divelab/Sys2Bench huggingface dataset:
Question: A, B and C invest in a partnership in the ratio: 7/2, 4/3, 6/5. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 22,680, then what is B's share in the profit?
Options:
A)Rs. 2000
B)Rs. 3000
C)Rs. 4200
D)Rs. 5200
E)None of these
Rationale: Explanation :
Ratio of the initial investment = 7/2 : 4/3 : 6/5
= 105 : 40 : 36
From this ratio, we can assume that actual initial investments of A, B and C
are 105x, 40x and 36x respectively
A increases his share 50% after 4 months. Hence the ratio of their investments =
(105x * 4) + (105x * 150/100 * 8) : 40x * 12 : 36x : 12
= 105 + (105 * 3/2 * 2) : 40*3 : 36 * 3
= 105 * 4 : 40 *3 : 36 * 3
= 35 * 4 : 40 : 36
= 35 : 10 : 9
B's share = total profit * (10/54) = 22,680 * 10/54 = 4200. Answer : Option C
Answer: C
Question: Anita, Indu and Geeta can do a piece of work in 18 days, 27 days and 36 days respectively. They start working together. After working for 4 days. Anita goes away and Indu leaves 7 days before the work is finished. Only Geeta remains at work from beginning to end. In how many days was the whole work done?
Options:
A)16
B)77
C)99
D)14
E)12
Rationale: 4/18 + (x -7)/27 + x/36 = 1
x = 16 days. Answer: A
Answer: A
Question: Country C imposes a two-tiered tax on imported cars: the first tier imposes a tax of 14% of the car's price up to a certain price level. If the car's price is higher than the first tier's level, the tax on the portion of the price that exceeds this value is 8%. If Ron imported a $14,000 imported car and ended up paying $1440 in taxes, what is the first tier's price level?
Options:
A)$1600
B)$5333
C)$6050
D)$7050
E)$8000
Rationale: Let T be the tier price, P be total price = 14000
Per the given conditions:
0.14T + 0.08(P-T) = 1440 ----> T=5333. B is the correct answer.
Answer: B
Question: A train 500 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
Options:
A)298 m
B)300 m
C)800 m
D)967 m
E)1181 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (500 + x)/60 = 65/3
x = 800 m.
Answer: C
Answer: C
Question: Dacid obtained 86, 89, 82, 87 and 81 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Options:
A)79
B)99
C)88
D)85
E)75
Rationale: Average = (86+89+82+87+81)/5
= 425/5 = 85.
Answer:D
Answer: D
Question: In one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Options:
A)26
B)48
C)11
D)56
E)7
Rationale: Speed in still water = 1/2(a+b)km/hr
=1/2(14+8)km/hr=11 km/hr.
Answer:C
Answer: C
Question: What is the are of an equilateral triangle of side 12 cm?
Options:
A)36âˆš3 cm2
B)74âˆš3 cm2
C)64âˆš3 cm2
D)64âˆš5 cm2
E)14âˆš3 cm2
Rationale: Area of an equilateral triangle = âˆš3/4 S2
If S = 12, Area of triangle = âˆš3/4 * 12 * 12 = 36âˆš3 cm2;
Answer:A
Answer: A
Question: If one-third of one-fourth of a number is 18, then three-tenth of that number is:
A. 35
Options:
A)23
B)87
C)26
D)64.8
E)01
Rationale: Explanation:
The number is 1/3 of 1/4 is =15 then 1/3 Ã— 1/4 = 18
Number is 216 then 216 Ã— 3/10 = 64.8
Answer: D
Answer: D
Question: The true discount on a bill of Rs.4320 is Rs.720.The banker's discount is
Options:
A)862
B)864
C)866
D)868
E)None of these
Rationale: Solution
P.W	= Rs.(4320 - 720)
= Rs. 3600
S.I on Rs. 4320	=Rs.(720/3600 x 4320)
= Rs. 864.
Answer B
Answer: B
Question: How many revolutions will it take for a circular wheel of 1.52 m radius to travel a distance of 1 km?
Options:
A)7554.2
B)3554.2
C)1554.2
D)9454.2
E)9554.3
Rationale: 2 * 22/7 * 1.52 * x = 9554.3
x = 1000
Answer: E
Answer: E
Question: Pat, Kate, and Mark charged a total of 126 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate?
Options:
A)18
B)36
C)72
D)70
E)108
Rationale: 70
all u do is do
2:1:6=>2x+x+6x=126=>x= 14
28:14:84
84-14=70
Answer D
Answer: D
Question: Find the area of a cuboid of length 12cm , breadth 6 cm . and height 10cm.
Options:
A)400 cm cube
B)410 cm cube
C)720 cm cube
D)730 cm cube
E)480 cm cube
Rationale: Area of a cuboid = lxbxh =12cm x 6cm x 10cm = 720 cm cube
answer :C
Answer: C
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
Options:
A)20%
B)28%
C)22%
D)23%
E)29%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer:A
Answer: A
Question: A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
Options:
A)15 kmph
B)10 kmph
C)12 kmph
D)12.5 kmph
E)None of these
Rationale: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
ANSWER:D
Answer: D
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is?
Options:
A)50 km
B)58 km
C)60 km
D)70 km
E)65 km
Rationale: A
50 km
Let the actual distance traveled be x km. Then,
x/10 = (x + 20)/14
4x - 200 =>x = 50 km.
Answer: A
Question: What is the area of a square field whose diagonal of length 30 m?
Options:
A)287
B)269
C)450
D)200
E)230
Rationale: d2/2 = (30 * 30)/2
= 450
Answer:C
Answer: C
Question: Two trains start from A & B and travel towards each other at
speed of 70kmph and 80kmph resp. At the time of the meeting the
second train has traveled 200km more than the first.the distance
between them.
Options:
A)2500 km
B)3000 km
C)3500 km
D)4000 km
E)4500 km
Rationale: Let the distance traveled by the first train be x km
then distance covered by the second train is x + 200km
x/70 = x+200 / 80
x= 1400
so the distance between A & B is x + x + 200 = 3000 km
Answer is B.
Answer: B
Question: In a particular city there are 100 homes numbered from 1,2,3,..,100. The city was build by a builder from Chennai. There was 4 to 5 shops in the town which was build by a builder from Mumbai. The 2nd builder can build in 1½ times as compared to time by 1st builder. The 2nd builder builds in 15 days, then how many 2's are used by the builder from Chennai in
numbering the 100 homes?
Options:
A)17
B)18
C)19
D)20
E)21
Rationale: in the last line it should be given
the builder from Chennai in numbering the 100 homes?
then ans is 20
ANSWER:D
Answer: D
Question: A container has 40L milk. 4L milk is taken out and replaced with water, the process done three times. What is the amount of milk now left?
Options:
A)29.16L
B)29.19L
C)29.12L
D)29.11L
E)29.14L
Rationale: Explanation:
In regard to the problem let after n times liquid in the container is x and liquid removed is y
=>Liquid in container= x
=>Liquid removed= y
After one trial, quantity of pure liquid= x- (1-y/x)
After n trials quantity of pure liquid = x - (1 -y/x)n
Therefore, Putting the values ( x = 40L y = 4L N=3) and solving
=> 40- (1-4/40)3
= 29.16L
ANSWER:A
Answer: A
Question: An outlet pipe can empty 3/4 of a cistern in 12 minutes. In 4 minutes, what part of the cistern will be emptied?
Options:
A)1/2
B)1/3
C)1/4
D)1/5
E)1/6
Rationale: 4/12 * 3/4 = 1/4
The answer is C.
Answer: C
Question: A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
Options:
A)14020
B)11289
C)68928
D)14000
E)16881
Rationale: 25*12: 30*12: 35*8
15:18:14
14/47 * 47000
= 14000
Answer: D
Answer: D
Question: Which voltage source converts chemical energy to electrical energy?
Options:
A)23
B)39
C)27
D)98
E)72
Rationale: Answer: Option B
Answer: B
Question: A and B can do a work in 8days, B and C can do it in 12days; A,B and C together can finish it in 6days. A and C together will do it in?
Options:
A)8days
B)10days
C)12days
D)7days
E)5days
Rationale: A+B+C 1day work = 1/6
A+B 1day work = 1/8
B+C 1day work = 1/12
A+C 1day work = 2*1/6 - 1/8+1/12 = 1/3 - 5/24 = 3/24 = 1/8
A and C together will do the work in 8 days.
Answer is A
Answer: A
Question: What percent is 2 minutes 24 seconds of an hour?
Options:
A)6%
B)8%
C)4%
D)2%
E)9%
Rationale: 2mt 24s =144s
(144*100)/(60*60)=4%
ANSWER:C
Answer: C
Question: A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
Options:
A)65
B)80
C)85
D)82
E)89
Rationale: Speed = (240/24)m/sec = 10 m/sec.
Therefore, Required time = (240 + 650)/10 sec
= 89 sec.
Answer is E.
Answer: E
Question: The total of the ages of Mahesh, Suresh, Ramesh is 93 years. Ten years ago, the ratio of their ages was 2:3:4. What is the present age of Mahesh?
Options:
A)32years
B)38years
C)42years
D)35years
E)30years
Rationale: Let ages of Mahesh, Suresh, Ramesh 10years ago be 2x,3x,4x
2x+10 + 3x+10 +4x+10 = 93
x = 7
Ramesh present age = 4*7+10 = 38 years
Answer is B
Answer: B
Question: The cost price of a radio is Rs.1390 and it was sold for Rs.890, find the loss %?
Options:
A)18%
B)12%
C)22%
D)35%
E)21%
Rationale: 1390 ---- 500
100 ---- ? => 35%
Answer:D
Answer: D
Question: Jack and Jill went up and down a hill. They started from the bottom and Jack
met jill again 20 miles from the top while returning. Jack completed the race
1 min a head of jill. if the hill is 440 mts high and their speed while down
journey is 1.5 times the up journey. how long it took for the Jack to
complete the race ?
Options:
A)10.6 min
B)11.6 min
C)12.6 min
D)13.6 min
E)14.6 min
Rationale: Let speed and time of Jack be s1 & t1 & Jill having s2 & t2.
Time taken for Jack to travel 440 miles up and 20 miles down
= Time taken for Jill to travel 440-20=420 miles up
440/s1 + 20/1.5s1 = 420/s2
68/1.5s1= 420/s2
68s2= 63s1
s2 = 63s1/68 ---(1)
Now from the second given condition- Jack reaches 1 min before Jill. So
t2-t1=1
880/s2 - 880/s1 = 1
1/s2 - 1/s2 = 1/880
from equation (1) put value of s2
Solving and putting value of s1 in t1=d/s1 (d=880)
t1 = 12.6 min
ANSWER:C
Answer: C
Question: The S.I. on a certain sum of money for 5 years at 6% per annum is half the C.I. on Rs. 3000 for 2 years at 15% per annum. The sum placed on S.I. is?
Options:
A)1525.2
B)1256.3
C)1612.5
D)1548.5
E)1254.5
Rationale: C.I. = [3000 * (1 + 15/100)2 - 3000]= (3000 * 23/20 * 23/20 - 3000) = Rs. 967.5.Sum = (483.75 * 100)/(5 * 6)= Rs.1612.5Answer:C
Answer: C
Question: If 18 is 15 percent of 20 percent of a certain number, what is the number?
Options:
A)9
B)36
C)40
D)600
E)400
Rationale: Let the certain number be x.
=> (15/100)*(20/100)*x = 18;
300x=18*10000;
3x = 1800;
x=1800/3
=> x=600;
Ans is (D).
Answer: D
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
Options:
A)67
B)68
C)26
D)11
E)21
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer:B
Answer: B
Question: Avg cost of 3 apples and 5 bananas isRs. 40.The avg cost of 5 apples and 8 bananas is Rs.65.Find the total cost of 15 apples and 15 bananas?
Options:
A)75
B)90
C)80
D)130
E)110
Rationale: Avg cost of 3 apples and 5 bananas is Rs. 40
(3 apple + 5 bananas) 8=40
therefore 1 apple cost is 40/8=5, so 3 apple cost is 3x5=15 and 5 bananas cost is 5x5=25
Again, avg cost of 5 apples and 8 bananas is Rs.65
(5 apple + 8 bananas) 13=65
therefore 1 apple cost is 65/13=5, so 5 apple cost is 5x5=25 and 8 bananas cost is 8x5=40
So 15 apple cost is (15/a)=75 and 15 bananas cost is (15x5)=75
ANSWER:A
Answer: A
Question: An officer was appointed on maximum daily wages on contract money of Rs. 4956. But on being absent for some days, he was paid only Rs. 3894. For how many days was he absent?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: HCF of 4956, 3894 = 354
(4956 - 3894)/354 = 3
ANSWER:A
Answer: A
Question: A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?
Options:
A)37 ½ days
B)22 days
C)31 days
D)22 days
E)21 days
Rationale: Explanation :
Work done by A in 20 days = 80/100 = 8/10 = 4/5
Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)
Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)
Work done by A and B in 1 day = 1/15 ---(2)
Work done by B in 1 day = 1/15 – 1/25 = 2/75
=> B can complete the work in 75/2 days = 37 ½ days
Answer : A
Answer: A
Question: John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
Options:
A)16%
B)16.66%
C)17.66%
D)17.98%
E)18%
Rationale: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
B
Answer: B
Question: The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 6 years?
Options:
A)14300
B)29859
C)14500
D)14600
E)15400
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 × 120/100^6 = 29859
B)
Answer: B
Question: A book is bought for Rs.675 and sold for Rs.900, find the profit percentage?
Options:
A)30 %
B)33%
C)33 1/3%
D)40%
E)45%
Rationale: 675--->225
100--> 33 1/3%
ANSWER C
Answer: C
Question: Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum?
Options:
A)20
B)25
C)27
D)29
E)30
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131
a + b + c = √400 = 20
A
Answer: A
Question: A man has Rs. 480 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 ?
Options:
A)80
B)90
C)95
D)98
E)100
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
B
Answer: B
Question: Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/3 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?
Options:
A)3.25
B)3.6
C)4.2
D)4.4
E)6
Rationale: Time taken by First tank Fill 1/3 the tank = 6 hours
i.e. Time taken by First tank to Fill 1 complete the tank = 18 hours
Time taken by Second tank Fill 2/3 the tank = 6 hours
i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours
in 1 Hour, Both tanks together Fill the tank = (1/18)+(1/9) = 1/6 tank
i.e. Time taken by Both tank to Fill 1 complete the tank = 6 hours
Answer: option E
Answer: E
Question: (X+1 )is an even number and Y is a positive odd number. Which of the following expressions cannot be even?
Options:
A)(X+1)Y
B)Y
C)(X+1)^Y
D)(Y+1)^3
E)(Y+1)^2
Rationale: Y WILL BE ODD
B
Answer: B
Question: If x^2 + 1/x^2 = √12, what is the value of x^4 + 1/x^4 ?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = √12 andSQUAREboth sides:
(x² + 1/x²)²= 12
So, (x² + 1/x²)(x² + 1/x²) = 12
Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 12
Simplify: x⁴ + 1/x⁴ = 10
Answer: A
Answer: A
Question: Find the L.C.M of 16, 25, 24 and 10.
Options:
A)1000
B)1400
C)1320
D)1200
E)1650
Rationale: Explanation:
4 x 5 x 2 x 3 x 5 X 2= 1200
Answer: Option D
Answer: D
Question: The smallest value of n, for which n+3 is not a prime number, is
Options:
A)1
B)2
C)6
D)8
E)3
Rationale: (1 + 3) = 3.
(2 + 3) = 5.
(3 +3) = 6.
( 4+ 3) = 7.
which is not prime , n=3.
ANSWER:E
Answer: E
Question: If the number92737*2 is completely divisible by 8, then the smallest whole number in place of * will be?
Options:
A)2
B)1
C)3
D)4
E)None of these
Rationale: The number 7x2 must be divisible by 8.
x=1 as 712 is divisible by 8.
Correct Option : B
Answer: B
Question: Jerry travels 8 miles at an average speed of 40 miles per hour, stops for 15 minutes, and then travels another 20 miles at an average speed of 60 miles per hour. What is Jerry’s average speed, in miles per hour, for this trip?
Options:
A)35
B)42.5
C)44
D)50
E)52.5
Rationale: Total Time taken by jerry = (8/40)*60 Minutes + 15 Minutes + (20/60)*60 Minutes = 47 Minutes
Average Speed = Total Distance / Total Time = (8+20) miles / (47/60)Hours = 28*60 / 47 = 35 Miles per hour
Answer: option A
Answer: A
Question: X Y
+Y X
________
The sum of the two digit numbers above is a three digit number PQ3, where each letter X, Y, P, and Q represents a different non zero digit. Which of the following can be the value of X?
I)	7
II)	8
III)	9
Options:
A)I only
B)II only
C)III only
D)I , II and III
E)I and II only
Rationale: it can be a combination of 9,4 or 8,5 or 7,6
I choose D as an answer.
Answer: D
Question: List R contains five numbers that have an average value of 40. If the median of the numbers in the list is equal to the mean and the largest number is equal to 20 more than two times the smallest number, what is the smallest possible value in the list?
Options:
A)12
B)16
C)20
D)24
E)28
Rationale: The middle number is 40.
Let the smallest number be x. Then the largest number is 2x+20.
To make x as small as possible, let's make the remaining numbers as large as possible.
So the second largest = the largest = 2x+20.
The second smallest should be equal to the median.
The numbers are x, 40, 40, 2x+20, 2x+20.
x + 40 + 40 + 2x + 20 + 2x + 20 = 5*40 = 200
5x = 80
x = 16
The answer is B.
Answer: B
Question: The length of a room is 6 m and width is 4.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 900 per sq. metre.
Options:
A)25650
B)25750
C)26550
D)26750
E)25725
Rationale: Area = 6 × 4.75 sq. metre.
Cost for 1 sq. metre. = Rs. 900
Hence total cost = 6 × 4.75 × 900
= 6 × 4275 = Rs. 25650
Answer is A.
Answer: A
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average of the team?
Options:
A)23 years
B)67 years
C)15 years
D)88 years
E)66 years
Rationale: Let the average of the whole team be x years.
11x - (26 + 29) = 9(x - 1)
= 11x - 9x = 46
= 2x = 46 => x = 23
So, average age of the team is 23 years.
Answer:A
Answer: A
Question: The volume of water in a certain tank is x percent greater than it was one week ago. If r percent of the current volume of water in the tank is removed, the resulting volume will be 90 percent of the volume it was one week ago. What is the value of r in terms of x?
Options:
A)x+10
B)10x+1
C)100(x+10)
D)100( x+10/x+100)
E)100 ( 10x+1/10x+10)
Rationale: Given that, the water was increased by x percent -> then reduced by r percent -> to 90 percent of what it was one week ago.
Consider, the 100 units of water was increased by 20% to 120 units -> then reduced by 25% of 120 (i.e. by 30 units) -> to 90 units.
i.e. Pick numbers as x = 20% and r = 25%
Substitute x=20 and identify the answer that gives r=25
A) x+10 --20+1=30
b) 10x+1 --200+1=201
c) 100(x+10) --100(20+10)=3000
d) 100( x+10/x+100) --100(20+10/20+100) = 100(30/120)=25
e) 100 ( 10x+1/10x+10) -- 100(200+1/200+10)= 100(201/210)
Hence choice(D) is the answer.
Answer: D
Question: Indu gave Bindu Rs.500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
Options:
A)0.2
B)1.2
C)3
D)4
E)0.8
Rationale: 500 = D(100/4)2
D = 0.8
Answer: E
Answer: E
Question: A chair is bought for Rs.800/- and sold at a loss of 10% find its selling price
Options:
A)Rs.500/-
B)Rs.510/-
C)Rs.515/-
D)Rs.720/-
E)Rs.540/-
Rationale: Loss = 800*10/100 = 80
S.P = C.P - Loss
= 800- 80
=Rs.720/-
Answer :D
Answer: D
Question: What will Rs.1500 amount to in three years if it is invested in 20% p.a. compound interest, interest being compounded annually?
Options:
A)2592
B)2348
C)2377
D)2999
E)2772
Rationale: Explanation:
The usual way to find the compound interest is given by the formula A = .p(1+r/100)^n
In this formula,
A is the amount at the end of the period of investment
P is the principal that is invested
r is the rate of interest in % p.a
And n is the number of years for which the principal has been invested.
In this case, it would turn out to be A =1500(1+20/100)^3
= 2592.
Answer: A) Rs.2592
Answer: A
Question: Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
Options:
A)2:9
B)2:7
C)1:6
D)1:4
E)1:3
Rationale: Ratio of A / Ratio of B = (Average Wt of Mixture - Wt of B)/(Wt of A - Average Wt of Mixture)
=> Ratio of A / Ratio of B = (4 - 2)/(10 - 4) = 2/6 = 1/3
So they should be mixed in the ratio 1:3
Answer - E
Answer: E
Question: When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 36?
Options:
A)3
B)4
C)12
D)32
E)5
Rationale: n = 5p + 1 = 6,11,16,21,26,31
n = 7q + 3 = 3,10,17,24,31
=>n = 36m + 31
To get this, we need to take LCM of co-efficients of p and q and first common number in series.
So we need to add 5 more to make it
36m + 36
Answer - E
Answer: E
Question: If a 10 percent deposit that has been paid toward the purchase of a certain product is $150, how much more remains to be paid?
Options:
A)$880
B)$990
C)$1,350
D)$1,100
E)$1,210
Rationale: 10/100P = 150 >> p= 150*100/10 = 1500
1500 - 150 = 1350
ANSWER:C
Answer: C
Question: By selling 66 metres of cloth a person gains the cost price of 22 metres. Find the gain percent.
Options:
A)22%
B)22 1⁄2%
C)33%
D)33 1⁄3%
E)None of these
Rationale: Let C.P. of one metre of cloth = 1
then C.P. of 66 metres of cloth = 66
Gain = C.P. of 22 metres = 22
% gain = 22⁄66 × 100 = 331⁄3%
Shortcut method :
If on selling ‘x’ articles, a man gains equal to the C.P. of ‘y’ articles, then % gain = y⁄x × 100
∴ % gain = = 22⁄66 × 100 = 331⁄3%
Answer D
Answer: D
Question: 6 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. If the committee has to include at least 5 professor, how many ways can this committee be formed?
Options:
A)36
B)60
C)72
D)80
E)4
Rationale: you count up combinations twice.
6*9*8... and let me name 6 with students A,B,C,..,G
after choosing a professor, when you choose Student A and B, you can choose A first, then B. Or B first, then A. Both combination are same.
I don't think that's the only mistake.
4 is a factor of = 2^2*1^2
18 is a factor of = 2^1*3^2.
These are very different numbers and you cannot divide 18 with something to get to 4. ans E
Answer: E
Question: If A^2 + B^2 = 15 and AB = 10, what is the value of the expression (A - B)^2 + (A + B)^2
Options:
A)10
B)20
C)60
D)30
E)70
Rationale: (a-b)^2 = a^2 + b^2 - 2ab = 15-20= -5
(a+b)^2 = a^2 + b^2 + 2ab = 15+20=35
so (a+b)^2 + (a-b)^2 = 35 - 5 = 30
D
Answer: D
Question: What is the greatest positive integer x such that 3^x is a factor of 9^7?
Options:
A)5
B)14
C)10
D)20
E)30
Rationale: What is the greatest positive integer x such that 3^x is a factor of 9^7?
9^7 = (3^2)^7 = 3^14
B. 14
Answer: B
Question: There are 190 items that are members of set U. Of these items, 49 are members of set B, 59 are not members of either of set A or set B, and 23 are members of both sets A and B. How many of the members of set U are members of set A ?
Options:
A)72
B)85
C)94
D)105
E)108
Rationale: You had the answer almost right. The x = 82 refers to ONLY set A.
However what's being asked is how many members are part of set A. This will include:
1. Only Set A
2. Set A and Set B
So the answer is Set A = 82 + Set AB = 82+23 = 105
D
Answer: D