RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A man rows his boat 120 km downstream and 60 km upstream, taking 2 hours each time. Find the speed of the stream?
A.6
B.15
C.17
D.18
Answer: B.15
Explanation: Speed downstream = d/t = 120/(2 ) = 60 kmph
Speed upstream = d/t = 60/(2) = 30 kmph
The speed of the stream = (60 - 30)/2 = 15 kmph
Answer:B
Question: What is the sum of all possible solutions to the equation √2x^2−x−9 = x+1 ?
A.-2
B.2
C.3
D.5
Answer: D.5
Explanation: First of all notice that since LHS is the square root of a number, it must be non-negative (the square root function cannot give negative result), then the RHS must also be non-negative: x+1≥0 --> x≥−1
Square the equation: 2x^2−x−9=x^2+2x+1 --> x^2−3x−10=0 --> x=-2 or x=5. Discard x=-2 because it's not >=-1. We are left with only one root: 5.
Answer: D
Question: Jayes can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows?
A.40 minutes.
B.1 hour and 30 minutes.
C.1 hour.
D.1 hour and 40 minutes.
Answer: C.1 hour.
Explanation: Rate =Output/Time
Jayes Rate=25/20=5/4
Dylan Rate=25/60=5/12
Combined rate = 5/4+5/12= 20/12
CombinedRate*CombinedTime= CombinedOutput
20/12*t=150
t=90 mins => 1 hr 30 min
Question: What positive number, when squared, is equal to the cube of the positive square root of 14?
A.64
B.32
C.8
D.4
Answer: D.4
Explanation: Let the positive number be x
x^2 = ((16)^(1/2))^3
=>x^2 = 4^3 = 4
=> x =4
Answer D
Question: A money lender lends Rs.1500 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit?
A.2205
B.1978
C.1653.75
D.2827
Answer: C.1653.75
Explanation: A = 1500(21/20)2
= 1653.75
Answer: C
Question: A welder received an order to make a 1 million liter cube-shaped tank. If he has only 2x5 meter sheets of metal that can be cut, how many metal sheets will be required for this order? (1 cubic meter = 1,000 liters)
A.92
B.90
C.60
D.78
Answer: C.60
Explanation: The question say:A welder received an order to make a 1 million liter cube-shaped tank. (1 cubic meter = 1,000 liters)
In other words, the tank is going to have a volume of 1000 cubic meters. That would equal 1 million liters.
A cube with a volume of 1000 cubic meters must be (10 meters) x (10 meters) x (10 meters).
The question doesn't specify whether this tank should have a closed top or an open top. (The real GMAT is good about specifying things like that.) Here, we are going to assume a closed top, only because if the top is open, we don't use enough metal --- we get an answer smaller than any of the answer choices. A closed-top cube, a full cube, has 6 sides, each of which is (10 meters) x (10 meters). That's a total surface area of 600 sq m.
The question tells us:he has only 2x5 meter sheets of metal that can be cut.
Each sheet has an area of 10 sq m. How many of these need to fill up 600 sq m? 600/10 = 60. He needs 60 sheets.
Answer =C
Question: If a man crosses a 600 m long street in 5 minutes. What is his speed?
A.6.9 km/hr
B.7 km/hr
C.7.2 km/hr
D.8.9 km/hr
Answer: C.7.2 km/hr
Explanation: distance = 600 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distancetime=600300=2m/s=2×185 km/hr=365 km/hr=7.2 km/hr
C
Question: Find the area of trapezium whose parallel sides are 12 cm and 16 cm long, and the distance between them is 14 cm?
A.288 cm2
B.277 cm2
C.285 cm2
D.196 cm2
Answer: D.196 cm2
Explanation: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (12 + 16) * (14)
= 196 cm2
Answer: D
Question: 10, 15, 22.5, 33.75, 50.62, (...)
A.60
B.60.75
C.75.93
D.76.33
Answer: C.75.93
Explanation: 10
(10Ã—3)Ã· 2 = 15
(15Ã—3)Ã· 2 = 22.5
(22.5Ã—3)Ã· 2 = 33.75
(33.75Ã—3)Ã· 2 = 50.62
(50.62Ã—3)Ã· 2 = 75.93
Answer is C
Question: A can complete a project in 20 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 15 days before completion of project, then in how many days the project will be completed?
A.18
B.19
C.20
D.21
Answer: D.21
Explanation: A's 1day work=1/20;
B's 1day work=1/30;
(A+B) 1day work=(1/20+1/30)=1/12;
It is given that A leaves the work 15 days before completion of the project..
Thus,B alone does the remaining job in 15 days.
So,In 15 days ,B can do 1/2 w ..
Thus,(A+B) have worked (1-1/2)=1/2 w..
(A+B)can do 1/12 work in 1 day...
They did 1/2 w in 6 days.
Total days=(6+15) = 21
ANSWER:D
Question: Find the next number in the series
3,3,5,4,4,3,5,5,4,3,...
A.3
B.4
C.5
D.6
Answer: D.6
Explanation: (3, 3, 5), (4 ,4 ,3), (5, 5, 4), (3, x, y)
In first group , middle digit = 3
In 2nd group , middle digit = 4
In 3rd group , middle digit = 5
In 4th group , middle digit should be 6
ANSWER:D
Question: On a certain farm the ratio of horses to cows is 4:1. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 7:3. After the transaction, how many more horses than cows would the farm own?
A.20
B.40
C.50
D.60
Answer: D.60
Explanation: Originally, there were 4k horses and k cows.
3(4k-15) = 7(k+15)
12k-7k = 105+45
5k = 150
k = 30
The difference between horses and cows is (4k-15)-(k+15) = 3k-30 = 60
The answer is D.
Question: Two people stand back to back next to the rails in a small railway station. As the head of the express train that passes the station reaches them, they start to walk parallel to the rails. As the tail of the train reaches each of them, they stop, having walked 30m and 40m respectively.
If they both walked with identical, constant speed and the train kept its speed as well, can you tell how long the train was?
A.140m
B.240m
C.340m
D.440m
Answer: B.240m
Explanation: Let d be the length of the train, and
let t1 be the time it took for the tail of the train to reach
the first person, and
let t2 be the time it took for the tail of the train to reach
the second person.
By time t1, the head of the train is d-30 meters beyond the point where it passed the two people.
By time t2, the head was d+40 meters beyond where it passed the two people. The ratio of these distances,
d-30 : d+40
is equal to the ratio of t1:t2, because the train is moving at a constant speed.
Since both people walk at the same constant rate, this ratio is 3:4.
d-30 : d+40 = 3:4
The product of the means equals the product of the extremes, so
3(d+40) = 4(d-30)
3d + 120 = 4d - 120
240 = d
Answer B
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 3 : 3?
A.16
B.48
C.277
D.92
Answer: B.48
Explanation: Let the distances between city A to B and B to C be 3x km and 3x km respectively.
Total time taken to cover from A to C
= (3x)/40 + (3x)/60 = (9x + 6x)/120 = 15x/120 = x/8 Average speed = (3x + 3x)/(x/8) = 48 kmph.
Answer:B
Question: What will be the difference between simple and compound interest at 12% per annum on a sum of Rs. 1000 after 4 years?
A.94.19
B.94.12
C.93.5
D.64.1
Answer: C.93.5
Explanation: S.I. = (1000 * 12 * 4)/100 = Rs. 480
C.I. = [1000 * (1 + 12/100)4 - 1000] = Rs. 573.5 Difference = (573.5 - 480) = Rs. 93.5
Answer: C
Question: There are three departments having students 66,58,24 .In an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only (No mixing of departments). Find the minimum number of rooms required?
A.73
B.74
C.75
D.76
Answer: B.74
Explanation: WE NEED TO TAKE GCD WHICH IS 2
THUS ALL THE ROOMS WILL HAVE 2 STUDENTS OF THE SAME DEPT
1) 66/2 = 33
2) 58/2 = 29
3) 24/2 = 12
TOTAL NO. OF MIN ROOMS REQD = 33+12+29 = 74
ANSWER:B
Question: Every student in a certain classroom was given a lollypop. 1/3 of the students were given a green lollypop, 1/4 of the students were given a yellow lollypop, and all of the other students were given a red lollypop. After lunch, 1/4 of the students who had green lollypops and 2/3 of the students who had yellow lollypops left the classroom; the other students did not leave. What fraction of all students have either a green or yellow lollypop?
A.5/9
B.4/9
C.2/3
D.4/7
Answer: B.4/9
Explanation: Lets pick smart numbers. Total number of students in the classroom: 12
Green lollypop (1/3): 4
Yellow lollypop (1/4): 3
Red lollypop (5/12): 5
After lunch
Green lollypop: 3
Yellow lollypop: 1
Red lollypop: 5
New Total number of students in the classroom: 9
Green and yellow lollypops: 4
Answer 4/9 or B
Question: What is the sum of all the composite numbers up to 12?
A.228
B.28
C.60
D.49
Answer: D.49
Explanation: Explanation:
4 + 6 + 8 + 9 + 10 + 12 = 49
Answer: D
Question: If 10^(v-1)< 0.000125 <10^v, what is the value of an integer v?
A.-4
B.-3
C.-2
D.3
Answer: B.-3
Explanation: -> Multiply 10^6- > (10^6){10^(v-1)}<125<(10^6)(10^v) -> 125 is bigger than 100
-> (10^6)(10^(v-1))=100 -> 10^(6+v-1)=10^2, v+5=2 -> v=-3
Thus, the answer is B
Question: Total ages of p,q,r be 27.P is two years elder than Q. Who is twice as old as R. Then how old is Q?
A.10
B.12
C.14
D.16
Answer: A.10
Explanation: p+q+r=27.........(1)
p= q+2
q= 2r
so,r=q/2
(1)........ is
q+2+q+q/2= 27
or,2q+q/2=25
5q=50
so,q =10
ANSWER:A
Question: A person crosses a 1080 m long street in 14 minutes. What is his speed in km per hour?
A.4.1
B.4.5
C.4.6
D.5.4
Answer: C.4.6
Explanation: Speed = 1080/(12x60) m/sec
= 1.3 m/sec.
Converting m/sec to km/hr =1.3 x(18/5) km/hr
= 4.6 km/hr.
ANSWER :C
Question: A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
A.4/7
B.3/7
C.2/7
D.11/7
Answer: A.4/7
Explanation: Let number of balls = (6 + 8) = 14.
Number of white balls = 8.
P (drawing a white ball) = 8/14
= 4/7
Answer should be A
Question: The music class consists of 4 girls and 7 boys. How many ways can a group of 3 be formed if it has to include at least one boy?
A.155
B.158
C.161
D.165
Answer: C.161
Explanation: Classic combination problem
At least 1 boy = Total - all girls
All girls = C(4,3) = 4
Total combination = C(11,3) = 165
Ans = 165-4 = 161
ANS:C
Question: If Rs. 782 be divided into three parts, proportional to 1/2:1/3:3/4, then the first part is?
A.A)426
B.B)526
C.C)247
D.D)204
Answer: C.C)247
Explanation: Given ratio
= 1/2:2/3:3/4 = 6:4:9
1st part = 782 * 6/19
= Rs. 247
Answer:C
Question: In a sequence of 12 numbers, each term, except for the first one, is 12^14 less than the previous term. If the greatest term in the sequence is 12^15, what is the smallest term in the sequence?
Thus, A12 = A1+12-1d
Where d is the difference between each pairs of consecutive terms. Since each term is 1211 less than the previous term, d=-1211Click individual answer choices for specific explanations.
From what I undersltand the formula for an arithmetic sequence represents
some-number-in-the-sequence= first-number-in-sequence +the-place-of-that-number - 1x the-difference-of-each-#-in-the-sequence
A.12^14
B.0
C.12^11
D.11·12^11
Answer: A.12^14
Explanation: there are total 12 terms. andgreatestterm is 12^15. Each term is 12^14 less than previous one. What does this signify? This shows it is an AP - a decreasing one. (NoticeEach term is 12^14 less than previous one')
Therefore, 12^15 is the first term of the AP and -12^14 is the difference between successive terms, the smallest term should be the last one.
Last term = First term + (n-1)*d
therefore, Last term = 12^15 + 11*(-12^14)
=> Last term = 12^15 - 11*12^14
=> Last term = 12^14 (12-11) = 12^14
Which is the smallest term.
Hence Ans A it is.
Question: The sequence a1, a2, a3, a4. a5 is such that an = a n-1 +5 for 2≤ n ≤ 5. If a5 = 35 what is the value of a1 ?
A.1
B.6
C.15
D.16
Answer: C.15
Explanation: Here, each value of an is the previous value plus 5
Since the numbers are less, the fastest way to solve this problem is to successively subtract 5 from a5 till you reach a1
a5 = 35
a4 = 30
a3 = 25
a2 = 20
a1 = 15 <<<< Ans C
Question: A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
A.6 litres, 6 litres
B.6 litres, 7 litres
C.7 litres, 5 litres
D.5 litres, 5 litres
Answer: A.6 litres, 6 litres
Explanation: Let the cost of 1 litre milk be Re. 1
Milk in 1 litre mix. in 1st can =	3	litre, C.P. of 1 litre mix. in 1st can Re.	3
4	4
Milk in 1 litre mix. in 2nd can =	1	litre, C.P. of 1 litre mix. in 2nd can Re.	1
2	2
Milk in 1 litre of final mix. =	5	litre, Mean price = Re.	5
8	8
By the rule of alligation, we have:
C.P. of 1 litre mixture in 1st can C.P. of 1 litre mixture in 2nd can
3
4
Mean Price
5
8
1
2
1
8
1
8
Ratio of two mixtures =	1	:	1	= 1 : 1.
8	8
So, quantity of mixture taken from each can = 1/2	x 12 = 6 litres
Option A
Question: Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?
A. 11%
A.11 1/9%
B.11 1/8%
C.11 9/9%
D.11 5/9%
Answer: A.11 1/9%
Explanation: 900 --- 100
100 --- ? => 11 1/9%
Answer:A
Question: Three pipes of same capacity A,B,C can fill a tank in 24 hours. If there are only two pipes A and B of same capacity, the tank can be filled in?
A.12
B.24
C.6
D.36
Answer: D.36
Explanation: The part of the tank filled by three pipes in one hour
= 1/24
=> The part of the tank filled by two pipes in 1 hour
= 2/3 * 1/24 = 1/36.
The tank can be filled in 36 hours.
Answer:D
Question: Twenty percent of Country Y's yearly exports come from fruit exports. One-sixth of all fruit exports from Country Y are orange exports. If country Y generates $3 million from its orange exports, how much money does it generate from its yearly total of exports?
A.$21.25m
B.$25.5m
C.$90m
D.$127.5m
Answer: C.$90m
Explanation: 2/10*1/6*(total) = 3
1/30*(total) = 3
(total) = 3*30 = 90
Answer: C.
Question: Becky, Merry and John want to share a chocolate bar evenly.
What part of the bar will each of them take?
What part of the bar will Becky and Merry have together?
A.1/3
B.2/3
C.2/4
D.None of these
Answer: B.2/3
Explanation: Solution
The children need to divide the bar into three pieces. So everyone will take 1/3 of the chocolate bar.
Two girls together will have two pieces, hence, mathematically speaking, they will have 2/3 of the bar
Answer B
Question: A man jogging inside a railway tunnel at a constant speed hears a train approaching the tunnel from behind at a speed of 30 km/h, when he is one third of the way inside the tunnel. Whether he keeps running forward or turns back, he will reach the end of the tunnel at the same time the train reaches that end. The speed at which the man is running is:
A.6 km/hr
B.8 km/hr
C.10 km/hr
D.12 km/hr
Answer: C.10 km/hr
Explanation: Explanation :
Let the train is at distance y km from the tunnel and the length of the tunnel is x km. Man is at point C which is x/3 km away from B.
A ----------- B -------------- C ----------------D
<---- y------><------x/3-------><------2x/3------->
AB=y, BC =x/3 and CD =2x/3.
Let, M km/h be the speed of man.
Now, train is at A and man is at C and both will take same time for reaching from B.
=>y/30=x/3M.
=>M=10x/y . ----------------------(i)
Also, train and man will take some time for reaching at D.
=>(x+y)/30=2x/M.
=>M=20x/(x+y). ---------------------(ii)
From both the equations we get: x=y
And on putting value in any equation we get: M = 10 km/hr.
Answer : C
Question: If 45-[28-{37-(15-*)}]= 58, then * is equal to:
A.-29
B.-19
C.19
D.29
Answer: C.19
Explanation: 45-[28-{37-(15-*)}]= 58 => 45-[28-{37-15+*}]=58
45-[28-37+15-*]=58 => 45[43-37-*]=58
45-[6-*]=58 => 45-6+*=58
39+*=58 => *=58-39
= 19
ANSWER:C
Question: X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?
A.Rs.14400
B.Rs.26400
C.Rs.12000
D.Rs.12500
Answer: A.Rs.14400
Explanation: Explanation :
Ratio of the investment = 21000 : 17500 = 210 : 175 = 42 : 35 = 6 : 5
Share of X in the profit = 26400 * (6/11) = 2400 * 6 = 14400 .. Answer : Option A
Question: If 0.75: x :: 5:8, then x is equal to:
A.1.29
B.1.28
C.1.20
D.1.21
Answer: C.1.20
Explanation: Explanation:
(x * 5) = (0.75 *8)
X=6/5 = 1.20
Answer: C) 1.20
Question: A train running at the speed of 60 km/hr crosses a pole in 5 seconds. Find the length of the train.
A.83.33
B.882
C.772
D.252
Answer: A.83.33
Explanation: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 5 = 83.33 meter.Answer: A
Question: Difference of two numbers is 1660. If 7.5% of the number is 12.5% of the other number , find the number ?
A.2490 and 4150
B.249 and 415
C.2400 and 4100
D.2290 and 4350
Answer: A.2490 and 4150
Explanation: Let the numbers be x and y. Then , 7.5 % of x =12.5% of y
X = 125*y/75 = 5*y/3.
Now, x-y =1660
5*y/3 –y =1660
2*y/3= 1660
y =[ (1660*3)/2] =2490.
One number = 2490, Second number =5*y/3 =4150
Answer is A.
Question: A set of numbers has an average of 40. If the largest element is 4 greater than 3 times the smallest element, which of the following values cannot be in the set?
A. 85
B. 90
C. 125
D. 50
Answer: C. 125
Explanation: Ans: C
Solution: we are given the relation between smallest and the largest term. so let the smallest a and largest be 3a+4
so the avg = 50
which tells us that any value of a must be less than 40
so a<50 means, largest value 3a+4 <(3*40)+4
=largest value must be <124
so 125 can not be the value in the set.
Question: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition), when the digit at the unit’s place must be greater than that in the ten’s place?
A.54
B.60
C.50
D.2 x 4!
Answer: B.60
Explanation: The digit in the unit’s place should be greater than that in the ten’s place. Hence if digit 5 occupies the unit place then remaining four digits need not to follow any order. Hence the required numbers = 4!. However, if digit 4 occupies the unit place then 5 cannot occupy the ten’s position. Hence digit at the ten’s place will be one among 1, 2 or 3. This can happen in 3 ways. The remaining 3 digits can be filled in the remaining three places in 3! ways. Hence, in all we have (3 x 3!) numbers ending in 4. Similarly, if we have 3 in the unit’s place, the ten’s place can be either 1 or 2. This can happen in 2 ways. The remaining 3 digits can be arranged in the remaining 3 places in 3! ways. Hence, we will have (2 x 3!) numbers ending in 3. Similarly, we can see that there will be 3! numbers ending in 2 and no number ending with 1.
Hence, the total number of numbers = 4! + (3 x 3!) + (2 x 3!) + 3!
= 4! + 6 x 3! = 24 + (6 x 6) = 60
ANSWER:B
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
A.10 kmph
B.23 kmph
C.75 kmph
D.56 kmph
Answer: A.10 kmph
Explanation: Speed of the boat in still water
= (60+80)/2
= 70 kmph. Speed of the stream
= (80-60)/2
= 10 kmph.
Answer:A
Question: In how many ways can a group of 22 friends be seated round 2 tables if one of the tables can seat 12 and the other can seat 10 people?
A.15C5 * 9! *4!
B.15C3 * 8! *3!
C.15C4 * 9! *3!
D.22C2 * 11! *9!
Answer: D.22C2 * 11! *9!
Explanation: 12 people can be selected from 22 people in 22C12 ways.
Remaining 10 people can be selected from 10 people in 10C10 ways.
Now, arranging 12 people on a round table = (12-1) ! = 11!
Arranging 10 people on a round table = (10-1) ! = 9!
Hence, total number of ways = 22C12 * 11! * 10C10 * 9!
= 22C2 * 11! * 9!
D
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
A.31/32
B.31/38
C.31/30
D.31/37
Answer: A.31/32
Explanation: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
Answer:A
Question: Henry got a weekly raise of $963. If he gets paid every other week, write an integer describing how the raise will affect his paycheck.
A.693
B.396
C.963
D.691
Answer: C.963
Explanation: Let the 1st paycheck be x (integer).
Henry got a weekly raise of $ 963.
So after completing the 1st week she will get $ (x+963).
Similarly after completing the 2nd week she will get $ (x + 963) + $ 963.
= $ (x + 963 + 963)
= $ (x + 1926)
So in this way end of every week her salary will increase by (C)$ 963.
Question: Present ages of X and Y are in the ratio 2:3 respectively. Four years hence this ratio will become 3:4 respectively. What is X's present age in years?
A.8
B.36
C.37
D.39
Answer: A.8
Explanation: Let the present ages of X and Y be 2x and 3x years respectively.
Then, (2x + 4)/(3x + 4) = 3/4
4(2x + 4) = 3(3x + 4) =>8x+16=9x+12 => x=4
X's present age = 2x = 2*4 = 8
ANSWER:A
Question: A tree increases annually by 1/8th of its height. By how much will it increse after 2 years, if it stands today 64 cm high?
A.72 cm
B.74 cm
C.75 cm
D.81 cm
Answer: D.81 cm
Explanation: Increase % = (1/8 x 100)%
= 12 1/2 % = 25/2 %
height after 2 years =(64 x(1+(25/2x100)power of 2)) cm
= (64 x 9/8 x 9/8 ) cm= 81 cm
Answer is D
Question: If 32455 × 3145208 × m^100 is divisible by 5, which of the following could be the value of m?
A.6000209
B.5644564
C.2345678
D.1000000
Answer: D.1000000
Explanation: The first two terms are not divisible by 5, so we need the third term to be divisible by %. The only way that (m^10) is going to be a multiple of 5 is if m is a multiple of 5. Therefore, we need the single answer that is a multiple of 5.
Answer =(D)
Question: ABCD is a parallelogram on xy rectangular coordinate plane, three of the four vertices of parallelogram are (5,15) , (5,45) and (-5,15). Which can be the coordinate of fourth vertex?
A.(-5,-5)
B.(5,45)
C.(-5,-25)
D.(-5,10)
Answer: B.(5,45)
Explanation: A(-5, 15)
B(5, 15)
C(5, 45)
X(-5, 45): Parallelogram=Square=AXCB, where AX||CB, AX=CB, XC||AB, XC=AB
Y(-5, 5): Parallelogram=AYBC, where AY||BC, AY=BC, AC||YB, AC=YB
Z(15, 45): Parallelogram=ACZB, where AC||ZB, AC=ZB, CZ||AB, CZ=AB
Ans:B
Question: {3, 5, 8, y}
For the above mentioned Set, Mean of the set is equal to Range of the set then find out possible values of y
A.16/5, 28/3
B.4, 16/5
C.4, 16/5, 28/3
D.4, 28/3
Answer: D.4, 28/3
Explanation: The set can have the following forms:
1. {3,5,8,y} , range = y-3 and mean = 4+y/4, y= 28/3
2. {3,5,y,8} , range = 5 and mean = 4+y/4, y=4
3. {3,y,5,8} , range = 5 and mean = 4+y/4, y=4
4. {y,3,5,8} , range = 8-yand mean = 4+y/4, y=16/5. But as y<3 (assumed here), y=3.2 can not be true. Hence reject this case.
Thus the possible values are 4 and 28/3.
D is the correct answer.
Question: A small college reduced its faculty by approximately 23 percent to 195 professors. What was the original number of faculty members?
A.253
B.208
C.224
D.254
Answer: A.253
Explanation: If x is the original number of faculty members, then after 23% reduction in faculty members number is .77x
but we are given .77x = 195
x = 253
So the original number of faculty members is 253
Correct Answer - A
Question: A book is bought for $32 and sold for $56. What is the profit in percentage?
A.15
B.35
C.75
D.25
Answer: C.75
Explanation: 56/32 = 1.75
The answer is C.
Question: When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?
A.Rs. 21,000
B.Rs. 22,500
C.Rs. 25,300
D.Rs. 25,800
Answer: C.Rs. 25,300
Explanation: 85 : 18700 = 115 : x
x = (18700 x 115)/85 = 25300.
Hence, S.P. = Rs. 25,300.
Answer: Option C
Question: There are many numbers that can be expressed as the sum of three squares in three different ways.
Can you find out the smallest of such number?
A.87
B.54
C.29
D.30
Answer: B.54
Explanation: B
54
7^2 + 2^2 + 1^1
6^2 + 3^2 + 3^2
2^2 + 5^2 + 5^2
Question: In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 3/4 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 30 shiny igneous rocks, how many total rocks does Cliff have?
A.30
B.45
C.60
D.120
Answer: D.120
Explanation: We can start with the known quantity and then go on to find the others.
Shiny igneous ricks are 30. These are (3/4) of total igneous rocks.
(2/3)*Total igneous rocks = 30
Total igneous rocks = 30 * (4/3) = 40
Total sedimentary rocks = 2*Total igneous rocks = 2*40 = 80
Total number of rocks = 40 + 80 = 120
Answer (D)