RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: What percent of 15 kg is 30 gms ?
A.25
B.66
C.20
D.19
Answer: C.20
Explanation: Explanation:
Required percentage = (30/15000 * 100)% = 1/5% = 0.2%
Answer: C) .20%
Question: Imagine an analog clock set to 12 o'clock. Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap? How would you determine the exact times of the day that this occurs?
A.11
B.12
C.22
D.24
Answer: C.22
Explanation: 22 times in a day.
12,1 hours 60/11 minutes , 2 hours 120/11 minutes , ...so on till 12( 11 hours 660/11 minutes)
ANSWER:C
Question: The probability of a team winning a match given Matt is playing the match is 0.70. The probability of the team winning a match given Matt is not playing the match is 0.5. The probability of Matt playing any match is 0.8.
If it is known that the team has won the last match, what is the probability that Matt played the match?
A.0.8321
B.0.8484
C.0.8571
D.0.7531
Answer: B.0.8484
Explanation: Out of 100 matches:
Matt is plays in 80 and not plays in 20.
Out of 80 matches Matt plays in, team wins 0.70*80 = 56
Out of 20 matches Matt does not play in, team wins 0.5*20 = 10.
So, out of 100 matches 56 + 10 = 66 are won.
It is known that the team has won the last match. Out of 66 matches won, Matt is in 56: 56/66 = 0.8484...
Answer: B.
Question: A set of football matches is to be organized in a "round-robin" fashion, i.e., every
participating team plays a match against every other team once and only once. If 15
matches are totally played, how many teams participated?
A.4
B.5
C.6
D.7
Answer: C.6
Explanation: 2 ways to solve this problem..
summation(x)=n(n-1)/2
n(n-1)/2=15;
n^2-n-30=0
Ans : 6
ANSWER:C
Question: A man has Rs. 464 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
A.87
B.90
C.95
D.98
Answer: A.87
Explanation: Let number of notes of each denomination be x.
Then x + 5x + 10x = 464
16x = 464
x = 29.
Hence, total number of notes = 3x = 87.
A
Question: A jar was full with honey. A person used to draw out 20% of the honey from the jar and replaced it with sugar solution. He has repeated the same process 4 times and thus there was only 512 gm of honey left in the jar, the rest part of the jar was filled with the sugar solution. The initial amount of honey in the jar was filled with the sugar solution. The initial amount of honey in the jar was:
A.1.25 kg
B.1.29 kg
C.1.85 kg
D.3.25 kg
Answer: A.1.25 kg
Explanation: Answer: A) 1.25 kg
Question: An automobile parts supplier charges $25 per package of gaskets. When a customer orders more than 10 packages of gaskets, the supplier charges 4/5 the price for each package in excess of 10. During a certain week, the supplier sold 60 packages of gaskets. If 15 percent of the gaskets went to Company X, 15 percent to Company Y, and the rest to Company Z, what was the total amount, in dollars, that the parts supplier received in payment for the gaskets?
A.1340
B.1445
C.1375
D.1415
Answer: A.1340
Explanation: $25 per packet of gasket in case a customer orders less than 10
in case a customer orders > 10 price per gasket = 25*4/5=20
a certain week the supplier sold 60 gasket
1.he sold 15 % of the gaskets to X = 9 gaskets = 25*9= 225
2.he sold 15 % of the gaskets to Y = 9 gaskets = 25*9= 225
3.he sold remaining 70% to z =42 gaskets = 25*10 =250 + 20*32=890
thus ,total money earned
225+225+890 = 1340
Answer is A
Question: Tom drives from town E to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between E and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?
A.12
B.20
C.24
D.30
Answer: B.20
Explanation: Let's assume that it takes 4 hours to go from point E to B. Then the distance between them becomes 240 which makes distance between B and C 120. (240+120)/(4+x) gives us the average speed which is 36. You find x=6. So the question simplifies itself to 120/6=20
Hence the answer is B.
Question: if w,x,y,z represents the respective results obtained from rounding off the figure 8623.293 to the nearest thousand, hundred, ten and one, which of the following statements is accurate?
A.x<y<z<w
B.x<z<y<w
C.x<w<z<y
D.z<y<x<w
Answer: A.x<y<z<w
Explanation: 8623.293..
Nearest thousand 9000..w
Nearest hundred 8600..x
Nearest ten 8620..y
Nearest one 8623...z
x<y<z<w
The correct option is A
Question: In a lottery there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a blank?
A.2/3
B.6/7
C.5/7
D.8/7
Answer: C.5/7
Explanation: total draws = prizes+blanks= 10+25=35
probability of getting a blank = 25/35 = 5/7
correct option is C
Question: A factory produces 6500 toys per week. If the workers at this factory work 5 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
A.1375 toys
B.2375 toys
C.1300 toys
D.1375 toys
Answer: C.1300 toys
Explanation: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 5 days) by 5.
6500 / 5 = 1300 toys
correct answer C
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
A.3
B.5
C.6
D.4
Answer: D.4
Explanation: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4. Answer: D
Question: How many ways to draw 3 balls from 16 balls pool.(balls are numbered as 1 to 16 and are distinct)
A.460
B.560
C.660
D.760
Answer: B.560
Explanation: 16C3=(16*15*14)/(3*2*1)=3360/6=560
ANSWER:B
Question: A trader sells 5 pineapples per rupee, calculate the profit loss percentage if the trader bought the pineapples at 6 per rupee.
A.10 %
B.20 %
C.30 %
D.50 %
Answer: B.20 %
Explanation: Let he total number of pineapples bought by the shopkeeper be 12.
If he buys 6 a rupee, his CP = 5
He selling at 5 a rupee, his SP = 6
Profit = SP - CP = 6 - 5 = 1
Profit Percent = 1/5 * 100 = 20 %
Answer: B
Question: If 40% of a number is 20, then the number is
A.number is 50
B.number is 70
C.number is 90
D.number is 80
Answer: A.number is 50
Explanation: Solution:
Let "a" be the number we seek. We get
40% × a = 20
2 × 40% × a = 2 × 20 = 40
80% × a = 40
10% × a = 40 : 8 = 5
100% × a = 5 × 10 = 50
a = 50
Answer A
Question: if Juan takes 15 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
A.11x/y
B.11y/x
C.15x/y
D.11/xy
Answer: C.15x/y
Explanation: Answer is C.
The rate of running hards: 15 minutes per y hards.
Thus the time for running x hards = x hards * 15 minutes/y hards = 15x/y
Question: If 11.25 m of a uniform steel rod weighs 42.75 kg. what will be the weight of 6 m of the same rod?
A.22.8 kg
B.25.6 kg
C.28 kg
D.26.5 kg
Answer: A.22.8 kg
Explanation: Explanation :
Let the required weight be x kg. Then, Less length, Less weight (Direct Proportion)
=> 11.25 : 6 :: 42.75 : x
=> 11.25 x x = 6 x 42.75
=> x = (6 x 42.75) / 11.25
=> x = 22.8
Answer : A
Question: 12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for 2 days, all of them stopped working. How many women should be put on the job to complete the remaining work, if it so to be completed in 3 days?
A.15 women
B.85 women
C.75 women
D.65 women
Answer: A.15 women
Explanation: 1 man's 1 day work = 1/48; 1 woman's 1 day work = 1/60.
6 men's 2 day's work = 6/48 * 2 = 1/4.
Remaining work = (1 - 1/4) = 3/4
Now, 1/60 work is done in 1 day by 1 woman.
So, 3/4 work will be done in 3 days by (60 * 3/4 * 1/3) = 15 women.
Answer:A
Question: John sold an item for Rs.4900/- and incurred a loss of 30%. At what price should he have sold the item to have gained a profit of 30%?
A.8800
B.8900
C.9000
D.9100
Answer: D.9100
Explanation: Explanation:
30% loss means SP = 70% of CP
:. CP = Rs.4900x100/70 = Rs.7000.
The SP for a gain of 30% = 7000+30% of 3000 = 7000+2100 =Rs9100.
Answer: Option D
Question: How long does a train 110 meters long running at the speed of 72 km/hour take to cross a bridge 132 meters in length ?
A.15 seconds
B.12.1 seconds
C.10 seconds
D.8.1 seconds
Answer: B.12.1 seconds
Explanation: Explanation:
Speed = 72 km/hour = 72*(5/18) m/sec
= 20 m/sec
Total distance to be covered = 110+132 = 142 meters
Time = Distance/Speed
= 242/20 = 12.1 seconds
Option B
Question: Dustin's Pizza Shop sells Bread Sticks in orders of 2 and 8. A party of 12 guests would like to have at least 2 Bread Sticks a piece. Which of the following combinations would NOT be possible.
A.3 Orders of 8
B.2 Orders of 2, and 1 order of 8
C.4 orders of 2, and 2 orders of 8
D.3 orders of 2, and 3 orders of 8
Answer: B.2 Orders of 2, and 1 order of 8
Explanation: The correct answer would not allow each of the 12 guests to have AT LEAST 2 bread sticks a piece.
A=24 (24 divided by 12 is exactly 2 a piece)
B=12 (12 divided by 12 would only allow for 1 bread stick a piece) *Correct Answer*
C=24 (Same as Answer A)
D=30 (30 divided by 12 allows for each guest to have 2 bread sticks with 6 leftover)
E=26 (26 divided by 12 allows for each guest to have 2 bread sticks with 2 leftover)
The Correct Answer is B
Question: P and Q start a business with Rs.7000 and Rs.28000 respectively. Hoe should they share their profits at the end of one year?
A.1:3
B.1:4
C.1:5
D.1:6
Answer: B.1:4
Explanation: Explanation:
They should share the profits in the ratio of their investments.
The ratio of the investments made by P and Q =
7000 : 28000 => 1:4
Answer:B
Question: Complete the series:5, 20, 24, 6, 2, 8, ?
A.12
B.22
C.32
D.42
Answer: A.12
Explanation: The series is *4, +4, /4, -4, *4,....
That is 5*4 = 20, 20+4 = 24, 24/4 = 6, 6-4 = 2, and again 2*4 = 8 constructing the series 20,24,6,2,8,...so obviously the next operation will be +4, so 8+4 = 12 ANSWER:A
Question: How many numbers of 5 digits can be formed with the digits 0, 1, 2, 3, 4, 6 & 8 with no digit being repeated in the same number?
A.2170
B.2160
C.4396
D.4500
Answer: B.2160
Explanation: As we have 5 digits.. and having no repeation..
For the first digit can't be "0".. so, possibilities are 6..
for the second digit the possibilities are 6 including "0" also..
for the third digit there are 5 possibilities
for the fourth digit 4 possibilities
for the fifth digit 3 possibilities..
so, total no.of numbers can form is 6*6*5*4*3=2160
ANSWER:B
Question: Of a certain group of 100 people, 40 graduated from High School A, 65 graduated from College Y, and 30 live in City Z. What is the greatest possible number of people in this group who did not graduate from High School A, did not graduate from College Y, and do not live in City Z ?
A. 5
B. 15
C. 35
D. 65
Answer: C. 35
Explanation: 1. a+y+z+ay+yz+az+ayz+ none=100. Fornoneto be maximum others have to be minimum
2. We know the underlined portions sum to 65 and that is the minimum value of others
3. Maximumnone= 100-65=35=C
Question: A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:
A.2 km/hr
B.1 km/hr
C.4 km/hr
D.6 km/hr
Answer: B.1 km/hr
Explanation: Explanation:
Assume that he moves 4 km downstream in x hours.
Then, speed downstream = distance/time = 4/x km/hr
Given that he can row 4 km with the stream in the same time as 3 km against the stream
i.e., speed upstream = 3/4 of speed downstream
=> speed upstream = 3/x km/hr
He rows to a place 48 km distant and comes back in 14 hours
⇒48/(4/x)+48/(3/x)=14
⇒12x+16x=14
⇒6x+8x=7
⇒14x=7
⇒x=1/2
Hence, speed downstream =4x=4(12) = 8 km/hr
speed upstream = 3x=3(12) = 6 km/hr
Now we can use the below formula to find the rate of the stream
Let the speed downstream be a km/hr and the speed upstream be b km/hr, then
Speed in still water = 1/2(a+b) km/hr
Rate of stream = 1/2(a−b) km/hr
Hence, rate of the stream = 1/2(8−6)= 1 km/hr
Answer: Option B
Question: Three candidates contested an election and received 80020, 22908 and 45000 votes respectively. What percentage of the total votes did the winning candidate get ?
A.57.20%
B.54.09
C.45.10%
D.64.10%
Answer: B.54.09
Explanation: Explanation :
Total number of votes polled = (80020+22908+45000)
= 147928.
Required percentage = (80020/147928) X 100%
= 54.09%.
Answer :B
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
A.1350
B.8837
C.2377
D.3772
Answer: A.1350
Explanation: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 2 = Rs.1350 Answer: A
Question: In a division sum, the quotient is 40, the divisor 72 and the remainder 64, find the dividend?
A.2674
B.2944
C.2464
D.2924
Answer: B.2944
Explanation: Explanation:
40 * 72 + 64 = 2944
Answer : B
Question: A man walking at a rate of 15km/hr crosses a bridge in 20 minutes. The length of the bridge is?
A.1250m
B.1110m
C.950m
D.1000m
Answer: D.1000m
Explanation: Speed = 15*5/18 = 15/18 m/sec
Distance covered in 20minutes = 15/18 *20 *60 = 1000m
Answer is D
Question: f a < b < c , which of the following must be true?
(I) a < b^2
(II) b − a < c
(III) a^2 < b^2 < c^2
A.None
B.I only
C.II only
D.III only
Answer: A.None
Explanation: (I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2.
(II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1.
(III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1.
None of the options must be true.
Answer: A.
Question: In a college, the ratio of the number of boys to girls is 8 : 4. If there are 200 girls, the total number of students in the college is
A.420
B.520
C.600
D.720
Answer: C.600
Explanation: Explanation:
Let the boy are 8x and Girls are 4x
=> 4x = 200
=> x = 50
Total students = 8x+4x = 12x = 12(50) = 600
Option C
Question: If x is real, find the maximum value of the expression -2x^2 + 3x + 5.
A.2.145
B.6.125
C.8.725
D.11.885
Answer: B.6.125
Explanation: This is an equation of a downward facing parabola.
The maximum value is the top point of the parabola.
-2x^2+3x+5 = (-2x+5)(x+1)
The roots are 5/2 and -1.
The maximum value must be when x is halfway between these two points.
x = 0.75
The maximum value is -2(0.75)^2+3(0.75)+5 = 6.125
The answer is B.
Question: find value for x from below equation? x + 1 = -3
A.1
B.-4
C.-1
D.2
Answer: B.-4
Explanation: 1. Subtract 1 from both sides:
x + 1 - 1 = -3 - 1
2. Simplify both sides:
x = -4
B
Question: 0.007 x 0.45=?
A.0.00315
B.0.0315
C.0.315
D.0.0351
Answer: A.0.00315
Explanation: 7 x 45 = 315
Sum of decimal places =5
Therefore, 0.007 x 0.45 = 0.00315
Answer is A.
Question: Jim drove 768 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey?
A.432 miles
B.651 miles
C.387 miles
D.954 miles
Answer: A.432 miles
Explanation: The number of miles to drive to finish his journey is given by
1200 - 768 = 432 miles
correct answer A
Question: On Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 66% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?
A. 56.44%
B. 60%
C. 66%
D. 80%
Answer: A. 56.44%
Explanation: Chris won't be able to attend the game if it be raining on Monday eveningandTuesday evening. The probability of that is 0.66*0.66 = 0.4356. So, the probability that he will be able to attend is 1 - 0.4356 = 0.5644.
Answer: A.
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
A.2277
B.38000
C.26688
D.26666
Answer: B.38000
Explanation: CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100) = 38000
Answer: B
Question: A present value of a machine is $128000. Its value depletiation rate is 20% per annum then find the machine value after 3 years?
A.A)$54000
B.B)$48000
C.C)$9216
D.D)$32450
Answer: C.C)$9216
Explanation: P= $128000
R = 20%
T = 3 years
Machine value after 3years = P/(1-R/100)^T
=128000*3/5* 3/5 * 3/5
=$9216
Answer is C
Question: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 1 at its maximum rate ?
A.2hrs, 48mins
B.6hrs, 32mins
C.1hrs, 38mins
D.13hrs, 4mins
Answer: C.1hrs, 38mins
Explanation: The rate of pump 1 = 4x job/minute.
The rate of pump 2 = 2x job/minute.
The rate of pump 3 = x job/minute.
Given that x+2x+4x=1/56 --> x=1/392 --> (time) = (reciprocal of rate) = 392 minutes x/4= 1 hours and 38 minutes.
Answer: C
Question: A car dealership has 40 cars on the lot, 10% of which are silver. If the dealership receives a new shipment of 80 cars, 25% of which are not silver, what percentage of total number of cars are silver?
A.15%
B.18%
C.20%
D.21%
Answer: C.20%
Explanation: The number of silver cars is 0.1*40 + 0.25*80 = 24
The percentage of cars which are silver is 24/120 = 20%
The answer is 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 R 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 R of students that could have taken both geometry and biology, is 119.
Thus, the answer is 119 - 31 = 88.
Answer: D.
Question: The largest 3 digit number exactly divisible by 88 is?
A.A)9944
B.B)9954
C.C)9967
D.D)9969
Answer: A.A)9944
Explanation: Largest 4-digit number = 999
88) 999 (113
88
----
119
88
----
319
264
---
55
---
Required number = (999 - 55)
= 9944.
A)
Question: Donald duck can can swim his pool downstream(with the pool current helping time) in exact 40 seconds and upstream(against the pool current) in a pool in exact 60 seconds. The length of pool is 2 kilometers.
How long Donald duck can cover distance of one side at a still pool (with no current).
A.40 minutes
B.45 minutes
C.38 minutes
D.48 minutes
Answer: D.48 minutes
Explanation: D
48 minutes.
Donald duck's speed = X km/seconds
pool current speed = Y km/seconds
2/(X+Y) = 40
2/(X-Y) = 60
Solving the simultaneous equations gives X = 1/24
Therefore, to cover 2km will take 2/X = 48 seconds
Question: find the number, difference between number and its 3/5 is 56.
A.140
B.143
C.144
D.145
Answer: A.140
Explanation: Explanation:
Let the number = x,
Then, x-(3/5)x = 56,
=> (2/5)x = 56 => 2x = 56*5,
=> x = 140
Answer: Option A
Question: Given that 268x74= 19832, find the value of 2.68x.74.
A.1.9832
B.1.0025
C.1.5693
D.1.0266
Answer: A.1.9832
Explanation: Solution
Sum of decimals places	=(2+2)
= 4.
Therefore,	= 2.68×.74
= 1.9832
Answer A
Question: The product of digit is a Factor of a two digit number. Number of such digit are:
A.33
B.18
C.19
D.17
Answer: B.18
Explanation: Let the number be xy. So 10x+yxy=k10x+yxy=k. Here k is some interzer.
⇒⇒ 10x + y = kxy
⇒⇒ x(10 - ky) = - y
⇒⇒ x(ky - 10) = y
So x is a factor of y. The possibilities are,
11, 1×1=1; 12 , 1×2=2; 15 ,1×5=5; 24 ,2×4=8; 36 , 3×6=18
Answer:B
Question: Sita and Sinu together can do a work in 50 days. With the help of Smitha, they completed the work in 6 days and earn Rs.250. What is the share of Sinu if Sita alone can do the work in 100 days?
A.Rs.15
B.Rs.18
C.Rs.20
D.Rs.25
Answer: A.Rs.15
Explanation: Sinu’s one day’s work = 1/50 - 1/100
= (2-1)/100
= 1/100
Sinu’s 6 day’s work = 6/100* 1 = 3/50
Sinu completed 3/50 th of total work.
So, Sinu’s share= 3*250/50 = Rs. 15
ANSWER:A
Question: The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
A.767 cm
B.800 cm
C.266 cm
D.181 cm
Answer: B.800 cm
Explanation: Area of the square = s * s = 5(125 * 64)
=> s = 25 * 8 = 200 cm
Perimeter of the square = 4 * 200 = 800 cm.
Answer: B
Question: The ratio of money with Ram and Gopal is 7 : 17 and that with Gopal and Krishan is 7: 17. If Ram has Rs. 637, Krishan has ?
A.s. 2890
B.s. 2330
C.s. 3757
D.s. 1620
Answer: C.s. 3757
Explanation: Ram : Gopal = 7 : 17 = 49 : 119
Gopal : Krishan = 7 : 17 = 119 : 289
Ram : Gopal : Krishan = 49 : 119 : 289
Ram : Krishan = 49 : 289
Thus, 49 : 289 = 637 : N
&there N = 289 x 637 / 49
= Rs. 3757
Answer :C
Question: A fruit drink is made of orange, watermelon, and grape juice, where 15 percent of the drink is orange juice and 60 percent is watermelon juice. If the drink is made with 30 ounces of grape juice, how many ounces is the drink total?
A.120
B.160
C.190
D.200
Answer: A.120
Explanation: Let the total number of ounces in the drink be x.
% of orange = 15%
% of watermelon = 60%
% of grape = 100% - 75% = 25%
0.25x = 30
x = 120
Therefore there are a total of 120 ounces in the drink.
The answer is A.
Question: It takes 40 identical printing presses 15 hours to print 500,000 papers. How many hours would it take 30 of these printing presses to print 500,000 papers?
A.16
B.18
C.20
D.21
Answer: C.20
Explanation: 40 printing presses can do 1/15 of the job each hour.
30 printing presses can do 3/4*1/15 = 1/20 of the job each hour.
The answer is C.
Question: If n is a natural number, then (6n^2 + 6n) is always divisible by
A.6 only
B.6 and 12 both
C.12 only
D.18 only
Answer: B.6 and 12 both
Explanation: (6n^2 + 6n) = 6n(n + 1), which is divisible by both 6 and 12, since n(n+1) is always even.
Answer B.
Question: If 5% more is gained by selling an article for Rs. 600 than by selling it for Rs. 580, the cost of the article is?
A.127
B.688
C.400
D.121
Answer: C.400
Explanation: Let C.P. be Rs. x.
Then, 5% of x = 600 - 580 = 20
x/20 = 20 => x = 400
Answer: C
Question: The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 24. Which of the following integers is the higher of the remaining two integers?
A.32
B.86
C.84
D.22
Answer: C.84
Explanation: Let the four integers be A, B, C and D where A > B > C > D.
(A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)
A = 93, D = 39 and B - C = 24
(1) => B + C = 276 - (A + D) = 276 - 132 = 144.
B + B -24 = 144
B = (144 + 24)/2 = 84
Answer:Option C
Question: A committee of two students has to be formed. There are five candidates: Jane, Joan, Paul, Stuart, and Jessica. If Paul and Stuart refuse to be in the committee together and Jane refuses to be in the committee without Paul, how many committees are possible?
A.3
B.4
C.5
D.6
Answer: B.4
Explanation: Let's try a different problem with your approach. There are five people: A, B, C, D, E. Need to chose 3 for a committee. A and B cannot be chosen together. B and C cannot be chosen together. How many options?
Your approach: total 10 options, 5c3.
Now, assume the wrong scenario where A and B are chosen together. There are three such scenarios. (A and B are chosen, just need one more person.) So we have to subtract the three wrong options. Similarly, there are three wrong scenarios where B and C are chosen together.
This gives us 10-3-3=4 as the answer.
Yet this answer is wrong. There are five possibilities: ACD, ACE, ADE, BDE
B