RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Victor's job requires him to complete a series of identical jobs. If Victor is supervised at work, he finishes each job three days faster than if he is unsupervised. If Victor works for 144 days and is supervised for half the time, he will finish a total of 36 jobs. How long W would it take Victor to complete 10 jobs without any supervision?
A.34
B.52
C.60
D.70
Answer: C.60
Explanation: Rate when supervised = (job)/(time) = 1/t.
Rate when unsupervised = (job)/(time) = 1/(t+3).
For 144/2=72 days he is supervised and for 144/2=72 days he is unsupervised and does 36 jobs:
72/t + 72/(t+3) = 36 --> t=3 days --> t+3 = 6 days.
Victor to complete 10 jobs without any supervision will need W 10(t + 3) = 60 days.
Answer: C.
Question: A box measuring 90 inches long by 45 inches wide by 9 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective?
A.17
B.18
C.50
D.108
Answer: C.50
Explanation: least number of cubes will be required when the cubes that could fit in are biggest.
9 is the biggest number that could divide all three, 90, 45 and 9.
Thus side of cube must be 9, and total number of cubes = 90/9 * 45/9*9/9 = 50
Ans C it is.
Question: A car travels at a speed of 65 miles per hour. How far will it travel in 6 hours?
A.125 miles
B.225 miles
C.390 miles
D.425 miles
Answer: C.390 miles
Explanation: During each hour, the car travels 65 miles. For 6 hours it will travel
65 + 65 + 65 + 65 + 65+ 65 = 6 × 65 = 390 miles
correct answer is C) 390 miles
Question: A truck owner will refuel his vehicle at a rate of 2 gallons of diesel fuel every 5 seconds. If diesel fuel costs $ 2 per gallon, how long will it take for the truck owner to refuel his vehicle with $ 50 worth of diesel fuel?
A.50 seconds
B.1 minute
C.1 minute 20 seconds
D.20 minutes
Answer: A.50 seconds
Explanation: 2 gal / 5 sec
$2 / gal
$40/$2 = 20 gal
2 gal / 5 sec with 20 gal = 50 sec
A. 50 seconds
Question: Exactly 12% of the reporters for a certain wire service cover local politics in Country X. If 40% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics?
A.20%
B.42%
C.44%
D.80%
Answer: D.80%
Explanation: Let's assume there are 100 reporters --> 12 reporters cover local politics.
Now, as 40% of the reporters who cover all politics do not cover local politics then the rest 60% of the reporters who cover politics do cover local politics, so if there are x reporters who cover politics then 60% of them equal to 12 (# of reporters who cover local politics): 0.6x=12 --> x=20, hence 20 reporters cover politics and the rest 100-20=80 reporters do not cover politics at all.
Answer: D.
Question: If a^x = b^4y, then
A.log a/b= x/y
B.log a/ log b = x/y
C.log a/ log b = 4y/x
D.log b/a = x/y
Answer: C.log a/ log b = 4y/x
Explanation: a^x = b^4y => log a^x = log b^4y => x log a = 4y log b
=> log a/ log b = 4y/x
ANSWER:C
Question: A women purchased 3 towels @ Rs.100 each, 5 towels @ Rs.150 each and two towels at a certain rate which is now slipped off from his memory. But she remembers that the average price of the towels was Rs.150. Find the unknown rate of two towels?
A.400
B.450
C.500
D.550
Answer: B.450
Explanation: 10 * 150 = 1500
3 * 100 + 5 * 150 = 1050
1500 – 1050 = 450
B
Question: The remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder S of Y divided by 5?
A.S=1.
B.S=2.
C.S=3.
D.4.
Answer: B.S=2.
Explanation: X divided by 10 gives reminder of 2. X can be 2/12/22....
X+Y divided by 5 is 4. X+Y can be 4/ 9/ 19....
If X+Y= 4 and X is 2 then Y = 2 and Y/5 will give a reminder of 2
Similarly, if X+Y= 9 and X = 2, then y/5 will give a reminder of 2
Hence the answer must be 2 (B)
Also....
x+y=5m+4 and x=10K+2
hence 10k+2+y=5m+4 or y=5(m-2k)+2, m-2k being a constant remainder is 2 hence answer is B
Question: A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. If he makes exactly 98 cookies, what is the minimum number of chocolate chip cookies he makes?
A.7
B.14
C.21
D.28
Answer: B.14
Explanation: 7C+6P=98
We need to maximize P to minimize C so that the eq is also satisfied
Try substitution for CP to solve so that eqn is satisfied
The least value of C for which equation gets satisfied is 5
i.e. 7*2+6*14=14+84=98
Hence B is the answer
Question: Lagaan is levied on the 60% of the cultivated land. The revenue department collected total Rs. 3,84,000 through the lagaan from the village of Sukhiya. Sukhiya, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Sukhiya over the total taxable land of the village is:
A.0.20887
B.0.3887
C.0.33487
D.0.20833
Answer: D.0.20833
Explanation: Explanation:
Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x
\therefore Cultivated land of village = 384000x
\therefore Required percentage = \inline \frac{800x}{384000}\times 100 = 0.20833
Answer: D
Question: Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4, 1/3 and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?
A.1/32
B.7/8
C.9/64
D.5/64
Answer: A.1/32
Explanation: P(Xavier will solve)=1/4
P(Yvonne will solve)=1/2
P(Zelda will NOT solve) = 1- 5/8 = 3/8.
Now, we need to multiply all this Ps to find an answer:
p= (1/4)*(1/3)*(3/8) = 1/32.
Ans. A.
Question: The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 72 metres, what is its area?
A.315 sq.metres
B.260 sq.metres
C.280 sq.metres
D.380 sq.metres
Answer: A.315 sq.metres
Explanation: Let the length and breadth be 7x and 5x respectively.
Then, P = 2(7x + 5x) = 72 â‡’ x = 3
Area = 7 Ã— 3 Ã— 5 Ã— 3 = 315 sq.m.
Answer A
Question: If the area of circle is 616 sq cm then its circumference?
A.21
B.88
C.66
D.16
Answer: B.88
Explanation: 22/7 r2 = 616 => r = 14
2 * 22/7 * 14 = 88
Answer: B
Question: A man is 22 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is?
A.20
B.25
C.27
D.22
Answer: A.20
Explanation: Let the son's present age be x years.
Then, man's present age = (x + 22) years.
(x + 22) + 2 = 2(x + 2) x + 24 = 2x + 4 => x = 20.
Answer: A
Question: 1/2 + [(2/3 * 3/4)/4] - 9/16 =
A. 1/16
B. 19/16
C. 15/16
D. 9/13
Answer: A. 1/16
Explanation: We need to simplify the expression using PEMDAS.
Parentheses
Exponents
Multiplication andDivision
Addition andSubtraction
The calculation of an equation or expression must be carried out in the following order:
1) Operations within parentheses (or absolute value bars or radicals)
2) Exponents
3) Multiplication and division from left to right
4) Addition and subtraction from left to right
The answer is A.
Question: If x is to be chosen at random from the set {1,2,3,4} and y is to be chosen at random from the set {3,4,5}, what`s the probability that xy will be even?
A.1/6
B.2/3
C.1/2
D.1/3
Answer: B.2/3
Explanation: The product to be even either one or both must be even, so:
P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/4*1/3=2/3;
Or: P(xy=even)=1-P(xy=odd)=1-2/4*2/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1.
Answer: B.
Question: A man spends 75% of his income.If his income increases by 20%,then what will be his new expenditure?
A.61.5%
B.62.5%
C.63.5%
D.64.5%
Answer: B.62.5%
Explanation: Let Rs 100 be the income
Expenditure=Rs75
Increased income=Rs120
Expenditure in amount is same.
So, expenditure % =75/120 *100=62.5%
ANSWER:B
Question: The perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
A.13√2
B.15
C.48
D.75
Answer: A.13√2
Explanation: xplanation:
4a = 48 4a = 20
a = 12 a = 5
a2 = 144 a2 = 25
Combined area = a2 = 169 => a = 13
d = 13√2
Answer: A
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
A.22
B.77
C.36
D.88
Answer: C.36
Explanation: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer: C
Question: Kant and Jaya started a business by investing a certain amount, Jaya’s share is Rs.1400, out of annual profit of Rs.3800, then what is the ratio of investments of Kant and Jaya respectively ?
A.3:4
B.18:21
C.12:7
D.6:11
Answer: C.12:7
Explanation: otal profit = Rs.3800.
Jaya share = Rs.1400.
Kant share = Rs.3800 - Rs.1400 = Rs.2400.
Kant : Jaya = 2400 : 1400 => 12 : 7
Option C
Question: Two pipes A and B can fill a tank in 4 and 5 hours respectively. If they are turned up alternately for one hour each, the time taken to fill the tank is?
A.4 hrs 29 min
B.4 hrs 24 min
C.4 hrs 84 min
D.3 hrs 24 min
Answer: B.4 hrs 24 min
Explanation: 1/4 + 1/5 = 9/20
20/9 = 2 2/9
9/20 * 2 = 9/10 ---- 4 hours
WR = 1 - 9/10 = 1/10
1 h ---- 1/4
? ----- 1/10
2/5 * 60 = 24 = 4 hrs 24 min
Answer:B
Question: The sum of 3 consecutive numbers is definitely:
A.Positive
B.Divisible by 2.
C.Divisible by 3
D.Divisible by 4.
Answer: C.Divisible by 3
Explanation: If 1st term is x:
x+(x+1)+(x+2)=3x+3--->Always divisible by 3
If 2nd term is x:
(x-1)+x+(x+1)=3x--->Always divisible by 3
If 3rd term is x:
(x-2)+(x-1)+x=3x-3--->Always divisible by 3
Answer: C
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ?
A.5/5
B.5/9
C.5/3
D.5/8
Answer: B.5/9
Explanation: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216
= 5/9.
Answer:B
Question: Which of the following options must be true given the equation p=-q^6
I. If q is negative then p is negative.
II. q is negative.
III. q is non-negative.
A.I only
B.II only
C.III only
D.II and III only
Answer: A.I only
Explanation: I. p is negative --> not necessarily true, if q=0 then p=-q^6=0;
II. q is non-negative. q can take ANY value: positive, negative, zero. We don't have any restrictions on its value;
III. If q is negative then p is negative. p is negative means that q is not zero.
Answer: A (I only).
Question: 5670/(28*13.5) = ?
A.11
B.15
C.16
D.19
Answer: B.15
Explanation: B
15
? = 5670/378 = 15
Question: What is next in series
J F M A M ? ?
A.MS
B.SS
C.FJ
D.JJ
Answer: D.JJ
Explanation: D
JJ
Series is the name of months . January, February ...
Therefore June and July is the answer. Hence J J is correct option
Question: The HCF of two numbers is 62 and the other two factors of their LCM are 11 and 12. What is the largest number.
A.462
B.744
C.480
D.504
Answer: B.744
Explanation: Explanation:
HCF of the two numbers = 62
HCF will be always a factor of LCM
62 is factor of LCM
other two factors are 11 & 12
Then the numbers are (62 *11) and (62 x 12)
= 682 and 744
Answer: Option B
Question: A can finish a work in 18 days B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
A.5
B.5 1/2
C.6
D.8
Answer: C.6
Explanation: Explanation:
B's 10 day's work = 1/15 * 10 = 2/3
Remaining work = (1 - 2/3) = 1/3
Now, 1/18 work is done by A in 1 day.
1/3 work is done by A in (18 * 1/3) = 6 days.
ANSWER IS C
Question: A speaks truth in 75% case and B in 80% of the cases. In what percentage of cases are they likely to contradict each other, narrating the same incident?
A.40
B.23
C.35
D.60
Answer: C.35
Explanation: P( A)=75/100, P(B)=80/100
P( A’)=1/4
P(B’)=1/5
P( A and B contradict each other)=P(A).P(B’)+P(A’).P(B)
=35%
ANSWER C
Question: Arun went for a movie nine days ago. He goes to watch movies only on Thursdays. What day of the
week is today?
A.Wednesday
B.Saturday
C.Friday
D.Sunday
Answer: B.Saturday
Explanation: Explanation :
Clearly it can be understood from the question that 9 days ago was a Thursday
Number of odd days in 9 days = 2 (As 9-7 = 2, reduced perfect multiple of 7 from total days)
Hence today = (Thursday + 2 odd days) = Saturday
Answer : Option B
Question: A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:
A.Rs. 2000
B.Rs. 10,000
C.Rs. 15,000
D.Rs. 20,000
Answer: C.Rs. 15,000
Explanation: Principal = Rs. 100 x 5400
--------------- = Rs. 15000.
12 x 3
Answer: Option C
Question: There are 11 teams in a soccer league and each team plays each of the other teams once. How many games will be played in total?
A.40
B.45
C.50
D.55
Answer: D.55
Explanation: 11C2=55
The answer is D.
Question: 200 is increased by 25%. Find the final number.
A.200
B.210
C.250
D.190
Answer: C.250
Explanation: ExplanationFinal number = Initial number + 25%(original number) = 200 + 25%(200) = 200 + 50 = 250.Answer C
Question: In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number T and the smallest possible number of students that could have taken both geometry and biology?
A.144
B.119
C.113
D.88
Answer: D.88
Explanation: OFFICIAL SOLUTION:
First of all, notice that since 144 took geometry and 119 took biology, then the number of students who took both geometry and biology cannot be greater than 119.
{Total} = {geometry} + {biology} - {both} + {neither};
232 = 144 + 119 - {both} + {neither};
{both} = 31 + {neither}.
{both} is minimized when {neither} is 0. In this case {both} = 31.
The greatest possible number T of students that could have taken both geometry and biology, is 119.
Thus, the answer is 119 - 31 = 88.
Answer: D.
Question: Consider a quarter of a circle of radius 81. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.
A.86*(sqr2 -1)
B.88*(sqr3 -1)
C.4*(sqr7 - 1)
D.81* (sqr2 -1)
Answer: D.81* (sqr2 -1)
Explanation: I got 81/(sqr2 +1) and just forgot to multiply by (sqr2 -1).
Answer is D
Question: Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 6 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 6 minute mark.)
A.24
B.25
C.26
D.27
Answer: D.27
Explanation: 6 minutes is 360 seconds.
Lamp A and Lamp B will flash together every 24 seconds.
360/24=15.
In the time period, Lamp A and Lamp B will flash together 15 times.
Lamp A and Lamp C will flash together every 30 seconds.
360/30=12.
In the time period, Lamp A and Lamp C will flash together 12 times.
Lamp B and Lamp C will flash together every 40 seconds.
360/40=9.
In the time period, Lamp B and Lamp C will flash together 9 times.
All three lights will flash together every 2*2*2*3*5=120 seconds.
360/120=3.
We have counted these triple flashes three times, so we need to subtract three times the number of times that all three lights flash together.
The number of times that exactly two lights flash together is 15+12+9-9=27 times.
The answer is D.
Question: If Rs.3250 be divided among Ram, Shyam and Mohan in the ratio of 1/2:1/3:1/4 then the share of each are?
A.Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.750
B.Ram = Rs.7500, Shyam = Rs.1000, Mohan = Rs.750
C.Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.250
D.Ram = Rs.1500, Shyam = Rs.1080, Mohan = Rs.750
Answer: A.Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.750
Explanation: 1/2:1/3:1/4 = 6:4:3
Ram = 6/13 * 3250 = 1500
Shyam = 4/13 * 3250 = 1000
Mohan = 3/13 * 3250 = 750
Answer:A
Question: If S = {50, 72, 108, 120, 205}, how much less is the mean of the numbers in S than the median of the numbers in S?
A.2
B.3
C.5
D.8
Answer: B.3
Explanation: Mean = (50 + 72 + 108 + 120 + 205)/5 = 111
Median = 108
Difference = 111-108 = 3
Option B
Question: A man can row 8 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. What is the total distance traveled by the man?
A.7.82 km
B.6 km
C.5.76 km
D.5.66 km
Answer: A.7.82 km
Explanation: M = 8
S = 1.2
DS = 9.2
US = 6.8
x/9.2 + x/6.8 = 1
x = 3.91
D = 3.91 * 2 = 7.82
ANSWER:A
Question: If X and Y are sets of integers, X # Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 16 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X # Y consists of how many integers?
A.6
B.16
C.22
D.30
Answer: C.22
Explanation: The number of integers that belong to set X ONLY is 16-6=10;
The number of integers that belong to set Y ONLY is 18-6=12;
The number of integers that belong to set X or set Y, but not both is 10+12=22.
Answer: C
Question: The area of a rectangle is x2 + 4x -12. What are the dimensions of the rectangle (length and width)?
A.x + 6 , x + -2
B.x + 7 , x + -2
C.x + 8 , x + -2
D.x + 9 , x + -2
Answer: A.x + 6 , x + -2
Explanation: Solution
The main idea is to factor x2 + 4x -12
Since -12 = -2 × 6 and -2 + 6 = 4
x2 + 4x -12 = ( x + -2) × ( x + 6)
Since the length is usually longer, lenth = x + 6 and width = x + -2
Answer A
Question: Pipes A and B can fill a tank in 8 and 24 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
A.12 hr
B.28 hr
C.23 hr
D.24 hr
Answer: A.12 hr
Explanation: Explanation :
Part filled by pipe A in 1 minute = 1/8
Part filled by pipe B in 1 minute = 1/24
Part emptied by pipe C in 1 minute = 1/12
Net part filled by pipe A, pipe B and pipe C in 1 minute = 1/8+1/24−1/12=2/24=1/12
i.e, the tank will be filled in 12 minutes
Answer is A
Question: A straight pipe 3 yard in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard?
A. 1/6 and 1/4 only
B. 1/4 and 1/3 only
C. 1/6, 1/4, and 1/3
D. 1/12, 1/6 and 1/4
Answer: C. 1/6, 1/4, and 1/3
Explanation: Since we want to find the fractions, we can assume some other length of the pipe which will make calculation easier. Take the length of the pipe to be 12-meter long (the least common multiple of 3 and 4.
In this case the branch would be cut at3,4, 6,8, and 9meters (in black are given fourths of the length and in red thirds of the length).
Distinct lengths would be: 3=3/12=1/4, 4-3=1=1/3and 6-4=2=2/12=1/6meters long pieces.
Answer: C.
Question: 4211.01 + 22.261 - ? = 2645.759
A.1587.512
B.1586.532
C.1588.021
D.1586.422
Answer: A.1587.512
Explanation: Explanation :
Required Value = 4211.01 + 22.261 - 2645.759 = 1587.512. Answer : Option A
Question: What percent of a day is 4 hours?
A.12%
B.12.5%
C.13%
D.11.3%
Answer: B.12.5%
Explanation: Explanation :
Solution: required percentage = (4/100 * 24) = 12.5%
Answer : B
Question: A can do a piece of work n 7 days of 9 hours each and B alone can do it in 6 days of 7 hours each. How long will they take to do it working together 8 2/5 hours a day?
A.3
B.4
C.5
D.6
Answer: A.3
Explanation: A can complete the work in (7*9) = 63 days
B can complete the work in (6*7) = 42 days
--> A’s one hour’s work = 1/63 and B’s one hour work = 1/42.
(A+B)’s one hour work = 1/63+1/42 = 5/126
Therefore, Both can finish the work in 126/5 hours.
Number of days of 8 2/5 hours each = (126*5/(5*42)) = 3 day
Answer : A.
Question: A no.when divided by 221 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?
A.3
B.6
C.9
D.10
Answer: C.9
Explanation: 221 + 43 = 264/17 = 9 (Remainder)
C
Question: A and B started a business. A invests rs.6000 and b invests rs.8000 after 6 months c joined them with rs.6000 but b left with the capital.after one year they get a profit of rs.2600.the share of A is?
A.900
B.1100
C.1200
D.1000
Answer: C.1200
Explanation: 6000x12 : 8000x:6 : 6000x6 = 6:4:3
so A work 2600x6/13 =1200
so ans is 1200
ANSWER:C
Question: In a covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay double his speed, then he would take 1 hour less than Sammer. Abhay's speed is?
A.8
B.5
C.4
D.3
Answer: A.8
Explanation: Let Abhay's speed be x km//hr.
Then, 30/x - 30/2x = 3
x = 5 km/hr.
Answer: A
Question: In Country Q, the unemployment rate among construction workers dropped from 16 percent on September 1, 1992, to 9 percent on September 1, 1996. If the number of construction workers was 20 percent greater on September 1, 1996, than on September 1, 1992, what was the approximate percent change in the number of unemployed construction workers over this period?
A. 50% decrease
B. 30% decrease
C. 15% decrease
D. 30% increase
Answer: B. 30% decrease
Explanation: Country Q 1992 1996
No of construction workers 100 120
Unemployment Rate 16% 9%
Unemployed workers 16 11
% change in unemployed workers=(16-11)=5/16=~33% decrease
Closest ans=30% decrease
Ans=B
Question: A certain college's enrollment at the beginning of 1992 was 30 percent greater than it was at the beginning of 1991, and its enrollment at the beginning of 1993 was 10 percent greater than it was at the beginning of 1992. The college's enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?
A.43%
B.45%
C.50%
D.35%
Answer: A.43%
Explanation: Suppose enrollment in 1991 was 100
Then enrollment in 1992 will be 130
And enrollment in 1993 will be 130*1.1=143
Increase in 1993 from 1991 = 143-100= 43
Answer : A
Question: Ice-ColdIce-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors yellow, purple, orange, silver, blue and red. How many different ice-cream products have at least one stripe out of the following colors: yellow, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?
A.12
B.14
C.18
D.19
Answer: D.19
Explanation: IMO: D - 19
There are 6C3 = 20 ways to create different colored ice cream products. Out of these 20, only 1 (Silver, Blue, Red) will not contain at least one of the colors yellow, purple, or orange. 20 - 1 = 19.
The other way would be to calculate the number of ice cream products that contain at least one of the colors yellow, purple, or orange (YPO).
#1: Pick one out of YPO and two out of SBP: 3C1 * 3C2 = 3 * 3 = 9
#2: Pick two out of YPO and one out of SBP: 3C2 * 3C1 = 3 * 3 = 9
#3: Pick three out of YPO: 3C3 = 1
9 + 9 + 1 = 19
answer is D
Question: Four years ago, the ratio of ages of P and Q was 5:3. Ten years from now, the ratio of their ages will be 6:5. What is P's age at present?
A.11
B.12
C.13
D.14
Answer: D.14
Explanation: 3(P-4)/5 = (Q-4). Then Q = 3(P-4)/5 + 4
5(P+10)/6 = Q+10
5(P+10)/6 = 3(P-4)/5 + 14
25P+250 = 18P + 348
7P = 98
P = 14
The answer is D.
Question: Complete the sequence:
C E I O ?
A.M
B.W
C.S
D.D
Answer: B.W
Explanation: C+2=E
E+4=I
I+6=O
O+8=W
B
Question: Rose's grade was 70th percentile of the 60 grades for her class. Of the 40 grades from another class, 16 were higher than Rose's, and the rest were lower. If no other grade was the same as Rose's grade, then Rose's grade was what percentile of the grades of the two classes of two classes combined?
A.66th
B.70th
C.74th
D.82nd
Answer: A.66th
Explanation: 66th/70th/74th/82nd/85th
Correct option: A