RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Can you deduce the pattern and find the next number in the series?
6, 14, 26, 98, __?
A.276
B.277
C.278
D.279
Answer: A.276
Explanation: Solution:
276
Explanation:
6 = 1^1 + 2^1 + 3^1
14 = 1^2 + 2^2 + 3^2
36 = 1^3 + 2^3 + 3^3
98 = 1^4 + 2^4 + 3^4
Thus the next number will be
1^5 + 2^5 + 3^5 = 276
Answer A
Question: In an examination, 40% candidates failed in one subject and 30% failed in another subject while 10% failed in both the subjects. If 100 candidates appeared at the end of the examination how many passed in either subject but not in both?
A.50
B.75
C.60
D.100
Answer: A.50
Explanation: Failed in 1st subject = 40*100/100 = 40
Failed in 2nd subject = 30*100/100 = 30
Failed in both = 10*100/100 = 10
Failed in 1st subject only = 40-10 = 30
Failed in 2nd subject only = 30-10 = 20
Passed in either subject but not in both = 30+20 = 50
Answer is A
Question: At what price must Kantilal sell a mixture of 80kg. Sugar at Rs.6.75 per kg. with 120 kg. at Rs.8 per kg. to gain 20% ?
A.Rs.7.50 per kg
B.Rs.8.20 per kg
C.Rs.8.85 per kg
D.Rs.9 per kg.
Answer: D.Rs.9 per kg.
Explanation: Explanation:
Total C.P of 200 kg of sugar
= Rs.(80×6.75+120×8)=Rs.1500
C.P of 1 kg = Rs.[1500/200]=Rs.7.50
Gain required = 20%
S.P of 1 kg = (120% of Rs.7.50)
= Rs.[120/100×7.50]=Rs.9 per kg.
Correct Option : D
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/5 hours to fill the tank. The leak can drain all the water of the tank in?
A.17 hr
B.19 hr
C.22 hr
D.24 hr
Answer: C.22 hr
Explanation: Work done by the tank in 1 hour
= (1/2 - 2 1/5)
= 1/22 Leak will empty the tank in 22 hrs.
Answer:C
Question: If 4 people are selected from a group of 9 married couples, what is the probability that none of them would be married to each other?
A.1/33
B.2/85
C.1/3
D.56/85
Answer: D.56/85
Explanation: If we are to select 4 people from 9 couples WITHOUT any restriction, how many ways can we make the selection? 18!/4!14! = 3060
If we are to select 4 people from 9 couples WITH restriction that no married couple can both make it to the group, only a representative?
9!/4!5! = 126
But we know that to select a person from each couple, take 2 possibilities
126*2*2*2*2 = 2016
Probability = Desired/All Possibilities = 2016/3060 = 56/85
Answer: D
Question: 65 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?
A.64
B.128
C.151
D.216
Answer: C.151
Explanation: 65 small cube will make a large cube with 4 cubes in each line i.e.
Adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line.
Total number of small cubes in new cube = 6^3 = 216
Extra cube required = 216 - 65 = 151
Hence, C is the answer.
Question: What is the smallest five digit number that is divisible by 15, 24, 36, and 54?
A.10320
B.10800
C.10030
D.10380
Answer: B.10800
Explanation: 15 = 3 * 5
24 = 2^3 * 3
36 = 2^2 * 3^2
54 = 2 * 3^3
LCM = 2^3 * 3^3 * 5 = 1080
The smallest five-digit number that is a multiple of 1080 is 10*1080 = 10,800
The answer is B.
Question: Find the sum of all 3-digit nos that can be formed by 1, 2 and 3
A.5994
B.5042
C.6900
D.7002
Answer: A.5994
Explanation: No of such 3-digit nos = 27 (which is Ok)
1st no = 111, Last no = 333 (these r also Ok)
Hence their average = (111 + 333)/2 = 222
(couldn't understand how this formula is applied. I thought this holds true for an AP series only)
So, Sum = Number of nos X Average of the nos
= 27 X 222 = 5994 ANS:A
Question: How many ways are there to select a subcommittee of 9 members from among a committee of 17?
A.22888
B.24310
C.28791
D.27711
Answer: B.24310
Explanation: Explanation:
Since it does not matter what order the committee members are chosen in, the combination formula is used.
Committees are always a combination unless the problem states that someone like a president has higher hierarchy over another person. If the committee is ordered, then it is a permutation.
C(17,9)= 24,310
Answer: B)
Question: A river 4m deep and 65 m wide is flowing at the rate of 6 kmph the amount of water that runs into the sea per minute is?
A.25000
B.26000
C.27000
D.28000
Answer: B.26000
Explanation: Rate of water flow-6kmph--6000/60--100 m/min
depth of river--4m
width of river--65m
vol of water per min--100 *4*65---26000
Answer B
Question: A boy runs 200 metres in 24 seconds. What is his speed?
A.20 km/hr
B.24 km/hr
C.30 km/hr
D.32 km/hr
Answer: C.30 km/hr
Explanation: 200/24 * 18/5 = 30 km/hr
ANSWER:C
Question: If a person walks at 25 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is:
A.50 km
B.56 km
C.13.3 km
D.70 km
Answer: C.13.3 km
Explanation: Let the actual distance travelled be x km.
x/10 = (x+20)/25
25x = 10x + 200
15x = 200
x = 13.3 km.
answer :C
Question: If integers a and b are distinct factors of 30, which of the following CANNOT be a factor of 30?
I. a^b + b^2
II. (a + b)^2
III. a + b
A.. I only
B.II only
C.III only
D.I and II only
Answer: B.II only
Explanation: Factors of 30 are 1,2,3,6,5,10,15,30.
for options 1) & 3) consider a=2 and b=1 we find then 3 ,which is a factor
but for option 2) any values doesn't melts to any factor.
eg:-if we put a=3 and b=1 then (a+b)^2 =16 which is not a factor of 30
so Answer: B.
Question: If the sides of a triangle are 28 cm, 24 cm and 15 cm, what is its area?
A.180 cm2
B.112 cm2
C.776 cm2
D.666 cm2
Answer: A.180 cm2
Explanation: The triangle with sides 28 cm, 24 cm and 15 cm is right angled, where the hypotenuse is 28 cm.
Area of the triangle = 1/2 * 24 * 15 = 180 cm2
Answer: A
Question: 2 pipes A and B can separately fill a cistern in 10 and 15 mins respectively. A person opens both the pipes together when the cistern should have been was full he findsthe waste pipe open. He then closes the waste pipe and in another 4 mins the cistern was full. In what time can the waste pipe empty the cistern when fill?
A.6
B.8
C.10
D.12
Answer: B.8
Explanation: 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
B
Question: An error 8% in excess is made while measuring the side of a square. Now What is the percentage of error in the calculated area of the square?
A.6.64%
B.16.64%
C.15.64%
D.26.64%
Answer: B.16.64%
Explanation: Percentage error in calculated area
=(8+8+(8×8)/100)%=16.64%
ANSWER:B
Question: Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Six years ago Jim was 7 times as old as Sam. How old is Jim now?
A.8
B.12
C.16
D.20
Answer: D.20
Explanation: We're asked how old Jim is NOW. We're given three facts to work with:
1) Today, Jim is TWICE as old as Fred
2) Today, Sam is 2 years younger than Fred
3) Six years ago, Jim was 7 times as old as Sam.
let's TEST Answer D: 20
IF....Jim is currently 20 years old....
Fred is 10 years old
Sam is 8 years old
6 years ago, Jim was 14 and Sam was 2, so Jim WAS 7 times Sam's age. This is an exact MATCH for what we were told, so this MUST be the answer.
D
Question: One fast typist type some matter in 2hrs and another slow typist type the same matter in 3hrs. If both do combine in how much time they will take to finish.
A.10
B.11
C.12
D.13
Answer: C.12
Explanation: Fast's 1 hr work = 1/2
slow's 1 hr work = 1/3
1/2 + 1/3 = 5/6
they ll finish in 6/5hrs= 1 1/5 ==> 1 hr 12 mins
ANSWER:C
Question: The distance between two cities A and B is 330 Km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m and travels towards A at 75 Km/hr. At what time do they meet?
A.09
B.07
C.11
D.05
Answer: C.11
Explanation: Explanation:
Suppose they meet x hrs after 8 a.m
then,
[Distance moved by first in x hrs] + [Distance moved by second in (x-1) hrs] = 330.
Therefore, 60x + 75(x-1) = 330.
=> x=3.
So,they meet at (8+3) i.e, 11a.m.
Answer: C) 11 a.m
Question: In a school of 600 students, 45% wear blue shirts, 23% wear red shirts, 15% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)?
A.102
B.112
C.122
D.132
Answer: A.102
Explanation: 45 + 23 + 15 = 83%
100 – 83 = 17%
600 * 17/100 = 102
The answer is A.
Question: The probability of pulling a black ball out of a glass is 1/X. The probability of pulling a black ball out of a glass and breaking the glass is 1/Y. What is the probability of breaking the glass?
A.1/(XY).
B.Y/X
C.X by Y
D.1/(X+Y).
Answer: C.X by Y
Explanation: pulling a black ball out of a glass and breaking the jar both are independent events.
For 2 independent events, we know, P(a) * P(b) = P(a∩b)
If Prob of pulling a black ball out of a glass = P(a) and Prob of breaking the glass= P(b)
1/x * P(b) = 1/y ---> P(b) = x/y
Hence, answer should be C.
Question: Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of 2244 sq. metres.
A.A)25.4
B.B)26.7
C.C)24.3
D.D)22.5
Answer: B.B)26.7
Explanation: Explanation:
Clearly, the cow will graze a circular field of area 2244 sq. metres and radius
equal to the length of the rope.
Let the length of the rope be R metres.
Then, Π(R)2= 2244 => R2 = (2244 X (7/22)) = 714=> R = 26.72
Length of the rope = 26.72 m.
Answer: Option B
Question: The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is
A.1/2
B.3/4
C.3/5
D.3/7
Answer: A.1/2
Explanation: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2
Ans.(A)
Question: {9,4,3,5,7,12,10}
What value should be inserted into the above set of 7 values to get a median value of 6?
A.5
B.4
C.3
D.7
Answer: D.7
Explanation: Median is the middle number of a sorted distribution. In case of even number of items, Median will be the average of middle two values.
The question asks fora new number that will cause the median of new set at 12.
Mentionable that given set is already sorted and number of items of new set will be 7+1 = 8.
To get median 6,the sum of 4th5th Term should be 12 and luckilyit's exactly same in the existing series i.e. 5+7.
So to keep the median 6, the new item should be >=7
Answer is D
Question: One-fourth of the students at a nursery school are 4 years old or older. If 15 students have not yet reached their third birthday, and a total of 40 students are not between 3 years old and 4 years old, how many children are in the nursery school?
A.80
B.90
C.100
D.110
Answer: C.100
Explanation: x/4 students are > 4 yrs
15 students are < 3 yrs
x/4+ 15 = 40
x/4 = 25
x = 100
Answer: C
Question: A pharmaceutical company received $3 million in royalties on the first $20 million in sales of and then $9 million in royalties on the next $102 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $20 million in sales to the next $102 million in sales?
A.8%
B.15%
C.40%
D.52%
Answer: C.40%
Explanation: (9/102)/(3/20) = 30/54 = 58,5% it means that 9/108 represents only 58,5%. Therefore a decrease of 45%.
Answer C
Question: A miniature gumball machine contains 4 blue, 4 green, and 2 red gumballs, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color?
A.2/15
B.4/15
C.5/30
D.7/30
Answer: B.4/15
Explanation: The total number of ways to dispense 3 gumballs is 10C3=120.
The number of ways to choose one of each color is 4*4*2=32.
P(dispensing one of each color)=32/120=4/15.
The answer is B.
Question: Let f(x) = x^2 + bx + c. If f(5) = 0 and f(-3) = 0, then b + c =
A.18
B.-17
C.-15
D.-21
Answer: B.-17
Explanation: f(x) = x^2 + bx + c. If f(5) = 0 and f(-3) = 0, then b + c =
f(5) = 0= 25+5b+c--- Taking 25 to the other side
-> 5b+c= -25
f(-3) = 0= 9-3b+c --- taking -3b+c to the other side
-> 3b-c=9
When we add these 2 equations, we get 8b= -16---> b= -2
And while substituting b= -2 we get c= -15.
b+c= -17--- Answer B
Question: Three numbers are in the ratio 1:4:6 and their H.C.F is 7. The numbers are?
A.7, 28, 40
B.7, 28, 42
C.7, 28, 45
D.7, 21, 42
Answer: B.7, 28, 42
Explanation: Let the required numbers be x, 4x and 6x. Then, their H.C.F = x. So, x = 7.
The numbers are 7, 28, 42.
Answer: B
Question: A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 25 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
A.0.5024
B.2/5
C.1/2
D.3/4
Answer: A.0.5024
Explanation: It is a circle inscribed in a square.
Square side=25---> square(table) area=25^2
Circle diameter=20---> Circle area=PiR^2=100Pi (where Pi=~3.14)
covered fraction=100*3.14/25*25=~314/25*25=0.5024
A
Question: If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
A.30%
B.33%
C.33 1/3%
D.35%
Answer: C.33 1/3%
Explanation: 1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
ANSWER:C
Question: The sum of the first k positive integers is equal to k(k+1)/2. What is the sum of the integers from y to z, inclusive, where 0<y<z?
A.z(z+1)/2 - (y+1)(y+2)/2
B.z(z+1)/2 - y(y+1)/2
C.z(z+1)/2 - (y-1)y/2
D.(z-1)z/2 - (y+1)(y+2)/2
Answer: C.z(z+1)/2 - (y-1)y/2
Explanation: Or try plug-in method: let z=4 and y=3 --> then z+y=7. Let see which option yields 7.
A. z(z+1)/2 - (y+1)(y+2)/2 = 10-10=0;
B. z(z+1)/2 - y(n+1)/2 = 10-6=4;
C. z(z+1)/2 - (y-1)y/2 = 10-3=7 --> OK;
D. (z-1)z/2 - (y+1)(y+2)/2 = 6-10=-4;
E. (z-1)z/2 - y(y+1)/2 = 6-6=0.
Answer: C.
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
A.31/32
B.31/89
C.31/97
D.31/90
Answer: A.31/32
Explanation: 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: Option A
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
A.298 m
B.888 m
C.120 m
D.217 m
Answer: C.120 m
Explanation: Speed = (12/10 * 60) km/hr
= (72 * 5/18) m/sec
= 20 m/sec.
Length of the train
= 20 * 6
= 120 m.
Answer: C
Question: If four coins are tossed, the probability of getting two heads and two tails is -.
A.3/8
B.6/11
C.2/5
D.4/5
Answer: A.3/8
Explanation: Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
ANSWER:A
Question: 3 litre of water is added to 11 litre of a solution containing 42% of alcohol in the water. The
percentage of alcohol in the new mixture is
A.25%
B.20%
C.30%
D.33%
Answer: D.33%
Explanation: Explanation :
----------------------------------------------------------Method-1 to solve the question--------------------------------------
--------------------We have a 11 litre solution containing 42% of alcohol in the water=> Quantity of alcohol
in the solution= 11×42100Now 3 litre of water is added to the solution=> Total Quantity of the new
solution = 11+3=14Percentage of alcohol in the new solution=11×4210014×100=11×3100=33%-------------
---------------------------------------------Method-2 to solve the question---------------------------------------------------
-------%Concentration of alcohol in pure water = 0%Concentration of alcohol in mixture = 42quantity of
water : Quantity of mixture = 3 : 11Let the %Concentration of alcohol in the new mixture = x
By the rule of alligation, we have
%Concentration of alcohol : 0
in pure water %Concentration of alcohol
in mixture : 42
Mean %Concentration
x
42 - x x - 0 = x
But (42 - x) : x = 3 : 11
⇒42−xx=311⇒42−xx=311⇒42×11−11x=3x⇒14x=42×11⇒x=3×11=33=> The percentage of alcohol in the
new mixture is 33%
Answer : Option D
Question: Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/4 of all the paint. During the second week, he uses 1/6 of the remaining paint. How many gallons of paint has Joe used?
A.18
B.135
C.175
D.216
Answer: B.135
Explanation: Total paint initially = 360 gallons
Paint used in the first week = (1/4)*360 = 90 gallons.
Remaning paint = 270 gallons
Paint used in the second week = (1/6)*270 = 45 gallons
Total paint used = 135 gallons.
Option B
Question: What is the total % gain or loss if a trader sold two items for Rs.1500 each, and makes a profit of 20% from the first item and a loss of 12% from the second item.
A.2.4
B.4.4
C.1.4
D.12.4
Answer: A.2.4
Explanation: (20*12)/100 = 2.4%
Answer: A
Question: What least number must be substracted from 427398 so that the remaining number is divisible by 15?
A.3
B.1
C.16
D.11
Answer: A.3
Explanation: On dividing 427398 by 15, we get remainder = 3.
Required number be substracted
ANSWER:A
Question: If there are 9 horizontal lines and 9 vertical lines in a chess board, how many rectangles can be formed in the chess board?
A.1204
B.1296
C.1340
D.1754
Answer: B.1296
Explanation: Number of rectangles that can be formed by using m horizontal lines and n vertical lines
= mC2 × nC2
Here m = 9, n = 9
Hence, number of rectangles that can be formed
= mC2 × nC2
= 9C2 × 9C2 = (9C2)2
=(9×82×1)2=362=1296=(9×82×1)2=362=1296
ANSWER B 1296
Question: Today is Monday. After 63 days, it will be:
A.Monday
B.Sunday
C.Saturday
D.Friday
Answer: A.Monday
Explanation: Each day of the week is repeated after 7 days.
So, after 63 days, it will be Monday.
answer :A
Question: There are 5 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 8 other amateurs, what is the total number of chess games possible to be played in the tournament?
A.10
B.20
C.40
D.60
Answer: B.20
Explanation: Method 2:
Each person is one participant of 4 games. So there are in all 8*5 =40 instances of one participant games. But each game has 2 participants so total number of games = 40/2 = 20
B
Question: The food in a camp lasts for 32 men for 48 days. If eight more men join, how many days will the food last?
A.80 days
B.30 days
C.38 days
D.16 days
Answer: C.38 days
Explanation: one man can consume the same food in 32*48 = 1536 days.
8 more men join, the total number of men = 40
The number of days the food will last = 1536/40
= 38 days.
Answer:C
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
A.1871
B.9172
C.8797
D.8112
Answer: D.8112
Explanation: A = 7500(26/25)2 = 8112'
Answer:D
Question: Three grades of milk are 1 percent, 33 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?
A.y + 3z
B.(y +z) / 4
C.2y + 3z
D.3y + 3z
Answer: D.3y + 3z
Explanation: Soln:
The resulting equation is
=> (.01x + .03y + .03z)/(x+y+z) = 1.5/100
=> x + 3y + 3z = 1.5x + 1.5y + 1.5z
taking x to one side and y and z to other side we get
=> x = 3y + 3z
Ans is D
Question: A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed
A.50 km
B.52 km
C.54 km
D.56 km
Answer: C.54 km
Explanation: Explanation:
Let the length of the train be x meters,
Then, the train covers x meters in 8 seconds and (x + 180) meters in 20 sec
x/8=(x+180)/20 ⇔ 20x = 8 (x + 180) <=> x = 120
Length of the train = 120 m.
Speed of the train = (120/8)m / sec = m / sec = (15 ×18/5)kmph = 54 km
Answer: Option C
Question: A business finds that their ratio of spending to income is 5 to 9. Their total profit is $48,000. What is their total income?
A.$90,000
B.$108,000
C.$119,000
D.$126,000
Answer: B.$108,000
Explanation: Let x equal the amount of spending, and y equal the amount of income.
We know that x = 5/9y
We also know that x = y - 48000
Therefore we can simplify to:
y-48000 = 5/9y
We isolate y, and get:
4/9y = 48000
And to solve for y, we get:
y = 48000
Answer: B
Question: Points A, B, C, and D, in that order, lie on a line. If AB = 2 cm, AC = 5 cm, and BD = 6 cm, what is CD, in centimeters?
A. 1
B. 2
C. 3
D. 4
Answer: C. 3
Explanation: Putting a value to each point, lets use the following:
A - 0
B - 2 (AB = 2)
C - 5 (AC = 5)
D - 8 (BD = 6)
CD is 8-5 = 3.
Ans C
Question: In an examination 38% of students fail in English and 61% pass in Hindi and 23% fail in both. Find the actual failure percentage?
A.10%
B.12%
C.54%
D.28%
Answer: C.54%
Explanation: Explanation:
Fail percentage=38+61+23=54%
Answer: C
Question: I came across this problem in the GMATprep software and got it totally wrong!
A company consists of 6 senior and 4 junior staff officers. If a committee is created with 3 senior and 3 junior staff officers, how many possible committees are there?
A.12
B.44
C.56
D.80
Answer: D.80
Explanation: 6C3*4C3
=80=D
Question: Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
A.12:15:19
B.12:15:16
C.12:15:19
D.12:15:11
Answer: B.12:15:16
Explanation: Aman : Rakhi : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)
= 12:15:16
Answer:B
Question: a, b, and c are integers and a<b<c. S is the set of all integers from a to b, inclusive. Q is the set of all integers from b to c, inclusive. The median of set S is (3/4)*b. The median of set Q is (7.5/8)*c. If R is the set of all integers from a to c, inclusive, what fraction of c is the median of set R?
A. 3/8
B. 1/2
C. 11/16
D. 23/32
Answer: D. 23/32
Explanation: The answer isC: 11/16.
The key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean. For example, the mean and median of a set consisting of x, x+1, x+2, ... ,y will always be (x+y)/2.
For set S, consisting of numbers (a, a+1,...,b), the median is given to be 3/4*b:
(a+b)/2 = (3/4)*b
a = b/2
For set Q, consisting of numbers (b, b+1,...,c), the median is given to be 7.5/8*c:
(b+c)/2 = (7.5/8)*c
b = (7/8)*c
For set R, consisting of numbers (a, a+1,...c), the median needs to be found:
a = b/2 = (7/8*c)/2 = (7/16)*c
Median = (a + c)/2 = (7/16*c + c)/2 = (23/16)*c/2 = (23/32)*c (ANSWER D)
Question: If r = (x – 5)^2 + (x + 1)^2 – 6, then y is least when x =
A.-2
B.-1
C.0
D.2
Answer: D.2
Explanation: Let us transform the formula:
r = (x – 5)² + (x +1)² – 6 =
x² – 10x + 25 + x² + 2x + 1 – 6 =
2x² – 8x + 20 = 2 × (x² – 4x + 10) =
2 × ((x² – 4x + 4) + 6) =
2 × ((x – 2)² + 6)
Any square is greater or equal 0. Therefore the formula possess the least value when (x – 2)² = 0.
x – 2 = 0
x = 2
The correct answer is choice (D).
Question: From the starting point in a boat race, one competitor started to sail north at a speed of 1.4 Km/h, the other competitor started to sail west at a speed of 1.2 Km/h. What is the distance in Km between the two competitors after 5 hours?
A.9.21
B.12.
C.12.5.
D.14.
Answer: A.9.21
Explanation: Both competitors are sailing making angle of 90 degrees.
After 5 hrs one competitor will cover a distance of = 1.4 *5= 7 KM
And, other competitor will cover a distance of = 1.2*5= 6KM
distance between them after 5 hrs = (7^2+ 6^2)^1/2= 9.21 KM
A is the answer
Question: What is the highest integer that is the sum of 2 distinct prime integers, each smaller than 80 ?
A.140
B.152
C.153
D.169
Answer: B.152
Explanation: A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. Here are the first few prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.
Immediate two prime numbers before 80 are - 79 and 73
Sum = 79 + 73 = 152
Answer - B