have been "By weight Liquid 'X ' makes up..... "
Weight of Liquid X = 0.8 % of Weight of A + 1.8% of Weight of B
When 250gms of A and 700gms of B is mixed :
Weight of Liquid X = (0.8 * 250)/100 + (1.8* 700)/100 = 14.6gms
% of Liquid X in resultant mixture = (14.6/1000) *100 = 1.46%
A